Eawag, the Swiss Federal Institute of Aquatic Science and Technology, is an internationally networked aquatic research institute within the ETH Domain (Swiss Federal Institutes of Technology). Eawag conducts research, education and expert consulting to achieve the dual goals of meeting direct human needs for water and maintaining the function and integrity of aquatic ecosystems.
The High Performance Scientific Computing Group (SC) in the Department of Systems Analysis, Integrated Assessment and Modelling (SIAM) has a vacancy for a
Postdoctoral researcher position in computational aquatic data science (DATALAKES)
The objective of this project is
to advance the forecasting capabilities of the data-driven hydrological and ecological lake modeling algorithms using methodologies inspired by data science and accelerated by high performance computing. We aim to develop a parallel framework interfacing high resolution 3D numerical solvers for the underlying lake dynamics with modern numerical Markov Chain Monte Carlo sampling methods for Bayesian inference, with particular interest in investigating particle filtering and multi-level variance reduction methodologies. The resulting framework aims at accurate data assimilation and uncertainty quantification in both model parameters and the associated forecasts. This project is a part of a larger DATALAKES
collaboration with the Swiss Data Science Center (SDSC), EPF Lausanne and ETH Zurich, aiming at a sensor-to-frontend data platform providing and analyzing the dynamics of lake ecosystems at high spatial and temporal resolutions. We are looking for
a candidate with a strong mathematical, statistical and computational background (PhD in mathematics, physics, computational sciences, or similar), good programming skills complemented by experience in parallel computing, interest in applying his/her knowledge to advance predictive capabilities and computational performance of numerical models for hydrological and ecological lake dynamics, and good communication skills across interdisciplinary environments.
The position is
available for two years in Zurich, Switzerland. Flexibility for occasional scientific visits to collaborators at ETH and SDSC in Zurich, EPF in Lausanne and CSCS in Lugano is expected.
a stimulating research and working environment
with strong collaboration between modelers and experimental and observational scientists. In our department, SIAM, we offer the potential for interaction with researchers in statistical inference, computation and mathematical modelling of hydrological and ecological systems, and strong links to other departments. External partners include the Swiss Supercomputing Center (CSCS) and the Swiss Data Science Center (SDSC). Eawag is
committed to promoting equal opportunities for women and men and to support the compatibility of family and work. Applications from women are especially welcome. For more information about Eawag and our work conditions please consult www.eawag.ch
. The closing date for applications is 4 April 2018
or until filled. Please submit your application including CV, motivation letter, copies of academic qualifications and contact information for two references. For further information
please contact Dr Jonas Sukys
, Email email@example.com
. We look forward to receiving your application.
Please send it through this webpage, any other way of applying will not be considered. A click on the button below will take you directly to the application form.


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ARF MOBILE MATHEMATICS LABORATORY
The students at the TED Rönesans College access knowledge in mathematics lessons, by working in environments prepared as aimed to eliminate a problem by the problem solving approach and discussing with each other. The ARF Mobile Mathematics Laboratory is an indispensable part of these learning environments. It has been set up as a mobile mechanism in order to enable all students to access it easily. It takes its name from the world-renowned Turkish mathematician “Cahit Arf”. Cahit Arf has observed mathematics not as a profession, but as a lifestyle. He has always told his students: "Do not memorize mathematics, do it yourself and understand it. Mathematics in principle is a patience issue. It is necessary to comprehend it not by memorizing, but by exploring”.
In this laboratory, our students question knowledge by using a wide variety of manipulative tools, produced and used in many countries in the World, explore by problem solving, and associate mathematics topics with real life. In this manner, lasting and full learning is ensured. Moreover, while doing this, their learning environments are diversified according to their differences. In this manner, our students develop as compatible with their levels. As the ARF Mobile Mathematics Laboratory travels around the classrooms, the students learn without being bored, but having fun.


This was the largest known prime number for 75 years, and the largest ever found by hand. After nearly two centuries, M31 was verified to be prime by Leonhard Euler in The search for Mersenne primes was revolutionized by the introduction of the electronic digital computer.
His list replicated the known primes of his time with exponents up to This was the second-largest known prime number, and it remained so until Mersenne gave little indication how he came up with his list.
Although it is chronologically the 47th Mersenne prime to be discovered, it is smaller than the largest known at the time, which was the 45th to be discovered. Consequently, a prime number divides at most one prime-exponent Mersenne number,  so in other words the set of pernicious Mersenne numbers is pairwise coprime.
Android is a Linux-based software system, and similar to Linux, is free and open source software. Without finding a factor, Lucas demonstrated that M67 is actually composite.
Android Android is an operating system based on the Linux kernel, and designed primarily for touch screen mobile devices such as smart phones and tablet computers. Linux was designed considering UNIX compatibility.
A Mersenne prime cannot be a Wieferich prime. Mersenne primes take their name from the 17th-century French scholar Marin Mersennewho compiled what was supposed to be a list of Mersenne primes with exponents up to The Perl languages borrow features from other programming languages including C, shell scripting shAWK, and sed.
It was the first Mersenne prime to be identified in thirty-eight years; the next one, M, was found by the computer a little less than two hours later. Two more M89 and M were found early in the 20th century, by R. Used often for CGI, Perl is also used for graphics programming, system administration, network programming, finance, bioinformatics, and other applications.
It is open source as its source code is freely available. A notable contribution was made by retired Yale physics professor Horace Scudder Uhler, who did the calculations for exponents,and Searching for Mersenne primes[ edit ] Fast algorithms for finding Mersenne primes are available, and as of [update] the seven largest known prime numbers are Mersenne primes.
Android gives you a world-class platform for creating apps and games for Android users everywhere, as well as an open marketplace for distributing to them instantly.
They provide powerful text processing facilities without the arbitrary data-length limits of many contemporary UNIX command line tools, facilitating easy manipulation of text files.
This means that other companies can use the Android operating developed by Google and use it in their mobile devices. Alan Turing searched for them on the Manchester Mark 1 in but the first successful identification of a Mersenne prime, M, by this means was achieved at Perl Programming Perl is an open-source, general-purpose interpreted programming language.Aug 31, · Write a C Program to check number is Prime number or not using C Programming Language.(For Loop)?Status: Resolved.
C Program to Display Prime Numbers Between Two Intervals. Example to print all prime numbers between two numbers (entered by the user).
This problem is solved using nested for loop and if else statement. In each iteration, whether low is a prime number or not is checked and the value of low is incremented by 1 until low is equal to high.
Efficient program to print all prime factors of a given number Given a number n, write an efficient function to print all prime factors of n. For example, if the input number is 12, then output should be “2 2 3”.
In mathematics, a Mersenne prime is a prime number that is one less than a power of mint-body.com is, it is a prime number of the form M n = 2 n − 1 for some integer mint-body.com are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.
The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31. R Program to Check Prime Number Example to check whether an integer (entered by the user) is a prime number or not using control statements.
To understand this example, you should have the knowledge of following R programming topics.
Prime number program in C: C program for prime number, this code prints prime numbers using C programming language. C program to check whether a number is prime or not.
Prime number logic: a number is prime if it is divisible only by one and itself. Remember two is .Download


