AN INTRODUCTION TO NEWTONIAN
by Edward Kluk
Dickinson State University, Dickinson ND
How vertical and horizontal motions
This applet simulates all kinds of projectile motion with low gravity acceleration and makes possible to time these motions. A motion can start from eleven marked heights at the distance 0 m. Its initial speed and direction are selectable from three labelled choice boxes. If default sign "+" is selected, a selected projection angle counts counter clockwise from a dotted horizontal line. Otherwise it counts clockwise. Every time the red object reaches the edge of the vision field it stops and Reset button is activated. This button let us restore initial conditions for the last motion. The clear button restores default initial conditions for the motion and repaints the vision field. Finally, if the path tracer is on, a path of the object is drawn in the vision field.
We already know mathematical models for free fall and undisturbed motion on a frictionless and impenetrable horizontal plane that eliminates a gravitational pull . A natural question arises what will happen if a body starts with nonzero horizontal speed without a support of the horizontal impenetrable plane. A simple experiment with a body sliding with some horizontal speed off a table shows the body motion as a combination of vertical and horizontal motions. As we already know an accurate timing of this kind of motion is not possible without high tech devices like a fast photography. Some camcorders have fixed time between consecutive frames and they can be used to study this kind of motion. But even with such camcorder our experiment would be complicated.
It is much simpler to go back to our fictitious planet with the very low gravity acceleration simulated in the applet. Start it with all default settings except of speed which should be set at 0.20 m/s. This will simulate a case of the motion of our current interest. Measure all time intervals the moving object needs to reach each consecutive vertical dotted line from its starting point. These consecutive dotted lines are in a distance of 1 m from each other. Therefore in the first measured time interval the object covers 1 m in horizontal direction , in the second interval 2 m, and so for. A total distance covered by the object for each interval is greater than that because it moves simultaneously in both horizontal and vertical directions. Graphing horizontal distance versus time you will get exactly the same result as for the motion along a horizontal frictionless plane. Namely, the horizontal component of object's speed vH remains constant because your graph is a straight line. The slope of this line represents the mentioned above horizontal component of the speed. Let us introduce a two dimensional Cartesian frame of reference with an origin at zero height and zero displacement which is in the lower left corner of the vision field, x axis directed horizontally to the right and y axis directed vertically up. Then, you should be able to conclude from your graph that the elapsed time t and x coordinate of the object in the Cartesian reference frame are related by the following formula
How vertical and horizontal motions
representing a uniform motion (motion with a constant speed and no
change of direction) along x axis.
Now it is time to collect next set of data related to change of object's vertical position. Measure all time intervals the moving object needs to reach each consecutive horizontal dotted line from its starting point. These consecutive dotted lines are also in a distance of 1 m from each other. Relying on your experience with a free fall motion you may expect that a covered vertical distance d may be proportional to t 2 rather than t. Graph d versus t 2 looking for "experimental" confirmation of this hypothesis. Your results including value of acceleration should be practically identical like for the free fall case. After all you are on the same low gravity acceleration planet. Therefore
where the acceleration a should be about 0.01 m / s 2.
Math helps to reach more conclusions
The vertical distance d covered by the falling object is related to its y coordinate. If an initial y coordinate is denoted as yo then
Mathematical forms of x and y as functions of time deduced from our "experimental" results show that the motion of the object is composed of two independent simple motions. The horizontal motion with a constant speed vH and vertical free fall with a constant acceleration a. They are independent in this sense that a modification of the horizontal motion by changing its initial speed vH does not influence the vertical motion and a modification of the vertical motion by changing its acceleration does not influence the horizontal motion. To check "experimentally" the first of these two properties of this kind of motion, make timing for a vertical component of motions with initial horizontal speeds 0.1 m / s and 0.15 m / s. If horizontal and vertical components of these motions are independent then the vertical timings for both selected motions should be the same within of an experimental accuracy. You should be aware that if an air resistance plays an important role the horizontal and vertical components of motion are not independent anymore.
Calculating t from the formula for x and substituting the result to the formula for y gives the following result
In the defined above Cartesian reference frame this relation formally describes a parabola with opening down and vertex at x = 0 and y = yo. The upper part of the right branch of this parabola describes the path of the object. To visualize it, run the applet with the path tracer on and other parameters as defaults. Surprisingly enough, Galileo knew that paths for this kinds of motion are parabolic. Now insert into the parabola equation for yo and vH their default values 10 m and 0.25 m / s . Select a few simple values for x and calculate respective y values comparing them with values for the same x values along the trace left by the object. If our mathematical model of horizontal projectile motion is correct the calculated and "experimental" y values should be in a good agreement.
If at this point you do understand:
the objectives of this lesson are fully achieved. If you have doubts try to read it once more concentrating on them, but do not try to memorize this text. Physics is not about memorizing, it is about understanding.
|Last update: Jan 10, 1997||E - mail to Edward Kluk|
|Copyright (c) 1996 Edward Kluk|


- (also Platonic body)noun one of five regular solids (a tetrahedron, cube, octahedron, dodecahedron, or icosahedron).
English new terms dictionary. 2014.
Look at other dictionaries:
Platonic solid — In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all… … Wikipedia
Platonic solid — Geom. one of the five regular polyhedrons: tetrahedron, octahedron, hexahedron, icosahedron, or dodecahedron. [1950 55] * * * also known as regular polyhedron Geometric solid all of whose faces are identical regular polygons and all of whose… … Universalium
Platonic solid — noun any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent • Syn: ↑regular polyhedron, ↑regular convex solid, ↑regular convex polyhedron, ↑Platonic body, ↑ideal solid • Hypernyms:… … Useful english dictionary
Platonic solid — noun Any one of the following five polyhedra: the regular tetrahedron, the cube, the regular octahedron, the regular dodecahedron and the regular icosahedro … Wiktionary
platonic solid — /plətɒnɪk ˈsɒləd/ (say pluhtonik soluhd) noun any one of the five regular polyhedrons (tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron) … Australian English dictionary
Platonic hydrocarbon — Platonic hydrocarbons are the molecular representation of platonic solid geometries with vertices replaced by carbon atoms and with edges replaced by chemical bonds. Not all platonic solids have a molecular counterpart:* Tetravalent carbon… … Wikipedia
Platonic body — noun any one of five solids whose faces are congruent regular polygons and whose polyhedral angles are all congruent • Syn: ↑regular polyhedron, ↑regular convex solid, ↑regular convex polyhedron, ↑Platonic solid, ↑ideal solid • Hypernyms:… … Useful english dictionary
Platonic — Plato s influence on Western culture was so profound that several different concepts are linked by being called platonic or Platonist, for accepting some assumptions of Platonism, but which do not imply acceptance of that philosophy as a whole.… … Wikipedia
solid — solidly, adv. solidness, n. /sol id/, adj. 1. having three dimensions (length, breadth, and thickness), as a geometrical body or figure. 2. of or pertaining to bodies or figures of three dimensions. 3. having the interior completely filled up,… … Universalium
Platonic — adjective Of or relating to the ancient Greek philosopher Plato or his philosophies. See Also: Plato, Platonically, Platonism, Platonist, Platonistic, Platonic body, Platonic hydrocarbon, Platonic solid … Wiktionary