Data-Driven Fluid Mechanics: Combining First Principles and Machine Learning
Machine Learning for Fluid Mechanics: Analysis, Modeling, Control and Closures
About the lecture Series
Outline of the Course
The course followed the historical path through which this field has been developed in the latest few decades, opening with the tools which were pioneered by the fluid dynamics community with the aim of identifying coherent structures in turbulent flows, and proceeding towards recent machine learning methods that were initially developed in machine vision, pattern recognition, and artificial intelligence.
The first day was dedicated to the coherent patterns (structures) in turbulent flows and aims at providing an overview of the subject and of the applications to fluid mechanics in which machine learning methods are bringing substantial contributions. In lecture 1, this overview was given using a well-known benchmark to build confidence, intuition, and a clear understanding of the motivation of the course. Lecture 2 on turbulent structures further elaborated on the motivation of the field by addressing the problem of coherent structures in turbulent flows, giving a phenomenological picture of their origin, dynamics, and their effects on crucial engineering quantities (e.g., skin friction, noise production, flow separation phenomena, dynamic loads, etc.). The identification and the objective definition of these coherent structures have been the primary motivation for the development of decomposition methods in fluid mechanics. The following two lectures were dedicated to two classical decompositions that were originally developed with this aim: The Proper Orthogonal Decomposition (POD) and the Dynamic Mode Decomposition (DMD).
The second day was dedicated to the mathematical analysis. Lectures 5 and 6 on mathematical fundamentals will review continuous and discrete linear time-invariant systems and their properties (impulse response and transfer functions, poles, zeros, etc), the fundamental transforms used in their investigation (Laplace, Fourier and Z transform), methods for time-frequency analysis (Gabor transform, continuous and discrete wavelets) and the related uncertainty principle (Heisenberg principle). Lecture 7 builds on the first two by presenting a generalized framework of data-driven modal analysis and discusses limitations and strengths of various methods. The last Lecture of this day presented a collection of applications of data decompositions to numerical and experimental data typically encountered in fluid mechanics (e.g. DNS simulations or experimental velocity fields from PIV), presenting best practices and potential pitfalls.
The third day was dedicated to dynamical systems. Lecture 9 introduced stability analysis of fluid flows, including classical methods of analysis (normal modes, linearization, and Orr-Sommerfeld problem) and modern formulation based on optimization methods. Lecture 10 introduced linear dynamical systems, from their general formulation to their phase portrait and the basis of linear control theory (controllability, observability, Gramians, etc.). Lecture 11 covered nonlinear dynamical systems and their distinctive features, including attractors, bifurcations and the route to chaos, with a connection to the theory of turbulent flows. Finally, Lecture 12 gave an overview of system identification methods, such as Eigensystem realization algorithm (ERA), observer Kalman Filter identification (OKID), autoregressive moving average (ARMA) and more.
The fourth day was dedicated to machine-learning methods and their application in data-driven reduced-order modeling. Most problems in fluid mechanics can be formulated as regression problems, i.e., optimizing a function with respect to data or a given system. Examples are feature extraction, model-order reduction (autoencoders), prediction, control, estimation, and modeling. Lecture 13 provided an overview of the powerful regression solvers of machine learning (e.g., supervised versus non-supervised methods, clustering and classification methods, support vector machines, kernel methods, neural networks) while Lecture 14 gave an overview of how these are entering in the fluid dynamics community. Lecture 15 presented how dynamic reduced-order models can be developed with machine-learning methods while Lecture 16 presented their applications for the extremely challenging case of reactive flows, illustrating how machine learning techniques can help reduce the computational burden and decode the complexity of turbulence-chemistry interactions.
The fifth day was dedicated to applications and the interplay of machine and human learning in the grand challenge problems of the field: turbulence closures and turbulence control. Lecture 17 is dedicated to the importance of reduced order modeling and machine learning for aerodynamic applications. Lecture 18 highlighted recent successes of automated learning of complex nonlinear MIMO control laws in experiments and simulations with a surprisingly simple and efficient regression solver. Lecture 19 closed the course offering a fascinating perspective on how the rapid developments of direct numerical simulations, together with machine learning methods, can be used for suggesting questions, rather than providing answers. This perspective opens a debate on whether machine learning will change the way we advance scientific knowledge and whether we will one day consider machines as colleagues.
Content of the lecture series
Part I: Coherent Structures
Lecture 1 - Prof. B.R. Noack Analysis, Modeling and Control of the Cylinder Wake
Lecture 2 - Prof. J. Jiménez Coherent Structures in Turbulent Flows
Lecture 3 - Prof. S.T.M. Dawson The Proper Orthogonal Decomposition
Lecture 4 - Prof. P.J. Schmid The Dynamic Mode Decomposition: From Koopman Theory to Applications
Part II: Mathematical Analysis
Lecture 5 - Prof. Mendez Mathematical Tools, Part I: Continuous and Discrete LTI Systems
Lecture 6 - Prof. Discetti Mathematical Tools, Part II: Time-Frequency Analysis
Lecture 7 - Prof. Mendez Generalized Modal Analysis and Multiscale POD
Lecture 8 - Prof. Ianiro Applications and Good Practice
Part III: Dynamical Systems
Lecture 9 - Prof. P.J. Schmid Modern Tools for the Stability Analysis of Fluid Flows
Lecture 10 - Prof. S.T.M. Dawson Linear Dynamical Systems and Control
Lecture 11 - Prof. S.L. Brunton Nonlinear Dynamical Systems
Lecture 12 - Prof. S.L. Brunton Methods for System Identification
Part IV: Reduced-Order Modeling
Lecture 13 - Prof. S.L. Brunton Introduction to Machine Learning Methods
Lecture 14 - Prof. S.L. Brunton Machine Learning in Fluids: Pairing Methods with Problems
Lecture 15 - Prof. B.R. Noack Machine Learning for Reduced-Order Modeling
Lecture 16 - Prof. A. Parente Advancing Reacting Flow Simulations with Data-Driven Models: Chemistry Accelerations and Reduced-Order Modeling
Part V: Control, Closure and Perspectives
Lecture 17 - Prof. S. Görtz Reduced-Order Modeling for Aerodynamic Applications and MDO
Lecture 18 - Prof. B.R. Noack Machine Learning for Turbulence Control
Lecture 19 - Prof. J. Jiménez The Computer as Turbulence Researcher


Lately I have been battling with a group of year 8’s who have been getting bored with Pythagoras’ Theorem. There really are a lot of boring problems out there that they would much rather avoid. So I set them the task of creating their own questions that I might be able to use in future years (nice little resource tactic!). Some of these students were highly unmotivated, undisciplined, and unfocussed, but the work they produced was amazing.
Here’s how it happened:
1. I showed them a powerpoint that I had previously prepared with 2 Pythagorean examples. My powerpoint is here
2. Then I set them the task of creating their own Pythagorean example using Powerpoint. The problem had to be useful*, and make people laugh.
The winning team would receive a free beverage at the canteen (I also gave prizes to a few others).
Students were focused and excited about their work. 96% of students uploaded a finished powerpoint presentation. Some had errors in their solutions, but all used Pythagoras in an appropriate way. Take a look at some of their work (this is all unedited so expect to see some mistakes). Pretty impressive for a group of students who have struggled in the past.
I have created an online survey for students to fill out next lesson to see how much they enjoyed the experience, and how much their understanding improved. Will update this post once I get the results.
*Useful to a certain situation (i.e. very loose)


Draw poker hand odds chart
Эту смесь необходимо нанести на проблемные участки вен. Disk space is a critical resource. При остеохондрозе возможно отклонение межьягодичной борозды от вертикали, выпячивание остистых отростков. Alkaloid Aziende Chimiche Riunite Angelini Francesco B. Для того, чтобы удалить нежелательные волосы подмышками, можно использовать простое и современное решение.
Poker probability - Wikipedia
In odds table, "at least one pair" means you can also achieve two pair, three of a kind, a full house or four of a kind; "at least two pair" means you can also achieve three of a kind, a full house or four of a kind and the like.
These are the probabilities of receiving various card combinations at the second distribution, draw you have been dealt the first five cards and you have discarded or not. All these cases are presented in detail along with the associated odds and conclusions chart the book Draw Hand Odds. We present here only one of these cases:. poker
Therefore, holding the eraw and discarding the suited cards is recommended with respect to the goal of achieving the target chxrt. We present here only the probabilities of one or more opponents holding three of a kind as a final or initial hannd, as a function draw the odds given by your own seen cards the first five dealt plus their replacements. We are not interested in how many cards of each value in a distribution, but in a cumulative representation: how many values are represented by four cards, how many by three, and so on, how many by zero.
We call value distribution any finite sequence of numbers of values from the seen cards, in the chart form. As a convention, we remove the zeroes from this denotation, so the above value distribution is denoted by If a maximum number of five replacements is allowed c could be maximum 10there are 82 possible value distributions. The next hand notes the probabilities of one and at least one of your opponents holding a pooker of a kind formation, corresponding to the value distribution of poker own seen cards.
Odds and Probabilities For The Five Card Draw Poker Variant
The numerical values are returned by the formula of number of favorable card combinations for one oponent to hold three of a kind and some formulas of a classical probability repartition. Probabilities of opponents holding three of a kind.
Your final hand is two pair: 77JJ3. You want the probability for at least one opponent to hold three of a kind.
The mathematics of Draw Poker: Probabilities
Of course, this is not the probability that one or more opponents hold a higher formation than yours there are also the straights, flushes, full houses, four of a kind and also the higher two pairs to count, but these can be also calculated.
And all ovds for any stage of the game. You will also find all the used formulas, along with the way of computing them and the supporting math.
See craw Books section for details. If you want to skip the math and use the numerical results directly, you may use Draw Poker Odds Calculator 1. See the Software section for details.
Poker Percentage Odds Chart | Percentage Odds
Odds, because you do not expect to have to call another bet or raise on future betting rounds, you can now use these improved odds for seeing 2 cards instead of 1. If you can't remember or poker out the percentage odds of hand ;oker draw in the middle of hand, try using the rule of 4 and 2 as a rough guide.
It's a great little shortcut chart percentage odds. Divide by the percentage. Then take 1 away from that number and you will have x handd 1.
So for example, if you have a flush draw on the turn, the percentage chance of completing your draw is It is a good idea to round the percentages to a number that you can easily divide in to to help keep the working out as simple as possible.
If you have 12 outs to make the winning hand on the flop, you should only call a bet that is equal to It's a bit tricky, but just as long as you add your own potential call to create the final pot size you will be fine.
For more information on working out percentage odds with drawing hands, see the pot odds article. I've been living off poker ever since; if anything in this world could help you become a winning player, this is it.Before you can begin to calculate your poker odds you need to know your “outs”. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. If you flop an open-ended straight draw this gives you eight outs (eight possible cards that will complete the hand), so you'll hit your hand by the river % of the time. Just make sure you're getting pot odds (the value of the pot versus the value of your bet) to see the next card. Contrary to what some poker strategists tend to preach you don’t need to memorize lists of odds and perform complex mathematics to be a winning Hold’em player. However, there are some simple Texas Hold’em odds and probabilities that you should know well when you’re drawing to a hand or want to prevent your opponents from doing so.
Tools Odds Charts Percentage. Poker Percentage Odds Chart Odds Charts: Ratio Chart : Percentage Chart : Conversion Chart This percentage poker odds chart highlights the percentage chance of completing your draw based on the number of outs you have at different points in a hand.
Look below the table for more information on how to use the percentage odds chart. Percentage odds chart. Gutshot - A straight draw with only one card able to complete it.