When measuring short distances, it’s often difficult to gauge exactly how big or small a measurement is. Luckily, there are plenty of everyday objects around that can serve as good references when you’re trying to figure out how big or small something is. For example, many of us have used a no. 2 pencil in school or still purchase them for our kids’ school supplies. However, the length of a no. 2 pencil won’t help you estimate 4 centimeters because it’s only 7.5 inches long.
A better reference for this measurement would be a squash ball, which is approximately 7.62 centimeters in diameter. This would make it about as close to 4 centimeters as you could get without a calculator.
Another great reference for this measurement is the inch, which is a popular unit of measurement in the United States and other parts of the world. In the United States, there are 12 inches in a foot and 36 inches in a yard. A ruler is typically 12 inches long and has lines that represent different inches. The longest line represents one centimeter.
To convert centimeters to inches, you simply divide the centimeter value by 2.54. This will give you the corresponding number in inches. For example, to find out how many inches is 4 cm, you would simply divide 4 by 2.54, which would yield a result of 1.57 inches. You can also use the decimal form of this equation by multiplying by 16 to get fractional inches with 1/16th accuracy.


Dating 9's and 10's worksheets kindergarten
Ch 1: Ch 2: Ch 3: Ch 4: Ch 5: Ch 6: Ch 7: Ch 8: Ch 9: Ch 10: Ch 11: Ch 12: Ch 13: Harold Created Date: 9/20/2016 9:04:24 AM Worksheet Math 124 Week 3 2. .. Blends Worksheets Kindergarten Free , Online Clock , Worksheet Maker For Print a worksheet that is a great reference for teaching children the basics of measuring Title: volume-rectangular-prisms Created Date: 4/5/2018 9:05:48 AM a) Polyhedron:; CAMI Mataattathematicshematicshematics: Grade 10: Grade 10 consejos de amor para mi novia nuevos Dating 9's and 10's worksheets kindergarten
Form I-693 - USCIS. Dating 9's and 10's worksheets kindergarten
PsychSim 5 Worksheets. Browse PsychSim 5 Worksheets links. Flashcards - Module 9 · Flashcards - Module 10 · Flashcards - Module 11 · Flashcards mujer alfa definicion Dating 9's and 10's worksheets kindergarten 14 minutes ago Worksheet is suitable for Kindergarten - 1st Grade. Name Date Class Practice B Measures of Central Tendency and Variation Find the mean 28 2 1 1 0 Tens Ones B 4 2 11 3 1 NBT. about 30 min to travel 4 9 10 km b. Showing top 8 worksheets in the category - Algebra Regents Review. Algebra 1 students I hope you are learning and enjoying this regents review video to assist . Grades 8 and 9 Credit: 1 This course is a one-year Regents Level Course that . Final Dates for the Showing results 1 - 10 for 2017 regents exam schedule.
We will be learning about three specific types of transformations today: Reflections, . Reflections Author: Therapist Aid LLC Created Date: 6/18/2018 9:04:43 AM worksheet has 10 problems identifying an objects location and 10 problems imagenes de frases cortas Dating 9's and 10's worksheets kindergarten Football Captains. bus driver greeting. Wapakoneta City Schools will be the leader in providing excellent learning experiences for our students. Aug 25, 2015 - 11 min - Uploaded by LinkedIn LearningLearn how to use Microsoft Excel to calculate differences not just between dates, but times
9. Basic weekly support for all children up to 18 years (or up to 19 years if still in high school) (See 10. Weekly health insurance cost for children. Name & amount per child per week. $ Date: Prepared by: (Attorney for) (Plaintiff) (Defendant)


Greetings, and welcome to an intriguing exploration of the mysterious realm of mathematics! Mathematics has played a crucial role in human civilization, influencing our comprehension of the cosmos and enabling us to tackle intricate issues. This blog post aims to explore the fundamental principles of mathematics, revealing its concealed marvels and practical uses. Prepare yourself by mentally donning an imaginary apron and activating your cognitive faculties as we delve into the fascinating world of numerical analysis.
The Foundation of Mathematics
Mathematics is commonly considered a universal language that enables us to convey ideas and concepts with accuracy and precision. Using symbols, notations, and equations serves as a potent means of conveying intricate concepts across different cultures and periods.
The fundamental mathematics operations are addition, subtraction, multiplication, and division, which form the basis for more complex mathematical concepts. Comprehending these operations establishes the foundation for resolving issues in diverse fields.
This article aims to provide an overview of the various number systems in mathematics, including natural numbers, integers, rational numbers, real numbers, and complex numbers. Explore how these systems expand our comprehension of quantities and their interconnections.
Unlocking Mathematical Concepts
Mathematical modeling relies heavily on algebraic expressions, equations, and functions as the fundamental building blocks. Acquire the ability to manipulate symbols and solve equations to reveal concealed information.
Explore geometric concepts such as shapes, lines, angles, and dimensions. This course aims to introduce the principles of Euclidean geometry and its practical applications in various fields, such as architecture and art. Students will explore the fundamental concepts of Euclidean geometry, including points, lines, angles, and shapes, and learn how to apply these concepts to solve real-world problems. Through a combination of lectures, readings, and hands-on activities, students will gain a deeper understanding of the role of Euclidean geometry in everyday life.
Calculus is a branch of mathematics that deals with the study of change and motion. It is a powerful tool that can solve many problems related to these concepts. This course delves into the concepts of differentiation and integration and their applications in solving intricate problems in physics, engineering, and economics.
Explore the realm of unpredictability and fluctuation. Gain proficiency in probability theory and statistical analysis principles to enable you to make informed decisions and derive significant conclusions from data.
Mathematics in Everyday Life
Explore the fundamental role of mathematics in the financial industry, encompassing various applications such as interest computations and risk mitigation. This course aims to understand the foundational principles that form the basis of economic models and their application in predicting market behavior.
This article aims to explain the concepts of encryption and decryption. Mathematics plays a critical role in modern cybersecurity by safeguarding digital communication and securing sensitive information. Understanding how mathematical concepts are applied to protect data in the digital world is essential.
Examine mathematics’s role in driving technological progress by looking at how it has facilitated developments in computer science, electrical engineering, robotics, and telecommunications, among other areas.
Observe the union of mathematical principles and aesthetic qualities. Experience the aesthetic appeal of art and design by exploring patterns, symmetry, and mathematical concepts. This fascination extends from the architectural wonders of ancient times to the contemporary realm of digital art.
The Beauty and Mystery of Unsolved Problems
Embark on a mathematical exploration of some of the most well-known unresolved problems, including the Riemann Hypothesis, the Collatz Conjecture, and the P versus NP problem. Explore the current endeavors to unravel these enigmas that persist in captivating mathematicians globally.
Develop an understanding and appreciation for the meticulous process of mathematical proof, which serves as a fundamental aspect of mathematical inquiry. Gain an understanding of the pursuit of logical certainty by mathematicians and the impact of their discoveries on the development of the field.
In summary, applying mathematical principles provides a means of uncovering the world’s mysteries. We can utilize its potential and alter our viewpoints by comprehending its fundamental principles, examining its ideas, and implementing them in our daily routines. Mathematics is a subject that can be appreciated by students, professionals, and those with a general interest. It’s elegance and enigmatic nature can profoundly affect one’s life.
Prepare yourself with mathematical knowledge, hone your cognitive abilities, and begin a continuous pursuit of discovery and understanding. The field of mathematics is poised to divulge its mysteries and motivate individuals to explore the frontiers of understanding. Experience the adventure with pleasure!
The key to success in mathematics lies not solely in memorizing formulas but in adopting a mindset that enables one to explore vast possibilities. Perform calculations with ease and precision.


Practical Mathematics in Nuclear Medicine Technology 2nd Edition
Patricia Wells, MAE, CNMT
An essential tool for technologist students, the newly updated Practical Mathematics in Nuclear Medicine Technology helps enhance basic math skills within nuclear medicine technology and increases general knowledge of statistics, radiation safety, instrumentation, radiotherapy and clinical procedures.
Informative word problems and explanations throughout the publication help your students prepare for the CNMT exam and real-life situations. If you prepare others for a career in nuclear medicine technology, add this must-have book to your materials today!
Member price: $65
Non-member price: $85
Includes new and updated information on:
- Basic Math Skills for Nuclear Medicine Technology
- Radiation Protection
- Clinical Procedures


Weekdays at any time
Weekends at any time
EducationCurrently enrolled at HCC and finishing up my last semester this fall to obtain my AA in Med. Transfer. I plan to further my education and plan to attend USF or a private college to pursue my dreams on becoming a Physical Therapist.
ExperienceI currently work at a CGS. There I help people with disabilities and ensure them to better their daily lives.
I want to be a tutor because I believe that I work well with people since I am very friendly and a great listener. I also currently tutor one of my clients at work with her preparation in Math and Reading skills.
HobbiesMy hobbies and interest would be anything that deals with sports. I, myself love health and fitness since I am a very athletic person. I am also interested in helping individuals in their daily lives because I believe that everyone can learn something from someone to achieve their potential goals.
Psychology, College Algebra, GED, College Essays, COMPASS Mathematics, COMPASS Reading, COMPASS Writing Skills, Nutrition, Social Work, Special Education, Art, Reading, Study Skills, Study Skills And Organization, Test Prep, Math, 8th Grade Writing, 8th Grade Science, 8th Grade Reading, 11th Grade math, 9th Grade math, 9th Grade Reading, 9th Grade Writing, 10th Grade, 10th Grade math, 10th Grade Reading, 10th Grade Writing, 11th Grade, 8th Grade math, 11th Grade Reading, 11th Grade Writing, 12th Grade, 12th Grade math, 12th Grade Reading, 12th Grade Writing, 1st Grade, 9th Grade, 2nd Grade Writing, 4th Grade Reading, 4th Grade math, 4th Grade, 3rd Grade Writing, 3rd Grade Science, 3rd Grade Reading, 3rd Grade math, 3rd Grade, 4th Grade Science, 2nd Grade Reading, 2nd Grade math, 2nd Grade, 1st Grade Writing, 1st Grade Reading, 1st Grade math, ACT Reading, Algebra 1, 6th Grade Reading, 8th Grade, 7th Grade Writing, 7th Grade Science, 7th Grade Reading, 7th Grade math, 7th Grade, 6th Grade Writing, 6th Grade Science, Pre-Algebra, 6th Grade math, 6th Grade, 5th Grade Writing, 5th Grade Science, 5th Grade Reading, 5th Grade math, 5th Grade, 4th Grade Writing
Inquire about this tutor
The tutor will respond if they are available/interested.


Keno is a lottery like game that was originally brought to America by Chinese immegrants in the 1800s. The game was adapted as video keno to make it easy to play on the floor of a casino. The player picks numbers from a list that goes up to 80. The computer then randomly draws 20 numbers. The player gets a credit payout based on how many of the numbers the computer draws match the number the player picked. The more numbers the player picks, the larger the potential payout. In this version of Keno, the player can pick up to 15 numbers.


9 APR 2019
A pair of mathematicians from Australia and France have devised a new way to multiply numbers together, while solving an algorithmic puzzle that has perplexed some of the greatest math minds for almost half a century.
For most of us, the way we multiply relatively small numbers is by remembering our times tables– an incredibly handy aid first pioneered by the Babylonians some 4,000 years ago.
But what if the numbers get bigger? Well, if the figures get unwieldy – and assuming we don’t have a calculator or computer, of course – most of us would then turn to long multiplication: another useful trick we learn in school, and a trusty technique for multiplying basically any two numbers together.
There’s just one problem with long multiplication. It’s slow.
The reason it’s slow is because for every single digit in each number in the problem, you need to perform a separate multiplication operation, before adding all the products up.
This might not be a problem for you and me, who probably rarely resort to long multiplication ourselves. But it’s a drawback school kids are familiar with, laboriously trudging through their calculations as they learn the magic of multiplication.
More significantly, it’s a problem for computers, since their own bottlenecks in performing calculations are imposed by the limits of the abstract mathematics we ourselves can comprehend.
Basically, long multiplication is an algorithm, but it’s just not a particularly efficient one, since the process is inevitably painstaking.
As it happens, mathematicians actually have a way of calculating just how painstaking long multiplication is.
As mathematician David Harvey from UNSW in Australia explains, in a multiplication where both the numbers have 3 digits (n = 3), the number of separate multiplication operations involved is actually 9, which is n2:
The problem with this is that as the numbers get bigger, the amount of work involved scales up too, always being represented by n to the power of 2.
While it’s inefficient, the long multiplication algorithm was actually the most advanced multiplication algorithm we had until the 1960s, when Russian mathematician Anatoly Karatsuba discovered that n1.58 was possible.
A decade later, a pair of German mathematicians made another breakthrough: the Schönhage–Strassen algorithm, which conjectured – but never proved – that further refinements were possible, too.
“They predicted that there should exist an algorithm that multiplies n-digit numbers using essentially n * log(n) basic operations,” Harvey explains.
“Our paper gives the first known example of an algorithm that achieves this.”
According to the researchers, multiplying two numbers together with a billion digits each by the process of long multiplication would take a computer months to calculate.
Using the Schönhage-Strassen algorithm, it would take under 30 seconds, and with their new theoretical proof, it would be even quicker – theoretically – and may even represent the fastest multiplication algorithm that’s mathematically possible.
“In this sense, our work is expected to be the end of the road for this problem, although we don’t know yet how to prove this rigorously,” Harvey says.
“People have been hunting for such an algorithm for almost 50 years. It was not a foregone conclusion that someone would eventually be successful.”
It’s worth noting the new algorithm would only ever be useful for multiplying very big numbers together. How big exactly?
“We have no idea,” the researchers explain in an FAQ, although one example they give in the paper equates to 10214857091104455251940635045059417341952, which is a very, very, very big number.
The world’s maths community is still absorbing the new findings, which have yet to be peer-reviewed, but are already making waves.
“I was very much astonished that it had been done,” theoretical computer scientist Martin Fürer from Penn State University told Science News.
Now, hope has been restored, provided mathematicians can verify the work.
“If the result is correct, it’s a major achievement in computational complexity theory,” mathematician and computer scientist Fredrik Johansson from INRIA Bordeaux and Institut de Mathématiques de Bordeaux told New Scientist.
“The new ideas in this work are likely to inspire further research and could lead to practical improvements down the road.”
Meanwhile, Harvey and his co-researcher, Joris van der Hoeven from École Polytechnique in France, say their algorithm needs to be optimised, and they’re just hoping they haven’t stuffed something up in their proof.
“A lot of the work was convincing ourselves that it’s actually correct,” Harvey told AAP. “I’m still terrified that it might turn out to be wrong.”