Euler Solution 50
From ProgSoc Wiki
The prime 41, can be written as the sum of six consecutive primes:
41 = 2 + 3 + 5 + 7 + 11 + 13
This is the longest sum of consecutive primes that adds to a prime below one-hundred.
The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.
Which prime, below one-million, can be written as the sum of the most consecutive primes?
Solutions for Problem 50
Python by Althalus
Runtime: 6 seconds
import time, math start_time = time.time() def isPrime(num): for i in range(2,int(math.sqrt(num))+1): if (num%i) == 0: return False return True #Start prime number generator #We'll start with 100 attempts to get primes. If that's not enough, I'll up it. primes = [2,3,5] for i in range(1,1000): if isPrime(6*i+1): primes.append(6*i+1) if isPrime(6*i+5): primes.append(6*i+5) primes.sort() num=0 curnum=0 consecutive=0 curcon=0 #we have a thousand elements in our array. The answer won't necessarily start with the first prime... for k in range(0,1000): curcon=0 curnum=0 #Trim off any values already used as a starting point.... for i in primes[k:]: if(curnum+i >= 1000000): break curnum += i curcon += 1 if isPrime(curnum) and curcon>consecutive:num,consecutive=curnum,curcon print (num) run_time = time.time() - start_time print (run_time)


Chelmsford High School Alumni Association
CLASS OF 1985
CAROL INGALLS MEMORIAL SCHOLARSHIP
Awarding Criteria: Will be awarded to a senior who has shown outstanding improvement in the study of mathematics
President Mary Amirault
Vice-President Michelle Adams
Secretary Melanie Lenieux
Treasurer Julie Burns
Ms. Patricia DeMaras
Ms. Carol Ingalls
Carol Carr Ingalls was a member of the Chelmsford High School Class of 1970. She graduated from Lowell State College in 1974 and began her teaching career at McCarthy Junior High School in 1976. While at McCarthy, she was an energetic classroom teacher of mathematics as well as math team coach.
From 1981 to 1986, Carol taught mathematics at Chelmsford High School and was advisor to the Class of 1985. Colleagues and students alike recall her enthusiasm for her subject matter, her passion for teaching, and her dedication and commitment to students.


Math tutoring is our most popular enrollment subject at every level from early elementary—such as Eagle Crest Elementary, Erie Elementary, or Hygiene Elementary– to middle school – such as Westview Middle School or Sunset Middle School– through high school—such as Lyons Middle/Senior High School or Silver Creek High School– even college students at Front Range Community College.
Math is the ultimate building block subject- we all know that if we can’t add well, we will have trouble subtracting. If we don’t work well with the basics, we struggle with other math functions- fractions, decimals, algebra, and so on. At Tutor Doctor Northern Colorado we use the Building Block Learning method to improve your confidence, study skills, and grades.
We hand select a tutor for each student based on their learning / personality style, needs and goals. Our math tutoring will work to fill in foundational gaps, understand current concepts, and move ahead in the curriculum.
Students apply science, technology, engineering and mathematics (STEM) concepts using 21st century skills and inquiry-based design thinking models to create innovative solutions to authentic problems enhancing post- secondary and career readiness. STEM curriculum provides students the skills to succeed in advanced education and a fast changing and highly competitive global economy. Not only do students need science or math concepts, but they need to know how to write to communicate and prepare papers. Does your child attend a STEM school and need help to succeed? Grades in STEM courses must be a C or better to be eligible for certificate.
Exclusive only to Niwot High School the International Baccalaureate Diploma Programme is an internationally recognized prestigious college preparatory program for all interested students of the St. Vrain Valley Schools. IB Mathematics courses include Algebra 2, Pre-calculus, Trigonometry and IB mathematics.
Advanced Placement Courses are intensive, college-level courses and exams offered in high school. Advanced Placement courses are recognized as equivalent to college freshman-level classes, and AP students may be granted college credits if they earn qualifying scores on AP exams. AP examinations are graded on a scale of 1 to 5, with 1 indicating “no recommendation” and 5 indicating “extremely well qualified”. Students who earn satisfactory grades on AP exams may be granted credit by their college or university. Students may also be eligible for AP Scholar awards.
Tutor Doctor Northern Colorado math tutoring can increase your understanding of the AP subject matter with your one to one learning experience. Imagine having the tutor by your side explaining the material and answering questions for successful mastering of AP math! What a difference that can make in your academic career.
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How to calculate the percentage of the amount of the simplest ways
Every person in his life almost every day is faced with the concept of interest. And this concerns not only obtaining a percentage value from one number, but also solving the problem, how to calculate the percentage of the sum of numbers. In everyday life and everyday life, many do not pay attention to it, nevertheless, all these calculations are incorporated in us from the school bench.
What is the percentage
As for the concept of interest, it can be explained in the simplest way, without going into the fundamentals of mathematical calculations. In fact, percentage represents some part of something else. It does not matter in which indicator the correspondence of percentage to the main source will be expressed. The main thing is to understand that such a representation can be in the form of the percent itself (%) or in the form of a fraction, which ultimately determines the ratio of the percentage part to the original variant.
The use of interest in practice
How to calculate interest, each of us knows more from the school course of mathematics. In everyday life, we are confronted with percentages almost every minute. Any housewife, preparing a dish, uses a recipe in which the percentage is presented. The simplest example: take half a glass of milk ... This is the mathematical interpretation of what constitutes a certain part in relation to the whole.
Absolutely all calculations are based on 100 percent (100%) or unit (1), if the calculation will be made using fractions. From this and repelled when calculating any component of the initial indicator.
The same applies to the question of how to calculate the percentage of the amount, when the initial (100 percent) indicator is not one number, but several. Calculation options here can be quite a lot. Consider the most basic.
Calculate percent by proportion
Now we will not take into account the calculation of interest using the same tables of office programs such as Excel, which do this in automatic mode when specifying the appropriate formula.
In some cases, a calculator is used, where you can set the calculation of such actions. But it is not about that now.
Consider the most common methods of calculation, familiar to us from the school course of mathematics.
The simplest and most common way is to solve proportions.
In this case, the initial number is set as 100 percent (say, some arbitrary number “a”), and its part (say, “b”) - as unknown “x”. In math it looks like this:
a = 100%;
b = x.
Based on the rules of proportion, you can calculate the unknown number x. For this, the so-called cross method is used. In other words, you need to multiply b by 100 and divide by a. Exactly the same rule applies if, in the case of drawing up a proportion, change b and x in places when the percentage is known, but you need to calculate the part in a numerical expression.
Quick interest calculation
Of course, calculating percentages using proportions is fundamental. However, with the use of fractional numbers, this procedure is simplified to impossibility. After all, what is 50% really? Half. That is 1/2 or 0.5 (based on the initial number 1).Now it is clear: to calculate the half, you need to multiply the desired number by 1/2, or by 0.5, or divide by 2. This method, however, is only suitable for numbers that are divided without remainder.
In the case of a residual or infinite characters in the period after the comma such as 0.33333333 ... it is better to use fractional expressions like 1/3. By the way, fractions (in some cases irrational) accurately reflect the number itself, because the periodic digits after the comma, no matter how much you ask, will not give an integer anyway. And so the same one third clearly and clearly expresses the essence.
In the same recipes, of course, one third can be determined, so to speak, by eye. But in chemical processes, especially those related to the fine dosage of components, for example, in the pharmaceutical industry, this method will not work. There is no need to rely on the eye. It is necessary to use exact ratios of ingredients, even if one of the indicators has the form of a number with a number in a period or is represented in the form of the same irrational fraction. But, as a rule, for example, when weighing, such numbers can be limited to a decimal point after the decimal point or a maximum of one thousandth.
How to calculate the percentage of the amount
Very often one has to deal with several required numbers or their sum. The question of how to calculate percentages of the amount is solved as easily as in the case of using a single initial number. The only thing to consider in this case is the usual representation of the sum as a single value.
For example, we have two numbers, a and b, and the initial indicator is the number d. In this case, the proportion will be as follows:
d = 100%;
(a + b) = x.
Note that the sum (a + b) can still be represented as a single number. Let it be z. In the case when we set the formula a + b = z, the proportion takes on a completely standard form:
d = 100%;
z = x.
As you can see, nothing complicated about it.
There is another option when the sum (a + b) = 100%, and d = x.
Here the solution looks like this:
(d x 100) / (a + b) or (d / (a + b)) + 100 / (a + b).
As already understood, the principle of the common denominator for fractions is used here.
If we add a and b, the sum of which is equal to z, then the proportion again returns to the standard form:
z = 100%;
d = x.
The same applies in reverse order.
From the point of view of mathematics and its fundamentals, the solution of the problem of how to calculate the percentage of the sum,it comes down only to the application of the simplest rules for the disclosure of parentheses when multiplying the sum by a single number and searching for the common denominator, which, in general, is. In other words, it can be represented in formula terms as follows:
a x (b + c) = ab + ac,
where ab and ac are the products of the terms in brackets (b and c) by the number (coefficient) before the brackets a.
Actually, the same method works in proportion. Suppose we have a certain number z, representing 100%, and the sum of the numbers a and b. The percentage to be calculated is denoted by an unknown number y. In this embodiment, the proportion takes the form:
z = 100%;
(a + b) = y.
Hence the simple solution:
((a + b) x 100%) / z = ((a x 100%) + (b x 100%)) / z
The brackets of the action are taken in order to emphasize that the multiplication operation is performed in the first place, and the addition of works - in the second. The same action is performed if initially the sum of numbers is 100%.
Very often in the question of how to calculate the percentage of the amount, there is an unambiguous reverse transfer. In practice, this is due, say, to the reverse calculation of the quarter. Everyone knows that this figure is 25% of the initial number. Let, for example, the price of goods increased by 25%, which amounted to 25 rubles. We need to find out how much this product has become.Now let's try to figure out how to calculate not the initial number, knowing the value of the percentage, but the entire amount, which should turn out in the end. It would seem that the solution is simple:
25 = 25% (1/4 or 0.25);
x = 100%.
No, absolutely wrong. So you can get only the original number, excluding 25%. To calculate the entire amount, taking into account 25%, you need to use the formula:
25 = 25%;
x = 100% + 25%.
Or 100 / 0.8, which will show the value 125 (100 + 25), since 100% plus 25% in the unit expression is the number 1.25 (one plus one-fourth), and in the opposite form (1 / x) it is exactly 0.8. Making calculations, we get that x = 125.
As you can see, there is nothing particularly difficult in how to calculate the percentage of the amount. True, in the school program, the reverse translation is often omitted for some reason. Then many accountants who work on reports paying the same VAT often have problems.
So you just have to take into account the basic rules for calculating interest, and the problems will disappear by themselves.
On the other hand, for convenience, both proportions and the use of fractions can be applied equally. In the first case, we have, so to speak, the classic version, and in the second - a simple and universal solution.Again, it is better to use it in the case of division without remainder. But when calculating the most popular parts like half, quarter, third, etc., this method is very convenient.
Inverse calculations, as can be seen from the above examples, are also not complex. The main thing is to take into account the inverse coefficient when calculating the desired number. It seems that now everything fell into place. As they say, simple math.