Inclusion Probabilities: Simple Random Sampling
simple_rs_probabilities(N, prob = NULL, check_inputs = TRUE)
The number of units. N must be a positive integer. (required)
prob is the probability of being sampled must be a real number between 0 and 1 inclusive. (optional)
logical. Defaults to TRUE.
A vector length N indicating the probability of being sampled.
probs <- simple_ra_probabilities(N = 100) table(probs)#> probs #> 0.5 #> 200probs <- simple_ra_probabilities(N = 100, prob = 0.3) table(probs)#> probs #> 0.3 0.7 #> 100 100


We’ve made a few changes to the maths department this year. One of our big changes is our rewards system. We felt too much outstanding work was going on but going unnoticed. This spreadsheet houses all the exceptional maths work from the start of the last term until you leave the school.
To be outstanding, you can’t miss any of your homework deadlines, you must be a model student within the class and your book work must be of the highest standard.
If your spaces are left blank, it could be that you were “good” but only the outstanding mathematicians earn a place. Prizes will be linked into how many A2L scores of an A you gain throughout your time at TEMA.
So, how many have you got? Are you doing everything you should to get the next one? What prize are you going to get next?


Decisions, decisions—we all have to make them. When a business makes the wrong decision it can be a costly mistake resulting in financial loss, poor use of resources, and negative impact on a company’s image. Thankfully, a decision tree diagram can help. While it’s not a crystal ball, it can provide some valuable insight that can steer you in the right direction. One of the biggest benefits of a decision tree is that it can take emotions out of the equation.
Decision tree diagrams are often used by businesses to plan a strategy, analyze research, and come to conclusions. Lenders and banks use decision trees to calculate the riskiness of loans and investment opportunities. They are also a popular choice for infographics, often appearing in magazines or shared on social media. The point is that decision trees can be used to evaluate just about any question or concern and visualize possible outcomes.
One of the nice things about a Decision Tree Diagram is that there aren’t a lot of elements. The key elements are called nodes, and appear as a square or circle with branches (lines) connecting them until a result is reached. Squares represent decisions, while circles are for uncertain outcomes.
Nodes have a minimum of two branches extending from them. On each line write a possible solution and connect it to the next node. Continue to do this until you reach the end of possibilities and then draw a triangle, signifying the outcome.
Once you’ve got the basic layout of a decision tree complete, you can add values to each line to garner more intelligence. Here’s how to do it:
1. Look at each line and add an amount to each.
2. To analyze your options numerically, add an estimate for the probability of each outcome. Note: When adding percentages all the lines from a single node need to equal 100, if you’re using fractions they need to add up to 1.
3. Assign a possible amount to each triangle at the end of the branches.
4. Calculate the results by multiplying the result by the percentage probability for each end branch in that outcome and subtract the cost of that course of action. You’ll end up with an estimate of what that particular outcome could yield.
Here’s an example:
Note: If you have a large tree with many branches, calculate the numbers for each square or circle and record the results to get the value of that decision. Start on the right side of the tree and work towards the left


Introduction to decision aid
In particular occasions, there is simply no "best" decision to take. There may be a clear need to make a choice between several actions, but none of them is objectively the best one. "Any" of the actions would be acceptable, with no reason to choose one more than the other.
A teacher may need to decide in which order his students will present the result of their work to the other students. He may wish to be "fair", and decide "at random" who will start instead of using another method, as the alphabetical order of the students names, which would not be "fair" for all students.
A company that wishes to give a part of its profits to charities might be interested in using some kind of random method in order to determine to which charity the gift will be made.
Random methods have therefore their place in a computer library devoted to decision aid. As for all methods, random methods have to be used properly and in the right circumstances: it would of course not be acceptable for a doctor to use them to choose the medication for his patients...
Generating random sequences of numbers that are "truly" random is quite a difficult task for a computer. Many studies have been made on the subject, and DECIDE includes a function DECIDE__Random that allows the user to generate random numbers using several efficient methods.
"...random numbers should not be generated with a method chosen at random" (KNUTH 1998).
An easy way to make a choice using random numbers generators is to number all actions from 0 to n, and to generate a random number r. The remaining of the division of r by n (r modulo n) will give the number of the action to choose.


Finding attractors of dynamical systems via recurrences
Conceptual models describing, for example, the dynamics of physical, biological, chemical or even social systems can be represented in a compact form by so-called 'dynamical systems' using differential equations. Most of these models feature multistability, meaning that the model has several different long-term states (formally called attractors). In which of these attractors the model ends up to depends uniquely on its initial condition. For multistable systems it is therefore important to be able to both identify all attractors in the system, but also map which initial conditions end up to which attractor (formally called the basin of attraction). Datseris and Wagemakers created an algorithm that can find the attractors and their basins for any dynamical system. Ground breaking about this work is that it only requires the defining equations of the dynamical system. The implementation of the method was published directly as part of an internationally acclaimed software library for dynamical systems, allowing scientist to utilize this algorithm using only 10 lines of code.
In climate science, we encounter multistability when, e.g., studying the glaciation cycles of Earth’s past. A simple model that captures the existence of two Earth states, one snowball, one like today, can be written as
which only means that the planetary albedo decreases with temperature, being 0.7 at -20°C and 0.3 at 0°C. This model only has a single variable, and hence it is rather straightforward to identify its attractors and their basins. If the model starts with an initial temperature less than 250K, it will always converge to final temperature of 230K (snowball Earth). If the initial temperature is above 250K, the model will always converge to 288K (today). Of course, reality is much more complicated. For example, Gelbrecht et. al. (2021) expanded the model above to also include a spatial component of atmospheric advection and dissipation. In this case, it is much harder to estimate “by hand” what are the attractors of the system, and practically impossible to estimate their basins.
This is where the method of Datseris and Wagemakers comes into play, and can automate the process. The method makes use of one of the most fundamental statements in dynamical systems theory: the Poincaré recurrence theorem. It states, that, while on an attractor, the system will sooner or later return to the position it was some time ago. Then the method finds these recurrences, and with some further internal logic, it identifies attractors and their basins.
As the method is available as open source, here is an example of how one would compute the attractors and their basins for the system of Gelbrecht et. al. (2021) using the following Julia language code snippet:
Datseris, G. and A. Wagemakers (2022) Effortless estimation of basins of attractions. Chaos 32. https://doi.org/10.1063/5.0076568
Gelbrecht, M., Lucarini, V., Boers, N. et al. (2021) Analysis of a bistable climate toy model with physics-based machine learning methods. Eur. Phys. J. Spec. Top. 230, 3121–3131 (2021). doi.org/10.1140/epjs/s11734-021-00175-0
Dr. George Datseris
Max Planck Institute for Meteorology