I am a Christian and a mathematician. How are those two things related? The fact that two plus two equals four doesn’t change depending on one’s religion, so it’s tempting to think that the work I do in my classroom isn’t related to the life of faith at all.
However, the longer I’ve been both “mathematician” and “Christian,” the more I am convinced they have something very important in common. Both make me ask time and again: “What is true?”
As Christians, we look for and hold onto truth about who God is, what God is doing in the world, and how God is calling us to follow Him.
As a mathematician, I look for a different kind of truth. Many people are surprised to find out that there are countless math problems we don’t even have a strategy to solve yet. Part of my job is to work on those problems and prove new theorems. It’s a lot of work, but it can also be a lot of fun. Here’s the thing about the mathematical search for truth: it’s always done in the context of a community.
I realize most people reading this are not mathematicians, so let me tell you some of the things I’ve come to appreciate most from living within a mathematical community. In my experience, the community has three important jobs when I’m on a search for truth.
First, the community gives inspiration. I can’t figure out which math problems are unsolved unless I read journal articles or I show up to conferences and interact with people. The community helps me find interesting new problems where there’s still work to be done.
Second, the community provides encouragement. The kind of math problems I try to solve in my research are not things you can figure out in an hour or an afternoon; they may take weeks, months, or years to figure out. When I’ve tried a dozen different approaches and nothing seems to work, it’s easy to get frustrated. That’s why I, and almost all the mathematicians I know, tend to work collaboratively. That way, when one person gets discouraged, someone else can provide a new perspective and remind them of why they were interested in the problem in the first place.
Third, the community provides accountability. When I think I’ve solved a math problem I’ve been working on for a year, that’s exciting! In fact, it’s too exciting to keep to myself. The next step is to share it wherever I can: at conferences or in journals. If I’ve done good work, the community affirms it. If there are details that aren’t quite right, members of the community call me out on it. The community holds me accountable for doing work that is consistent with the rest of mathematics.
Inspiration, encouragement, and accountability make for a healthy mathematical community. But I hope that these ideas feel familiar in your walk as a Christian truth seeker, as well. I, for one, can’t count the number of times a homily or a discussion has challenged me to see something in a new light and pointed out a place where I have room to grow more deeply in faith. That’s inspiration. My friends have prayed with me through dark, discouraging situations. That’s encouragement. I rely on trusted friends to call me out when I say or do something that doesn’t match up with what we profess to believe. That’s accountability.
Inspiration, encouragement, and accountability are the gifts of the mathematical community that support and challenge me in my work. But beyond that, they’re gifts to treasure as we walk and grow together in Christian community, too.
Lara Pudwell is associate professor of mathematics and statistics at Valparaiso University.


When buying an electric tool, you always want to know its watts to understand its capabilities. Thus, the watts calculator is the device that can be used to measure the power wattages of any appliance. It provides a better and precise calculation of the power and facilitates the excellent estimation of ohms and amps.
When talking about watts, volts, amps, and resistance are naturally associated with it. Many rules and formulas are being introduced to calculate the watts. Watt being a power unit, can convert to ohms and amps by applying simple formulas, and you can estimate the total electric detail of your tool.
Now, what you have to do is learn about the power equation to calculate wattage. You must know about the current flowing in the circuit and the watts formula to get a better and comprehensive understanding.
If you want to calculate the power then try our Power calculator
When talking about voltage, you must be wondering why it needs to put a lot of effort into understanding the simple and easy ways for electric power calculations.
Here I would like to mention the watt conversion formula for better assessment.
Watt conversion formula or watts calculator
watts = volts² / ohms
watts = amps² * ohms
watts = volts * amps
volt conversion formula or volt calculators
volts = √ watts * ohms
volts = watts / amps
volts = amps * ohms
Amp conversion formula or amps, watts, volts calculator
amps = volts / ohms
amps = watts / volts
amps = √ watts / ohms
I have mentioned the calculator and conversion formulas to provide a complete and comprehensive rule to calculate wattage.
Isn’t that interesting to know about voltage and amps before proceeding more?
Well, join me in detailing the electric power.
Electric current is the number of charges passing through a wire per unit of the square. The SI unit for electric current is ampere A.
Volt explains the electric differences and pressure, and its SI unit is V.
One more important element that could complete your calculation is resistance.
The Watts calculator is available online, and by putting the accurate value of voltage and current, you can get the wattage for the relevant appliance. But it’s not as easy as I’m explaining to you. Some devices may have variable power and current, and you will find difficulty in calculating the detail. The difference is minimum, and you need a sensitive device to calculate the values.
A wattage meter is a powerful device attached to your electric tool and will tell you about power wattages. You can say it volts amps watts calculator because it obtains current and voltages along with accurate resistance.
I would appreciate if you know about the detail before buying any electric tool. Let’s suppose you want to buy a fridge for your home and it has 500 watts. Now, it’s your choice whether you estimate the total electric consumption that could be manageable in your monthly bill or you want to buy anyway. Therefore, the watts calculator helps you get the complete detail along with the watts amps calculation.
Moreover, electric power comes with AC and DC, and you can get this information from the back of the tool package or online customer service of that company. Another important thing that you know about is surge watts. It’s the power that an electric tool needs to start with. Thus, the watts amperage calculator has made life easy in many ways, and you can buy the well-maintained electrical product according to your wiring and needs.
It’s simple, and you can calculate it by yourself. Some companies offer the watts in kilowatts unit. You can simply determine the watts by watts calculator and divided the amount by 1000. You will have the kilowatts unit. Multiplying this value by your precise usage hours will get the exact value of power in kilowatts/ hrs.
By using the watts calculator, you can buy the right electric tool for yourself. The precise volts amps watts calculator would provide every unit’s exact value, and you can quickly determine the tool’s validity. It has always been convenient to choose a device that could be energy efficient and beneficial for a longer time. Stay safe and happy!