Addition is done by encrypting the numbers and then sending them to a centralized server. The centralized server then redistributes the two numbers to peers, who add them. The peers send the result back to the server, who sends it back to your computer, and your computer decrypts it. However, the numbers are never decrypted by the server or the peers. These peers have added two numbers together without even knowing what they are. This is done using a mathematical construction known as the Paillier Cryptosystem.
The Paillier Cryptosystem only allows for the addition of numbers, it supports what is known as Partially Homomorphic Encryption scheme. Recently (2009), Craig Gentry constructed a Fully Homomorphic Encryption scheme (FHE), permitting both the addition and multiplication of numbers. FHE is not used here due to practical considerations. FHE could have a potentially enormous impact for cloud computing firms and privacy advocates. Readers interested in current implementations of FHE are directed to HElib (sadly incomplete).


This is the lowest price ever for these on Amazon. Earlier today the price was $79.95.
-Magnetic Tiles Building Set
-60-piece set of multi-colored, geometric magnetic building tiles with project guide
-Square and triangular tiles adhere on all sides for infinite 2D and 3D building possibilities
-Open-ended manipulative building set engages children of all ages in creative play
-Develops spatial awareness and problem-solving, logical thinking, and math reasoning
-Recommended for children from 3 and up; hours of fun for children and adults
Amazon offers free shipping with $35+ orders or get free next-day shipping on all orders with a free trial of Amazon Prime. Prime members can share benefits with a Household member here, allowing them to double up on Amazon Prime promos! A 6 month trial and discounted Prime membership is available with Amazon Student. EBT/Medicaid Cardholders can save on Prime Membership here.


AVISO de ClasificadosOnline
Los patronos NO le piden dinero ni un depósito para trabajar, si lo piden es un negocio, inversion o Fraude. NO envíe dinero para trabajar, tampoco ofrezca información personal, por teléfono o email. Evite el Fraude
goal is to help pupils develop critical-thinking abilities by gaining an understanding of mathematic concepts.
Requisitos - Requirements
actively instruct students, create lesson plans, assign and correct homework, manage students in the classroom, communicate with parents, and help students prepare for standardized testing. Math teacher job duties higher grade levels. In middle and in high schools, for example, math teachers may need to help students prepare for graduation and college entry exams, while in elementary schools the mastery of basic skills is of paramount importance.
arithmetic and problem-solving skills is one of the many duties of a math teacher. An undergraduate degree is required for most math teaching jobs, as well as certification. However, licensure is to be required, but can show some grades in college that are excellent and a degree in mathematics.


Each week the mathcounts problem of the week features an new fun math problem this problem can be used for competition practice with your math club or in the classroom. Mathcounts resources mathcounts books art of problem solvings introductory subject textbooks are ideal for students preparing for mathcounts as are aops volume 1 . 2016 2017 math edge problem solving competitive math training for mathkangaroo matholympiads mathcounts amc effectively in solving. 70 mathcounts 2011 2012 solutions to handbook problems the solutions provided here are only possible solutions it is very likely that you or your students will come
How it works:
1. Register a Free 1 month Trial Account.
2. Download as many books as you like ( Personal use )
3. No Commitment. Cancel anytime.
4. Join Over 100.000 Happy Readers.
5. That's it. What you waiting for? Sign Up and Get Your Books.


1. Population is the entire group of objects about which information is wanted.
2. A sample is a part or subset of the population used to gain information about the whole.
3. A sampling frame is the list of units from which the sample is chosen.
4. Convenience sampling refers to selections of whichever units of the population, not necessarily random, that are easily accessible; samples obtained in this way are often not representative of the population and can lead to misleading conclusions about the population.
5. Biased is the term for when a sampling method produces results that consistently and repeatedly differ from the truth about the population in the same direction.
6. Simple random sample (SRS) of size n refers to a sample of n units chosen in such a way that every collection of n units from the sampling frame has the same chance of being chosen. It is fair or unbiased.
7. Table of random digits is a list of the ten digits like 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 having the following properties:
a. The digit in any position in the list has the same chance of being any one of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
and b. The digits in different positions are independent in the sense that the value of one has no influence on the value of any other.
8. A parameter is a numerical characteristic of the population. It is a fixed number, but we usually do not know its value.
9. A statistic is a numerical characteristic of the sample. The value of a statistic is known when we have taken a sample, but it changes from sample to sample. Put simply, parameter is to population as statistic is to sample. Example: If out of 1,220 people, 1098 of this sample size responded "yes" to a question, then p equals 1,098 of 1,220 equals 0.90. It is reasonable to use this proportion p equals 0.90 as an estimate of the unknown population proportion p. But if a second sample size of 1,220 were taken, it is almost certain that there would not be exactly 1,098 positive responses. So the value of p will vary from sample to sample. This is called sampling variability.
10. A probability sample is a sample chosen in such a way that every unit in the sampling frame has a known non-zero chance (or probability) of being chosen.


Calculate the interest amount of the loan received by cashing by the real annual rate method or the add-on method. An add-on is an interest calculation method that comes from add on, which means “add-on,” and features easy-to-understand calculations and low apparent interest rates. Currently, add-on methods are rarely seen in consumer finance because the law requires that only the real annual rate be displayed. The add-on method calculates from the initial borrowing amount, whereas the real annual rate is calculated from the borrowing principal at that time. If you borrow 1 million yen with an add-on rate of 20%, the interest you will earn one year later will be 1 million yen x 20% = 200,000 yen. Then, the total repayment amount of 1.2 million yen is divided by the number of times to repay in one year, and the repayment amount at the time of division is calculated. Interest calculation and repayment amount calculation using the add-on method are easy to imagine and understand. If the actual annual rate is 20%, the final repayment amount will be 1.11 million yen if the repayment is made under the same conditions. In this way, even with the same 20% display, the interest will be completely different between the real annual rate method and the add-on method. The difference is whether you pay interest on the first loan or underestimate the amount of principal you earn as the repayment progresses. With the add-on method, the interest rate can be displayed lower than the real annual rate method, so it is easy to think that it is a good interest rate. Before you get a cash loan, you want to know in advance whether the interest rate is displayed as a real annual rate or an add-on annual rate.


School Age Eco-Camp Week 7 (7/29/2024) - Time to Tinker
This week campers will engage in a variety of STEAM activities!
Kindergarten-5th grade: This week campers will engage in a variety of STEAM activities. STEAM integrates science, technology, engineering, the arts, and math into learning activities. STEAM is designed to teach children to be innovators, to think critically, and to use creative approaches to solving real-world problems.


math worksheet template
Advanced Addition Drills Worksheets You May Select From Different Problems To Produce A Worksheet With Best Math Worksheets Ideas On Grade Math Stencil Letters Font Best Letter Template For Kids Ideas On Parent MultiplicationPracticeWorksheetsMultiplicationToX Gif Best Math Worksheets Images On Division Homeschool These Math Worksheets Feature Surface Area Calculation Practice Choose From Basic Or Intermediate Surface Area Worksheets Student Learn To Calculate Best Math Super Teacher Worksheets Images On Eighth Grade Math Worksheets Contain Exponents Scientific Notations Algebraic Expressions Function Volume Probability And More Best Th Grade Math Images On Math Teacher Teacher Math Worksheet Ideas About Math Logic Puzzles On Logic Puzzles Th Grade Math Worksheet Ideas About Math Logic Puzzles On Math Worksheets Th Grade Decimal Division Dmmb Worksheets Math Worksheets Th Grade Decimal Division Dmmb Worksheets Th
Related math worksheet template
DISCLAIMER: All images found here are believed to be in the "public domain". All of the images displayed are of unknown origin. We do not intend to infringe any legitimate intellectual right, artistic rights or copyright. If you are the rightful owner of any of the pictures/wallpapers posted here, and you do not want it to be displayed or if you require a suitable credit, then please contact us and we will immediately do whatever is needed either for the image to be removed or provide credit where it is due. All the content of this site are free of charge and therefore we do not gain any financial benefit from the display or downloads of any images/wallpaper.


This laboratory introduces students to graphing experimental
data sets, linear regression analysis, and determining the equation
of the linear fit equation. Several types of data sets are used to
introduce the concepts of using a spreadsheet to analyze data sets
and plot best fit equations for both linear and exponential data,
to select data points that should be eliminated from the fit, to
determine R-squared values for a data set, and to observe the
conditions under which extrapolation is unreliable. Student will
plot data sets, determine the best fit equations, and answer asked
for observations and to draw conclusions based on their
- Introduce the concept of graphical curve fitting.
- Illustrate how to convert data from exponential to linear
- Illustrate how to use the coefficients of the fitted curve to
calculate expected values.
- Compare and analyze the relative significance of dispensing
error and variability in a sample set.


I decided to buy some plastic eggs, take a permanent marker, and write down some math facts. On the top part of each egg I wrote down the multiplication statement and at the bottom, the answer (obviously mixing up the colours). Putting them in two baskets, all the students have to do is match the right top with the right bottom. This is great not only to keep students busy and practising their multiplication facts, but also for me to check after for assessment.
Problem is - I bought a bag of 40 eggs. What to do with the rest?
Some ideas I have...
- Write a different journal topic in each egg, and when the students are finished their work they have to pick an egg and write a journal entry.
- Put a little treat in each egg to give to the students for Easter break.
Any other ideas?? :)


|Learning Kinematics and Dynamics|
Relates to SENSOPAC Work Package 2: 2B.1, 2B.2, 2B.5 and Work Package 3: 3A.1
People involved: Djordje Mitrovic, Giorgios Petkos, Sethu Vijayakumar
Role within SENSOPAC
We develop machine learning algorithms for acquiring dynamics from movement data such that:
Recent anthropomorphic robots, most notably the one developed within the SENSOPAC project at DLR, feature a complex kinematic structure with many degrees of freedom (DOF). Consequently, the forward and inverse dynamics are very complicated, and an analytic derivation of these mappings is cumbersome, subject to approximations, or even impossible. Since an accurate model of the inverse dynamics is the key to precise, yet compliant control of the robot, it is desirable to learn such a model from data. More importantly, when learning an internal model of the dynamics, we can incorporate haptic information and therefore learn about the structure of the sensorimotor space. Furthermore, the model can be adapted to changes in the environment. Hereto, please also see our subproject Context Estimation and Switching.
Unfortunately, the inverse dynamics mapping (from the current state and the desired change to the necessary torques or motor commands) has a high input dimensionality (3 times the number of DOFs plus the haptic information), so many standard regression techniques designed for rather low dimensionalities fail.
Online learning in high dimensions
We develop non-parametric local weighted learning techniques, where we aim for robustness and the ability to learn in an online, incremental fashion. We approximate the global regression function by a mixture of multiple linear models, each of which is "responsible" in a certain region as determined by a center and an automatically adapted distance metrics. The local regression models are learned using partial least squares, and leave-one-out cross-validation is utilized for ongoing assessment and complexity control of the model. Local models can be added and purged as required during training .
Bayesian treatment of open parameters
We investigate Bayesian methods to address the problem of open parameters like learning rates, forgetting factors, and initial distance metrics. By formulating a novel Randomly Varying Coefficient model, we bring together two separate lines of research: we combine the efficiency of non-competitive locally weighted learning schemes with the recognised modelling strength of Bayesian approaches .
As a deliverable (D2.6) for the SENSOPAC project, we will release a software package for regression that includes appropiate documentation and routines in MATLAB and C++. The underlying algorithm of that software package will be LWPR (Locally Weighted Projection Regression), which has matured over several years in our group.
While our learning algorithms are applicable for general purposes, within SENSOPAC the most important field of application is its deployment for internal model based control of a robot arm. We will also spent effort to unify our online learning algorithm with the (classical) control strategies currently used at the DLR labs.


Online Math Resources
PCMS Online Math Textbook: Pearsonsuccessnet.com
Student user names and passwords are shared with them by their teachers.
Description: IXL's math skills are aligned to the Massachusetts Curriculum Framework (Common Core), providing comprehensive coverage of math concepts and applications. With IXL's state standards alignments, you can easily find unlimited practice problems specifically tailored to each required standard. Even better, IXL automatically tracks student progress and displays proficiency scores in the state standards reports. These reports allow you to quickly evaluate student aptitude and identify trouble spots.
Khan Academy: http://www.khanacademy.org/
Description: A free learning resource tailored for your child. A free learning resource personalized for every student. Your child will get a personalized learning dashboard that will guide them through each subject like a personal coach while using state-of-the-art, adaptive technology that identifies strengths and learning gaps while suggesting skills to practice. Your child will also receive fun rewards along the way like badges, energy points, and avatars.
Description: A collection of math lessons/videos by grade and course. MathVids has certified math teachers on staff to ensure the accuracy of every video so you know what you are learning is correct.
Description: A collection of online resources from the National Council of Teachers of Mathematics.
Wolfram Alpha: http://www.wolframalpha.com/
Description: “Making the world’s knowledge computable” Wolfram|Alpha introduces a fundamentally new way to get knowledge and answers— not by searching the web, but by doing dynamic computations based on a vast collection of built-in data, algorithms, and methods.”
Description: A collection of websites to support mathematics learning.
Description: A game-based approach to learning and practicing mathematics. Students have login information provided from their math applications teacher.
Description: A library of virtual mathematics manipulatives by grade level and topic. Website: https://photomath.net/ Description: PhotoMath reads and solves mathematical expressions by using the camera of your mobile device in real time. It makes math easy and simple by educating users how to solve math problems.