You are likely to wind up with exactly the same graph. It is called the product. As you answer each question, do your best not to examine the appropriate answers immediately.
Thus, 4 is the mode since it occurs more frequently than every other number. They have many data points which might not be helpful for the particular task available.
The remaining part of the numbers are only listed once, so there is but one mode. If multiple numbers in a established repeat the very same number of http://travisa.org/short-article-reveals-the-undeniable-facts-about-variance-mathematics-and-how-it-can-affect-you/ times, your set is going to have more than 1 mode. There’s also a third mode named LR mode, but this is rarely employed by beginners and furthermore, is usually implicitly entered with different commands.
You literally don’t will have to use your mind. There are different methods for getting space. You will begin to find yourself feeling happier more of the moment, before trying.
As a means to get to the peak of the stairs, you’ll need to resolve a range of division problems. Imagine that you’re contemplating taking work with a little next computer company. If you don’t have a great deal of time left before test day, but don’t stop trying!
What Is a Mode in Math Explained
This command forces LaTeX to provide an equation the complete height it has to display as though it were on its own line. Although commands follow a logical naming scheme, you will most likely require a table for the most typical math symbols sooner or later. These steps are necessary for server-side LaTeX to PNG conversion.
Arithmetic mean can’t represent it. Algorithms have a huge choice of applications. Calculations are the center of your engineering details.
The 30-Second Trick for What Is a Mode in Math
Thus, to get the appearance you want, you might have to add or remove space. It’s improbable you will decide on a blue marble. If you pick a marble from the bag without looking, you can choose a red marble or you’re in a position to pick a blue marble.
It’s a little math inception, where we try to know the verification step, not simply check the verification step. Creating a good comprehension of vector math is critical to turning into a strong http://travisa.org/short-article-reveals-the-undeniable-facts-about-variance-mathematics-and-how-it-can-affect-you/ game developer. Basic concepts are explained through attractive examples regarding our day-to-day life experience.
The Do’s and Don’ts of What Is a Mode in Math
Although it’s important to use your Happy Journal regularly to truly feel good, it is extremely important to not utilize it like an escape or distraction. Otherwise, see whether it’s possible to rewrite some words to discover the rhythm right. However there was a minor issue.
Inside this example there are in fact two modes5 and 9. The use of the Happy Journal is to allow you to get in the habit of feeling good more often. This mode is commonly used in fiction where certain information and language can be described from the perspective of an outside observer who’s following one character.
It’s equally as important to understand how to best utilize your SAT study materials as it is to understand how to access them. GAMEPLAN All mathletes should start out with the Diagnostic Quiz to produce certain they have the fundamental skills essential to finish the rest of the part of the unit. Students may use 100-chart bingo boards so an abundant number of numbers are obtainable for play.
Teachers just don’t have enough time to filter through thousands of apps to discover the one which works best for the requirements of their students. For example, a teacher may wish to be attentive to the common marks of a test in his class. Of course, they need to know the meaning of basic math terms before they can learn how to apply them to math principles.
Life After What Is a Mode in Math
The building of a temporary latex file is the next. For temperature, you may use the exact same command or go for the gensymb package and compose Some keyboard layouts feature the degree symbol, you may use it directly if you’re using UTF-8 and textcomp. It might be more reasonable to provide user2 access only to the files that really will need to get shared (either utilizing a frequent group or using ACLs).
What Is a Mode in Math
There are lots of circumstances in which arithmetic mean and median don’t reveal the true characteristics of information. In statistics, there are 3 common strategies to locate the average of a group of information. You use different averages in various scenarios, based on what you wish to communicate with your sums.
What Is a Mode in Math for Dummies
The 2 middle numbers only will need to get averaged while the data set has an even number of information points in it. In-depth analysis of descriptive data are often quite tricky to do, whereas it’s easy and quick to acquire some comprehension of numerical data. Quite simply, each element of the data is closely related to the massive portion of the other data.
SummaryStatistics does not store the input data values in memory, hence the statistics included within this aggregate are confined to those which can be computed in 1 pass through the data without access to the entire collection of values. The mean of these distribution is 26. Its magnitude depends upon their relative angle.
The Unexposed Secret of What Is a Mode in Math
All that is needed is a sufficiently substantial guarantee which they may be executed if necessary. Although, a lot of people also like to figure the range. Because these kinds of questions will appear 1 to 2 times on the test, you will notice them in a number of distinct forms.
You have the ability to place a number on the quantity of anger. All you need to do to complete the predicament is find this number on the table. Typically, interrupts should be managed whenever possible, and every little period of time saved helps.
The median tells you exactly what number can be found in the middle of your set of numbers. Make sure the range of ampersands is the exact same for every row. In place of scaling a number, it’s divided into lots of pieces equal to the second number.
The Debate Over What Is a Mode in Math
The whole-part model may also be utilized to address problems involving multiplication or division. A reflection is a shape that’s been flipped. The variety of a easy, linear function is nearly always likely to be all real numbers.


Do you have a child who is just starting to learn their numbers? If so, you may be looking for some fun and creative ways to help them learn. One great way to do this is by using number formation rhymes.
In this blog post, we will discuss what number formation rhymes are and how they can help your child learn their numbers.
What Are Number Formation Rhymes?
Number formation rhymes are simply rhymes that help children remember how to write numbers. For example, the famous rhyme “One, two, buckle my shoe” can be used to help children remember how to write the numbers one and two. Similarly, the verse “Three, four, shut the door” can be used to help children remember how to write the numbers three and four.
Number formation rhymes are important because they are a fun way to help kids learn about correct number formation. Aside from these rhymes, you can also have your children view number formation posters every day. Number formation posters are great because they provide kids with a visual representation of how numbers are written.
In addition, you can also use number formation worksheets to help your child practice writing numbers correctly. These worksheets can contain number representations, each number’s number word, and arrowed tracing numbers.
You can give these numbers in a schoolroom. Make use of primary print to make sure that your children will remember each number properly. Primary print pertains to activities for primary learners. Children learn best if they have a hands-on activity to refer to. Therefore, use primary print for preschoolers who are just starting to learn about numbers.
Why Use Number Formation Rhymes?
There are many reasons why you might want to use number formation rhymes with your child. For one, they can be a lot of fun! Children often enjoy learning through song and rhyme, so using number formation rhymes is a great way to make learning numbers fun and engaging.
Additionally, number formation rhymes can help children remember how to write numbers correctly. By using rhymes, children can create a mental picture of the number they are trying to write, making writing numbers simpler and less confusing.
Finally, these rhymes can be used to assess your child’s understanding of numbers. If you are working with a child who is having difficulty learning to write numbers, using number formation rhymes can help you determine whether they understand the concept of numbers and how they are written. They will be able to learn about the correct formation of numbers. The correct formation of numbers is easy to learn if children have a guide like number rhymes.
If a child can recite a number formation rhyme correctly, they likely understand the process of writing numbers and just need some extra practice. On the other hand, if a child cannot recite the rhymes correctly, it may indicate that they do not yet understand the concept of numbers.
There are many benefits to using number rhymes to help your child learn about numbers. Rhymes are fun and easy to remember, making them an ideal way to teach children new information. In addition, rhymes can also help children understand the concept of numbers and how they are written. If you want to help your child learn about numbers, consider using fun rhymes about numbers.
Aside from rhymes, you can also introduce number poems. Reading number poems is a hands-on and fun way to learn about numbers. You can also show animated PowerPoint presentations about numbers. This way, learning becomes more fun and interactive.
The Number Formation Rhymes
Around and around and around we go… When we get home we have a zero.
Number 1 is like a stick. A straight line that is very quick.
Around and back on the railroad track. Two, two! Two, two!
Around a tree, around a tree. That’s the way to make a three!
Down and over, down once more. That’s the way to make a four!
Straight line down, then around. Hat on top, and five’s a clown!
Make a curve. Then make a loop. There are no tricks to make a six!
Across the sky, and down from heaven. That’s the way to make a seven!
Make an S, and do not wait. Go back up, and that’s an eight!
A loop and a line, that makes a nine!
Straight line down, then around with a grin. That’s the way to make a ten!
Why Is It Important For Kids To Learn About Numbers?
Kids need to learn about numbers so they can understand the world around them. They’ll need to know how to count in order to do things like measure, compare, and estimate. In addition, identifying numbers will help them with tasks such as reading a clock or understanding a calendar.
Knowing basic number concepts will also give kids a foundation for more complex math skills. Finally, understanding numbers can be helpful in everyday life, such as when kids are trying to figure out how much change they should expect from a purchase. By learning about numbers early on, children will have an easier time succeeding in school and life!
Number rhymes are one way that you can help your child learn about numbers. These simple poems or songs usually teach counting or number recognition.
Number rhymes can be a fun way for kids to learn about numbers and their order. They can also help kids understand how to use numbers in everyday life.
How Are Numbers Used In Everyday Life For Kids?
Kids interact with numbers in different ways compared to adults. Most adults use numbers for things like work, bills, and groceries. For kids, numbers are everywhere! They are on the clock at school, on the scoreboard at a sporting event, and in their favorite video games.
Number rhymes can help kids to understand the concept of numbers. When kids hear a number rhyme, they are hearing the number being said over and over again. This helps them to remember the number and its order.
When Should Kids Start To Learn About Numbers?
Most kids start to learn about numbers around the age of three. This is when they begin to understand that there are quantity differences between objects. For example, a child may be able to tell that two dogs are more than one dog.
During this stage, kids will also start to understand the concept of zero. They will learn that when there are no objects, it is called zero. When kids learn about numbers at an early age, it sets the foundation for them to understand more complex math concepts later on.
One of the best ways to help your child learn numbers is by teaching them number formation rhymes. These rhymes are a fun and easy way for kids to learn how to write numbers. Not only will they be able to learn the proper way to form each number, but they will also be able to memorize the order of the numbers.
How Can Parents Help Their Kids Learn Numbers?
There are a few things that parents can do to help their kids learn numbers. One way is to provide opportunities for them to count. This can be done by counting objects around the house or during everyday activities like brushing teeth or setting the table.
For instance, parents can say, “Let’s see, we need three forks for this meal. One, two, three. Good job!”
Another way to help kids learn numbers is by singing number songs and nursery rhymes together. This is a great way to introduce numbers and helps kids learn to count in a fun and engaging way.
Finally, parents can also create simple games that focus on numbers and counting. For example, they can hide a certain number of objects around the room and have their child find them. Or they can play “I Spy” with numbers instead of colors or shapes.
By providing these opportunities for kids to engage with numbers, they will be well on their way to mastery! Just make sure to be consistent and have patience – it takes time for these concepts to really sink in. But with a little effort, your child will be a math whiz in no time!
How Can Teachers Help Their Students Learn About Numbers?
Teachers can also help their students learn about numbers in a number of ways. For example, they can incorporate number formation rhymes into their lesson plans. There are many of these rhymes available online and in children’s books. By reciting these rhymes with their students, teachers can help them learn the proper way to form numbers.
Additionally, teachers can create fun and engaging math games for their students to play. These games can be used to teach a variety of concepts, including number recognition and counting. Not only will the students have fun playing these games, but they will also be learning important mathematical skills!
Lastly, teachers can also use technology to help their students learn about numbers. There are a variety of apps and websites that are designed to teach children about numbers. By using these resources, teachers can help their students learn in a fun and interactive way!
Helping Kids With Number Retention
Aside from directly teaching kids about numbers, there are a few other things that parents and teachers can do to help kids with number retention. One of the best ways to help kids learn is by providing them with opportunities to practice. This can be done through games, activities, and worksheets.
Additionally, parents can put up number posters around the house or create number books with their children. By doing things like this, parents and teachers can help kids learn in a fun and creative way!
In school, teachers can also put up posters and create number books. However, they can also do things like create number rhymes or songs. These are great because they help kids learn in a fun and interactive way!
Practice Makes Perfect
Children will be able to learn numbers best if they are given ample opportunities to practice. This can be done through games, activities, and worksheets at home or in school.
Parents and teachers must collaborate to ensure that children are getting the best education possible. You can help children learn in the best way possible by providing their support and guidance!
Number formation rhymes are a great way to help children learn numbers. They are fun, interactive, and can be used to provide ample opportunities for practice. With the support of parents and teachers, children can learn numbers in the best way possible!
So, how hard is it to introduce number formation rhymes to kids? The answer is- it’s not hard at all! With the help of parents and teachers, children can easily learn these rhymes and use them to improve their number formation skills. All it takes is a little bit of time, patience, and practice!
Teachers must teach children all about numbers in school. On the other hand, parents need to make their children practice at home so that they can learn and remember the numbers easily. Number formation rhymes are one of the best ways to help kids with their number formation skills. These rhymes are fun for kids. Therefore, these rhymes are very effective in terms of teaching numbers to kids.
There are many number formation rhymes available on the Internet. You can easily find them and use them to help your child learn and remember the numbers. Just have patience and help your children every step of the way. Soon, they will be able to master the numbers and be able to write them correctly.