The numbers are one of the first things that you learn in English as they form part of a vital basic vocabulary that you need for daily life.
Similarly, numbers are also one of the first things that you should learn when learning Italian because they are such a foundational part of daily language, especially the numbers from one to ten.
Knowing your numbers in Italian is very useful and they are also very easy to learn since they are quite similar to English anyway.
However, although it can be quite simple to learn the numbers from one to ten in Italian, it can be trickier when using bigger numbers or certain other number-related words.
Whether you want to order multiple pizzas when in Italy or impress your Italian friends with your number knowledge, knowing Italian numbers is certainly a vital language skill that will come in handy often.
This guide will break down all you need to know about counting in Italian and go over some other important Italian number-related words ensuring that you confidently know your way around the numbers in Italian.
Italian Numbers: The Basics
First things first, let’s go over the basic numbers from one to ten in Italian.
All it takes is a little practice to master these simple numbers. You will be surprised how useful they are when speaking Italian and you will instantly level up your daily Italian conversations.
1 – uno – one
2 – due – two
3 – tre – three
4 – quattro – four
5 – cinque – five
6 – sei – six
7 – sette – seven
8 – otto – eight
9 – nove – nine
10 – dieci – ten
Beyond “dieci” it is good to know your multiples of ten since they are both common and useful numbers to know and you will also be able to combine them with what you have already learnt above to create more complex numbers.
20 – venti – twenty
30 – trenta – thirty
40 – quaranta – forty
50 – cinquanta – fifty
60 – sessanta – sixty
70 – settanta – seventy
80 – ottanta – eighty
90 – novanta – ninety
The bigger numbers are certainly worth remembering as they also form the basis of more complex numbers and will help you with saying dates in Italian.
100 – cento – one hundred (the form stays the same even if it’s several hundred, e.g. quattrocento is four hundred)
1,000 – mille – one thousand (the form changes to mila for several thousand, e.g. quattromila is four thousand)
1,000,000 – milione – one million (the form changes to milioni if several million, e.g. due milioni is two million)
1,000,000,000 – miliardo – one billion (the form changes to miliardi if several billion, e.g. settanta miliardi is seventy billion)
In regards to dates, the rules on how to say the numbers often change depending on what you are referencing.
For example, if you want to reference a century like 1900 you would say “novecento” which is similar to how in English you would say “nineteen hundred” instead of “one thousand nine hundred”, although weirdly enough in Italian they actually use the word for “nine hundred” to talk about this period of time.
However, if you are talking about a specific date like for example 1980 you would say the full number as normal starting with the biggest number and end with the smallest. So 1980 would be “millenovecentoottanta” all written as one word, which means “one thousand nine hundred and eighty.
Special Cases With Italian Numbers
The only numbers we have yet to cover are the double-digit numbers after ten and the ones in between the multiples of ten.
Firstly, unlike in English where the numbers eleven and twelve don’t follow the pattern of the other teens, in Italian they do.
From eleven to sixteen, the numbers end in “dici”, which means “ten”, so you would say “undici” meaning “one-ten” and “dodici” meaning “two-ten”.
This pattern continues with “tredici”, “quattordici”, “quindici” and “sedici”.
However, between seventeen and twenty the order changes and the numbers start with “dici” instead so seventeen is “diciassette” meaning ‘ten-seven” and this is followed by “diciotto” and “diciannove”.
11 – undici – eleven
12 – dodici – twelve
13 – tredici – thirteen
14 – quattordici – fourteen
15 – quindici – fifteen
16 – sedici – sixteen
17 – diciassette – seventeen
18 – diciotto – eighteen
19 – diciannove – nineteen
This system of putting the bigger number first is followed for all subsequent double digit numbers, for example, twenty-two is “ventidue”, thirty-seven is “trentasette” and seventy four is “settantaquattro”.
The only exception to this rule is when dealing with numbers that end one or eight, “uno” or “otto”, where the vowel ending of the larger number gets dropped.
So when you want to say 21, the “i” from “venti” is dropped, turning venti-uno into “ventuno” and venti-otto into “ventotto”.
This pattern follows throughout the other multiples of ten for example, “ trentuno” (31) “trentotto” (38), “quarantuno” (41) and “cinquantotto” (58).
When creating a number with a three on the end the word “tre” has an accent on the end and becomes “tré” so 33 and 43 would be “trentatré” and “quarantatré” respectively.
Kinds Of Italian Numbers
When learning numbers it is good to cover all bases and study all three categories of numbers, cardinal numbers, nominal numbers and ordinal numbers, or “numeri cardinali”, “nominali”, and “ordinali” in Italian.
The cardinal numbers or “cardinali”, are the basic numbers that are used to denote quantity.
These numbers are the ones we have gone through above and you would use them to number things, for example when saying “one-hundred ducks” and “two horses” which in Italian would be “cento anatre” and “due cavalli”.
Cardinal numbers will be most useful to you in Italian when ordering drinks and food.
Nominal numbers are also pretty straightforward as they are simply a number in its number form and are not used to indicate the quantity of something or when counting.
You will usually see nominal numbers as a collection of numbers together such as phone numbers, house numbers and passport numbers.
These numbers are the same as cardinal numbers but their purpose is simply different.
You would never actually write out nominal numbers in the written form like you might for cardinal numbers, for example, it would be strange to write out your phone number using the words for the numbers instead of simply using the numbers themselves.
Ordinal numbers are numbers used when putting things in order for example “first” and “second”.
The ordinal words are obviously different to the written forms of cardinal and nominal numbers and are even modified in their number form.
Therefore, when learning Italian it is a good idea to learn your ordinal numbers so you can plan your day with others and organize what you will do “primo” (first).
Below we have listed the first ten ordinal numbers in Italian:
- primo – first
- secondo – second
- terzo – third
- quarto – fourth
- quinto – fifth
- sesto – sixth
- settimo -seventh
- ottavo – eight
- nono – ninth
- decimo – tenth
Ordinal number are also useful to learn in Italian when you need to ask for a fraction of something for example when asking for a “third of a pizza” or “un terzo di una pizza”
Interestingly if you wanted to order offal at a butchers shop in Rome, a common phrase to use is “quinto quarto” which directly translates to “fifth quarter”.
Italian Maths Terms
Since maths and numbers go hand in hand, it is useful to learn some Italian “mathematica” words so you know you are not confused if Italians ask you to do maths.
To ask someone the result of a maths equation you would say “quanto fa?” which literally means “how much does it make?”
“Quanto fa?” is a useful term when asking a shopkeep what the total cost is.
Other useful maths terms in Italian are “uguale” which means “equal”.
Below we have broken down the Italian words for the four main maths terms, adding, subtracting, multiplying and dividing.
- Plus = più
- Sum = “somma”
- “Quanto fa dieci più cinque?” = how much is ten plus five?
- Minus = meno (literally “less”)
- Difference = differenza or resto
- “Cento meno dieci uguale novanta” = one hundred minus ten equals ninety
- Multiply = per
- Product = prodotto
- “Dieci per dieci uguale cento” = ten times ten equals one hundred
- Divided by = diviso
- Quotient = quoto or quoziente
- “Cento diviso due uguale cinquanta” = one hundred divided by two equals fifty
- Percent = percento
- “Il quaranta percento della popolazione” = forty per cent of the population
Knowing how to give dimensions of something in Italian won’t really come in handy every day but if you ever need to buy a specific sized frame for a piece of art or a sofa that will fit in your flat then knowing dimensions is vital.
Luckily it is pretty simple to give dimensions, you simply say the two numbers separated with a “per” which in this case signifies “x” or “by” in a similar way to English.
- “Una cornice da venti per ottanta centimetri” = A twenty by eighty centimetre frame
Hopefully you now realize that learning the numbers in Italian is pretty simple and they follow simple patterns that are easy to follow.
Once you have memorized the Italian numbers and their associated words you will be able to have a more diverse conversation with others and have no trouble when ordering for multiple people when in an Italian bar or restaurant.
The best way to practice your numbers is to immerse yourself in the language and pick up when and how they are used in different contexts so you can easily act like a natural in Italian.
So…uno, due, tre! Get practicing your Italian numbers now!