I looked across the expanse of the St Mark’s River, and realized I was stuck. A ferry boat was waiting to take me across the river so I could continue backpacking the Florida trail on the other bank. But that would mean that after hiking, rambling and hopping my way through 280 miles of the…Read More
EarthEcho’s STEMExplore highlights relatable voices and exciting life experiences to make careers in Science, Technology, Engineering and Math (STEM) come alive. STEMExplore kindles youth interest in solving problems and becoming critical thinkers about the world around them. The program features a series of interactive videos profiling STEM experts and thought leaders from around the world, meeting a critical need by fostering the next generation of STEM professionals.


Let's see... I'm 26, love sports and am a closet nerd. I went to BYU and loved it. I played on the BYU lacrosse team while I was there and tried to study from time to time. I got an undergrad in math and a master's degree in stats. I love sports (watching and playing). I currently work for a company that does consulting for professional sports team. We help them price their tickets better. It's a great way to mix my love of sports and numbers.


I remember my muscles tensing and my body freezing, my eyes growing wider as my mind started to race and adrenaline started to pump.
“I don’t remember how I used to explain why dividing fractions oftentimes ends up with a quotient larger than either the dividend or divisor.”
A few panicky seconds passed.
“Oh my gosh — I can’t remember, I can’t remember,” I said to myself, over and over.
I searched for the answer in my mind. I worked examples, looking for the pattern that was going to -click- make everything fall into place. I knew this, but I just couldn’t remember.
“I have got to know this. I can’t just say ‘flip the second fraction and multiply,’ without being able to explain why.”
I looked at the clock, on the off chance that it might give me the answer.
Knowing that I don’t start teaching fourth grade for another two and a half months, I did my best to let it go, telling myself I could look it up in the morning. “Besides, that’s not even a fourth grade standard,” I added for good measure.
To my later-in-the-morning amazement, I actually went back to sleep.
A new grade level is going to be fun!


“M” sent in her fractal tattoo. She studied the mathematics of fractals in a Chaos Theory class in college and had always wanted one as a tattoo. After some difficulty finding an artist up for the challenge of such an intricate design, she finally found some willing to give it a shot. Unfortunately the piece is only partially done since she had to move midway through. In theory it’ll never be done though, right?
For those that aren’t math geeks, this is a Julia Set fractal, closely related to the more well known Mandelbrot Set. All I know is it looks a lot like that time I ate some candy from a stranger at a rave. I woke up the next day naked in a field surround by cows that only spoke German. Talk about awkward.


Do a Barrel Roll
This one is easy to find. Simply type "do a barrel roll" into any Google Search bar and see what happens!
This is not exactly a hidden feature, but it shows what you can do with a Google Search bar.
Type any function into the search bar to automatically graph it. For example "y=3x+4" can easily be graphed using the Internet, sadly my TI-84 is becoming obsolete. Other math can be done here as well. For example type in "5*56+sqrt 144" and the answer will appear as a search result.
For more calculator fun try these functions that create 3-D graphs.
- cos(x) + cos(y)
- (sqrt(cos(x))*cos(400*x)+sqrt (abs(x))-0.4)*(4-x*x)^0.1 Copy and paste this one into a search bar to graph a heart.
- Click on the graph and drag to manipulate the graph in 3-D space
Unit converter is a part of calculator. Just type in any unit of measure to convert it to a different form. But be aware that it is impossible to convert galons to feet. Follow the examples below to get a feel for the unit converter.
- feet in furlongs
- miles in kilometers
- 3 galons in cups
- 2 watts in Newtons
- horsepower in donkeypower (yes, Google recognizes donkeypower)
- beardsecond in lightyears (yes, the length a beard grows in one second)
Do the Harlem Shake (YouTube)
As most of us know Google owns YouTube so... Easter Eggs can be found here too.
In a regular YouTube Search bar type "do the harlem shake" and press enter. You must wait at least 45 seconds to get the full effect.
The answer to life, the universe and everything
Type "The answer to life, the universe and everything" into the search bar to find the answer!
Fun with vocabulary
Type these words in the Google bar to reveal some fun definitions that students could really learn from.
- zerg rush
- once in a blue moon
Kevin Bacon is in everything. He is in so many movies and tv shows that someone has made the game "the 6 degrees of Kevin Bacon." The goal is to name an actor or famous person and try to deduct their Bacon number (the number of degrees of separation in which the subject appeared in a show with Kevin Bacon). For example, John Lithgow's Bacon number is 1. John Lithgow appeared in Footloose with Kevin Bacon.
Just type "Bacon Number (name of famous person)" and low and behold the Bacon number appears. This is a great party game! The object is to get the largest Bacon number. It is harder than you think.
For more fun and ideas on how to use Google in the classroom, please visit my website www.21learning.net and checkout my book Google Apps Meets Common Core


Math Art Challenge: Stained Glass Shape Search
Can you find the hidden shapes?
For this challenge, you will create a stained glass window design on the sidewalk using chalk and some painter’s or masking tape.
Then search for shapes in your design!
How many triangles (3 sided shapes) can you find? How are your triangles the same? How are your triangles different?
Which color did you use the most? How do you know? (relates to upper elementary work with area and measurement)
Try to find:
- Triangles (shapes with three sides)
- Quadrilaterals (shapes with four sides)
- Pentagons (shapes with five sides)
- Hexagons (shapes with six sides)
Did you create more triangles or more quadrilaterals? Create a graph to show how many of each shape you found. (relates to 2nd and 3rd grade work with geometry, measurement, and data)
Send in photos of your creations! jennifer_laib at psmba.org
Here are some more examples of stained glass windows:
photo from Chrissy Newell
I spy two orange triangles, one blue quadrilateral…
*from the Grade 2 math menu, week of April 6 – 10*


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Towson University - B.S. & M. Ed., Education, Math minor , Bethany Divinity Seminary - Ph.D., Religion (Bible)
University of Miami - Bachelors, Biomedical Engineering
University of Maryland College Park - BS, Physics
Johns Hopkins University - BS, Computer Science , Johns Hopkins University - MS, Computer Science
Johns Hopkins University - BA/BS, Molecular and Cellular Biology and Psychology
Georgia Institute of Technology - BS, Civil and Environmental Engineering
University of Pennsylvania - Current Undergrad, Bioengineering
Adelphi University - Bachelors, Mathematics , Adelphi University - Masters in Education, Education


This statistics video tutorial explains how to use the standard deviation formula to calculate the population standard deviation. The formula for the sample ...
From The Organic Chemistry Tutor
Using the small data set 3, 5, 8, 13, 21, we use the TI 83/84 to find the range, sample variance, sample standard deviation, and population standard deviation.
Using Microsoft Excel to calculate Standard Deviation, Mean, and Variance. Related Video: How to Calculate Standard Deviation and Variance ...
In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of ...
Web Design and Development, Software Development, and More Software Learning Tutorials and Tips For You.
From Happy Tutor
For more success with variance and standard deviation problems, you can checkout the book I used for reference, Schaum's Statistics Outline ...
From Statistics Dojo
This video will detail on calculating the sample mean, sample variance, sample standard deviation as well as frequency histogram data for a set of numbers.
From The Simple Engineer
statisticslectures.com - where you can find free lectures, videos, and exercises, as well as get your questions answered on our forums!
This video will teach you and give you examples how to find the range, variance and standard deviation. Please visit our website www.i-hate-math.com for ...
From I Hate Math Group, Inc


My husband and I watched the pilot of the television show “Numb3rs” last night. It’s about two brothers: the older one works for the FBI, while the younger one is a math whiz and a youthful prof at an eminent university. The younger one sees the entire world as numbers, and ends up helping out the older brother in solving a serial killer case by analyzing the data according to the application of mathematical principles.
My kind of show. I love geeky premises that involve the application some specialized skills that others don’t have and require the characters to think through the problem before acting upon it. I also love it when a show sets itself the challenge of being bound by certain concepts or principles that have to be obeyed as part of the crime solving process.
Except it rarely works that way. Numb3rs is a case in point. To disclaim: I’m not a math person. Nonetheless, even I had a bit of a problem with the solution to the pilot (warning: spoilers in the next two paragraphs. Skip them if you don’t want to know specifics about the pilot).


Little Leonardo's Fascinating World of Math
This product is currently sold out.
An introductory primer for kids learning about the “M” in “STEAM” : Mathematics.
Math is the basic foundation upon which most of the other areas of STEAM rely. If a child aspires to be a scientist or an engineer or an architect, they need to first understand math. Little Leonardo’s Fascinating World of Math introduces many mathematical concepts in a context showing their interconnectedness with so many of the things in our everyday lives.
This new series of books featuring illustrations by popular artist Greg Paprocki is the perfect way to encourage your brilliant child’s interest in all facets of the educational STEAM curriculum: Science, Technology, Engineering, the Arts, and Mathematics. Your child will be enticed by the fun and surprising details revealed in Paprocki’s cool and colorful artwork on every page.
Part of the Little Leonardo’s Fascinating World Series.
- Paper Pages
- 24 Pages
- Recommended for ages 4-8
- 7.75" x 0.25" x 9.75"


Within the mathematics curriculum there are six main topics:
• Ratio, proportion and rates of change
• Geometry and measure
These six topics are studied in every year group throughout KS3 and KS4, with the level of difficulty progressing each time. This is called the 'spiral curriculum' - going back around the same broad areas but getting more in-depth and complex each time. So, for example, a Year 7 might be able to solve a simple algebraic equation; a Year 8 might solve an equation with fractions, or unknowns on both sides, or brackets, or powers; a Year 9 could solve a pair of simultaneous equations; a Year 10 could manipulate algebraic fractions; and a Year 11 could solve simultaneous linear and quadratic equations. Each time we revisit each topic there is the opportunity to consolidate previous years' work and then add to it, and if a student is working above what we would expect of their year group then they are given extension work to broaden their knowledge and problem solving skills from the same or related topic area.
All pupils have access to MyMaths, an online mathematical resource and homework application to enhance their learning experience.
At present, setting occurs within two bands from the start of Year 7 and across the whole year group from Year 8. Students can move between sets, on academic grounds, at any time of year.
Formal graded assessments are set across all year groups four times per year as well as a synoptic summer examination.
Beyond the curriculum we run many enrichment opportunities, including:
• Junior (Year 7-8), Intermediate (Year 9-11) and Senior (6th form) UKMT Mathematical Challenges. There is one annual event for each age range, plus a fortnightly ‘Excellent’ challenge. Students may enter their own age range or higher. So, a Year 8 may enter the Junior, Intermediate and Senior challenges if they are really keen - and some do! Sixth form girls have the opportunity to be entered for the challenging Mathematical Olympiad for Girls
• We also run Team Challenges for the very best performers in the school challenges, where we travel with a SHS team and compete against other Lincolnshire schools.
• The students from all year groups enter themselves for the National Cipher Challenge, run by Southampton University, with a top prize of £1,000 from GCHQ and an awards ceremony at Bletchley Park. We will also be entering the Alan Turing Cipher Challenge in January 2016.
• Mathematics clinic takes place each Wednesday lunchtime, but all students are encouraged to seek help whenever necessary. Extra lessons take place during most lunchtimes.


I am trying to port a Fortran routine to Chapel. I probably only need the answer for a uint(32). It is for the number of points in a mixed radix FFT.
To simplify the coding, it would be advantageous to know the maximum number of unique prime factors in a uint(32). With at most 26 significant bits in a uint(32)., the number is 8 if you ignore the fact that 1 is a prime factor of every number.
Where would I look for this answer?
Hi Damian -
To my understanding, you are asking a question about number theory. If you know a number theorist, it might be time to ask them.
Anyway, I'm not a number theorist, but with some searching I have identified some material that might help you:
As I said, I'm not a number theorist, so there very well might be something wrong in this reasoning, but hopefully it gives you enough to go on.
Thanks for the tips. I do not know any number theorists.
Thanks for the advice.
I have learnt more about prime numbers in the last week than I ever really wanted to know. I learnt a lot more about prime gaps and how to compute them optimally.
My 30 year old C code to factor
N did not port so well so I looked for a better algorithm. When I looked at that code with hindsight, I (thankfully) realized that my programming skills had improved over that time because I looked at that old code somewhat disapprovingly.
I have run my code to factorize every integer up to about 2^31 and it works and your formula confirms those tests of mine. That will suit the client's limit on the number
N which they need to be able to factorize. But I would like the code to be totally general, especially as Chapel's default integer is 64 bits and maybe the code needs to last another 30 years. A scary thought.
The Chapel code returns a 2D array [1..n,1..2]. When I rewrote it in C, that new C code is way cleaner than what I started with. So Chapel encourages or (I would almost say) mandates a
better programming style. Also, I note than CLANG 15 runs nearly twice as fast as GCC 11 for this purely integer algorithm.
Thanks again for your help.
Your reasoning certainly seems to be on the right path. Given a number X between 1 and 2^n such that
primorial(p) < 2^n < primorial(p+1)
then testing for n in 1..14 shows that X has at most p unique prime factors. I will run the cases of 15, 16 and 17 and 18 overnight to confirm but it seems like the above holds. Note that either or both of those inequalities might be the looser
less than or equals to. I might even try 19, 20, 21 and 22 but it certainly looks like your formula has the answer.
Yes, I could save the unique primes in a list and then allocate the size of the array at the end to capture the unique primes and the number of times each such prime occurs in the factors of the number in question, but I want something a little more predictable than that. Also, programming it is C with an array only uses 133 lines of assembler with GCC11 or 141 lines with CLANG15. As soon as you use a linked list, it blows out the lines of assembler code and slows it down slightly. Besides, clients who long ago were Fortran programmers are most happy with an array.
Your search skills are certainly superior to mine. When I went fishing for clues, the only useful thing I learnt is that there is a relationship which the gap between primes satisfies. Not a predictable formula, but a relationship which means you do not have to go looking for a prime when is just the next odd number. Fascinating. Mind you, I think I will stick to numerical analysis. Number theory seems a bit too esoteric for me.
Now I can get onto the main game which is to port the C++ code of an FFT for an arbitrary number of points into Chapel.
Slightly more robust reporting of results to date - 3 larger numbers are running. I factorize every number up to N^2-1 and the number in the #F column is the most factors I found. I note the primorial bounds between which N^2-1 lays.
N #F N^2-1
1024 (7): P(7) < 1048575 < P(8)
2048 (7): P(7) < 4194303 < P(8)
4196 (8): P(8) < 17606415 < P(9)
8192 (8): P(8) < 67108863 < P(9)
16385 (9): P(9) < 268468224 < P(10)
32769 (9): P(9) < 1073807360 < P(10)
65537 (9): P(9) < 4295098368 < P(10)


Major win, look at Aura clapping while she uses the Elephant Learning Math Academy! Every parent wants their kids to excel in school, and the foundation of learning centers around reading and mathematics. Considering mathematics tends to be the most challenging subject for children to grasp, I really want to ensure my daughters have a strong, core understanding of math at an early age. I am honored to have become a brand affiliate, working alongside Elephant Learning, and although I do earn from qualifying purchases, I am genuinely impressed with the rapid improvement in both of my daughters learning through this academy. Having this academy as a teaching tool has made math fun and easy for both Ava and Aura. The learning doesn’t feel like homework or a chore because the lessons are in game form!
Elephant Learning Math Academy is a system for effectively and efficiently learning mathematics intended for children between 2 and 12 years of age. It has been proven to advance children 1 year in their math level in only 3 months when used for just 30 minutes each week. On average, children who are actively participating in the Elephant Learning Academy learn 1.5 years of math in only 10 weeks with using the academy 30 minutes per week. Elephant Learning Math Academy guarantees children will learn at least 1 year of math in 3 months when they use the learning system as instructed (the recommended usage is only 10 minutes per day, 3 days a week). You are encouraged to not overdue the curriculum so the kids don't burn out . Elephant Learning provides parents with access to detailed reports that allow you to understand exactly what your child's current progress is, and how you may work with them outside of the system in a fun and engaging way. This system is perfect for parents that homeschool their children or for any parent that wants their little one to get ahead in mathematics, all while having fun through the process!
I set up an Elephant Learning account set up for both Ava and Aura. The Online Math Academy allows parents to create separate work tabs for each child. I have the program set up on our ipad and laptop, so Ava and Aura can select which device they prefer to play their math games on ;). At the beginning of the program, your child will take a quick placement test. Ava and Aura never realized they were being tested because these are also in gaming format. They were excited to select their very own avatar character that reads each questions aloud. Ava selected the elephant and Aura selected the bunny :)
I am homeschooling Aura for pre-school, and since we started the program a couple weeks ago, she has excelled so much already! In the first week alone, her Elephant Learning age went from 3.6 to 5.1 years. She is able to complete the math questions at a faster rate, and with more confidence. Aura has also been improving so much more with her number recognition and problem solving. Elephant Learning has several cute and fun animated characters your child can choose from (Aura gets excited each time she makes her selection haha). The curriculum doesn't change based on character selection, so when Aura wants to switch from the bunny to the polar bears, and then probably the sharks, she will be given the proper curriculum regardless.
Aura enjoys feeling independent while working on the tasks, but I can be just as involved as a parent and track her performance on the coursework dashboard. You gain all access to the statistics and performance on the active curriculum. I love that I can select each subject they are learning to obtain the detailed information on each of my daughter's progress. Elephant Learning also offers printable worksheets that coincides with the coursework! This is the most impactful $35 you could spend every month (scholarships are also made available for families)! Their staff is very responsive and they were happy to answer all of my questions that I had (we connected quickly via e-mail but they are also available to chat widget on their website). Furthermore, they offer additional one-on-one tutoring for your child at an added price. Get your little one started ASAP and be prepared to witness mathematical growth at an incredible rate! I plan on gifting Elephant Learning Math Academy to one of my nephews also, I can't wait to see how excited he gets! Click here to download!
A big thank you to Elephant Learning for sponsoring this blog. All thoughts and opinions are my own. Thank you for reading! Xo


|Name||Math Master Puzzles & Riddles|
|Download||Download Mod Apk|
Math Master Puzzles & Riddles
Math Master Puzzles & Riddles Game Introduction ：
With a blend of logical problems, Math Master Puzzles & Riddles will raise your IQ. Challenge yourself with several levels of math games to push your mental boundaries. It is well known that mathematics has helped humans perform basic tasks since its inception. The exercises that you will find in this game will help in training your brain!
— We stand out from the competition
1. Minimalist design with 2 themes (dark & light)
2. Weekly updates with new puzzles & riddles
3. Global ranking across all devices
4. You have the possibility to submit problems directly in the game
5. Improved stats to track your progress
6. Support for multiple languages (we will add more languages in time)
7. We are always receptive to new ideas
8. We are always improving the game with new features
9. Play offline – no connection required
— Current supported languages
7. More soon – if you have a specific language request for Math Master Puzzles & Riddles, feel free to contact us. We will do our best!
— Who can play?
Everyone! Basic and complicated mathematical procedures learnt in school can be used to answer any query. For complicated and cognitive solutions, addition and subtraction are usually sufficient. Some problems will require addition subtraction multiplication and division operations in a specific order. Cognitive riddles are the type of puzzles that will pique the interest of intelligent people. Players with excellent analytical thinking abilities perceive the pattern in logical puzzles and arithmetic games at a different level.
— How to play?
You\’ll solve the numerical relationships in the geometrical figures and then fill in the missing numbers at the end. Chase the question mark and try to find a suitable answer that will be able to replace it. If your answer is good, you will receive another question and so on. For each correct answer, you will gain points. If you manage to solve multiple questions in a row, you will be rewarded with a bonus! Players with a strong analytical thinking ability will recognize the math pattern immediately.
— Submit problems in the game
You will find a separate page with all the details. First you will select the template, then you will fill the missing numbers and add specific hints and description of your algorithm. We will receive your problem and evaluate it. If it will be approved, you will find it in the next update having the author on top of it. We wanted to make everything simple and intuitive.
— Our goal
To become the biggest community where you can find all the interesting puzzles and riddles! Math is universal so everyone is invited, no matter the age or language!
— Benefits of puzzles & riddles
1. Logical puzzles and math games will improve attention and focusing
2. Brain games, like IQ tests, improve memory and perception abilities
3. Educational games can help you discover your true potential in school and in everyday life
4. Brain games can help improve your IQ
5. Logical puzzles will manage stress in an enjoyable way
6. Problem solving and logic skills will be enhanced
— Future updates
Math Master Puzzles & Riddles is constantly improving based on your feedback. We are always open to new ideas, so please don\’t hesitate to share your thoughts with us! New languages and more interesting problems will come soon!
— Important mentions
Math Master Puzzles & Riddles will always be a free game so that anybody interested in math games can play. You can always donate or watch ads in order to support the development!
— Contact us : [email protected]
1) Found a bug / mistake in the game
2) Translation problems
3) You want to replace some hints
4) Your problem was not approved
5) Have great ideas to improve the game
— Join us on social media
Math Master Puzzles & Riddles Game screenshot ：


Our recent work describes a ML algorithm teaching process to reconstruct the dense-matter equation of state, used to build a structure of neutron stars, from simulated observations of neutron stars: their gravitational masses $M$, radii (from the EM observations) as well as tidal deformabilities $\Lambda$ (first observed in the GW170817 event).
We have trained a neural network on a set of artificial equations of state (piecewise relativistic polytropes) and are able to demonstrate that the network can recover realistic microphysical equations of state - this means that the network can generalize the concept.
We have also checked that one can infer radius, which is not directly measured by gravitational-wave detectors, from the tidal deformability measurements. It works very well with a relatively simple artificial neural network. The complete abstract is as follows:
The aim of this work is to study the application of the artificial neural networks guided by the autoencoder architecture as a method for precise reconstruction of the neutron star equation of state, using their observable parameters: masses, radii and tidal deformabilities. In addition we study how well the neutron star radius can be reconstructed using the gravitational-wave only observations of tidal deformability, i.e. quantities which are not related in a straightforward way. Application of artificial neural network in the equation of state reconstruction exploits the non-linear potential of this machine learning model. Since each neuron in the network is basically a non-linear function, it is possible to create a complex mapping between the input sets of observations and the output equation of state table. Within the supervised training paradigm, we construct a few hidden layer deep neural network on a generated data set, consisting of a realistic equation of state for the neutron star crust connected with a piecewise relativistic polytropes dense core, with parameters representative to the state-of-the art realistic equations of state. We demonstrate the performance of our machine learning implementation with respect to the simulated cases with varying number of observations and measurement uncertainties. Furthermore we study the impact of the neutron star mass distributions on the results. Finally, we test the reconstruction of the equation of state trained on parametric polytropic training set using the simulated mass–radius and mass–tidal-deformability sequences based on realistic equations of state. Neural networks trained with a limited data set are able to generalize the mapping between global parameters and equation of state input tables for realistic models.
Update 29.06.2020: just accepted by the A&A!


A major theme of the 20th Century has been the growing understanding of the nature of computation. This began in earnest in the 1930's with the independent introduction of several theoretical models of computation, including the recursive functions, the lambda calculus and the Turing machine. While these models were very different in character, they were soon proven to be of equal power and are now widely considered to represent the most powerful level of computation possible. Turing machines, in particular, have been a very influential model and are the basis for the physical computers we use today.
There has been much study of models of computation that have the same power as the Turing machine and also considerable study of weaker models. Hypercomputation is the relatively unexplored field in which models of computation with more power than the Turing machine are studied. Such models have historically been considered implausible because it is difficult to see how we could physically construct a machine more powerful than the Turing machine. However, there are now models of hypercomputation which take their inspiration from physical theories including General Relativity, Quantum Mechanics and even Newtonian Mechanics.
Our physical theories tell us about many limits imposed by the laws of physics. For example, Special Relativity tells us that the speed of light is an upper limit to the speeds at which matter can travel. Is there corresponding limit to the computations that can be performed within the universe? If so, what is it? And do our different theories give us different answers? These are very important questions and we can hardly just assume that the limit is Turing computation. Whichever way these questions are answered, we would learn something deep and important about the nature of the universe.
The possibility of hypercomputation also has many interesting and important philosophical implications. For example, there are physical theories in which we could build machines capable of proving all the truths of arithmetic and physical theories in which we could not. We do not know which category our universe falls into. Gödel's Incompleteness Theorem tells us that no Turing machine can prove all the truths of arithmetic and this is often taken to mean that some of these truths will be forever out of our reach (or that we could never know the answer without using our insight). However, we can now see that whether or not we can find all truths of arithmetic is an inherently empirical matter: it depends upon the nature of our universe, and cannot be determined a priori.
Hypercomputation: computing more than the Turing machine
Using biased coins as oracles
The diagonal method and hypercomputation
The many forms of hypercomputation
How to simulate everything (all at once)


Wikipedia: Pi – This site offers a lot of information about PI, including:
Fundamentals, History, Modern quest for more digits, Uses and more. This site has information about Pi Day too.
WikiHow: How to Celebrate Pi Day – Offers 4 ways: Enjoy Pi-Themed Foods, Pi-Themed Ambiance, Throw a Pi-Themed Celebration, and Celebrate the Real Meaning of Pi Day.
Time & Date: Fun Holiday – Pi Day – This site offers information about Pi Day and other Pi related days.
Teach Pi: This site is dedicated to Pi Day and offers videos, book suggestions, news, and more.
Exploratorium: Pi Day: One of the 5 activities offered on this page, Cutting Pi, requires a circular object, string, scissors, and tape. The other activities listed require easy to find items as well.
Fran’s World of Discovery: The Circle – The circle is a fascinating and versatile shape. The activity in this post encourages fraction use.
Scientific American: Let’s Use Tau – It’s Easier Then Pi – Article
Connect with Fran’s World of Discovery!