We revisit the scaling properties of growing spheres randomly seeded in d =2 ,3 , and 4 dimensions using a mean-field approach. We model the insertion probability without assuming a priori a functional form for the radius distribution. The functional form of the insertion probability shows an unprecedented agreement with numerical simulations in d =2 ,3 , and 4 dimensions. We infer from the insertion probability the scaling behavior of the random Apollonian packing and its fractal dimensions. The validity of our model is assessed with sets of 256 simulations each containing 20 ×106 spheres in two, three, and four dimensions.


Software →MathWorks MATLAB R2022a v126.96.36.1995300 Update 3 Only (x64) LINUX
x64 | File Size: 16.2 GB
Company MathWorks most complete software for computational computer produces; the main program the company that actually Passport is software MATLAB (short for Mat rix Lab Oratory and means lab Matrix) is one of the most advanced software, algorithms and math and a programming language developed generation fourth is possible to visualize and plot functions and data is provided. Icon and bookmark MATLAB with the manufacturer's logo is the same as the wave equation, L-shaped membrane and special functions have been extracted. MATLAB competitors such as Mathematica, Maple and Mathcad noted.
Facilities and software features MathWorks MATLAB:
-perform a variety of complex mathematical calculations and heavy
-Development environment for managing code, files, and data
-explore ways to achieve this solution
-A variety of mathematical functions for linear algebra, statistics, Fourier analysis, optimization, filtering, numerical integration and ...
-drawing two-dimensional and three-dimensional graphics functions for visualizing data as
-Design and construction of user interfaces under the programming languages ??C ++, C or Java
-Ability to test and measure the exact functions and graphs
-the possibility of communication signal processing, image and video
-There are various Jbhabzarhay engineering companies for specific applications such as
telecommunications, control, fuzzy, estimates, statistics, data collection, simulation systems,
neural networks, probability and ...
-Ability Computational Biology
-Windows 7 Service Pack 1
-Windows Server 2016
-Windows Server 2012
-Minimum:Any Intel or AMD x64 processor
-RecommendedAny Intel or AMD x64 processor with four logical cores and AVX2 instruction set
-Minimum:2 GB of HDD space for MATLAB only, 4-6 GB for a typical installation
-Recommended:An SSD is recommended A full installation of all MathWorks products may take up to 22
GB of disk space
-No specific graphics card is required.
-Hardware accelerated graphics card supporting OpenGL 3.3 with 1GB GPU memory is recommended.
-GPU acceleration using the Parallel Computing Toolbox requires a CUDA GPU
-For Polyspace, 4 GB per core is recommended
Download From Rapidgator
https://1dl.net/t5dyvjffz6hy https://1dl.net/fso5dh7vlshs https://1dl.net/759158o1hpjf https://1dl.net/iaddtmiyv16s https://1dl.net/loco2wlkec56 https://1dl.net/vgms8so1bkun https://1dl.net/vkj2i0owic6j https://1dl.net/mird5s9k7djc https://1dl.net/muzsm3of1ynk https://1dl.net/n3ellc8puk9s https://1dl.net/t8uwwpo3u61j https://1dl.net/5fr3z5d1fmu2 https://1dl.net/useowtqeai1d https://1dl.net/oz035kqc31ss https://1dl.net/cx0eiiz8hl6h https://1dl.net/gdzcjzn53gqh https://1dl.net/nfsimlaqhebr


Angular dimensions are for dimensioning between two linear objects.
Other Posts that Might be Of Interest
- cadmovie045 - Circular Dimensions
Circular dimensions are for dimensioning circles, arcs, and are based polylines. cadmovie045 https://youtu.be/pgMI4PyLxjQ
- New VectorWorks Available
Nemetschek North America announced today the release of its VectorWorks product line, complete with a…
- cadmovie044 - Linear Dimensions
There are two linear dimension tools, the Constrained Linear Dimension and the Unconstrained Linear Dimension…


The binary numeral system chart is a fundamental concept in computer science and digital electronics. It is the foundation of all modern computing technologies, from smartphones to supercomputers. Despite its importance, many people are still unaware of what binary is and how it works. In this article, we will explore the binary numeral system chart in a relaxed and easy-to-understand language.
What is Binary?
Binary is a numeral system that uses only two digits, 0 and 1, to represent numbers. It is a base-2 system, meaning that each digit represents a power of 2. For example, in the decimal system, we use ten digits (0 to 9), and each digit represents a power of 10. In binary, the right-most digit represents 2^0, the next digit to the left represents 2^1, and so on.
Why is Binary Important?
Binary is essential in computing because it is the language that computers understand. Every piece of data, including text, images, and videos, is stored and processed in binary form. Without binary, modern computing would not exist.
The Binary Numeral System Chart
The binary numeral system chart is a table that shows the binary representation of decimal numbers from 0 to 255. It is commonly used in digital electronics and computer programming to convert decimal numbers to binary.
How to Read the Chart
The chart has two columns; the first column shows decimal numbers from 0 to 255, and the second column shows their binary representation. To read the chart, find the decimal number you want to convert in the first column and then read its binary representation in the second column.
Binary arithmetic is the process of performing mathematical operations, such as addition, subtraction, multiplication, and division, using binary numbers. It follows the same rules as decimal arithmetic, but with only two digits.
Converting Binary to Decimal
To convert a binary number to a decimal number, we use the formula: decimal = (bn x 2^n) + (bn-1 x 2^(n-1)) + … + (b1 x 2^1) + (b0 x 2^0) where b is the binary digit (0 or 1), n is the position of the digit from right to left, and decimal is the decimal equivalent of the binary number.
Converting Decimal to Binary
To convert a decimal number to a binary number, we use the division-by-2 method. We divide the decimal number by 2 and write down the remainder (0 or 1). We then divide the quotient by 2 and write down the remainder again. We repeat the process until the quotient is 0.
The binary numeral system chart is a critical concept in computing and digital electronics. It is the foundation of all modern computing technologies, and without it, modern computing would not exist. Understanding binary is essential for anyone interested in computer science or digital electronics. We hope that this article has helped you understand the binary numeral system chart in a relaxed and easy-to-understand language.


Sudoku - wooden sudoku, coding puzzle, sudoku puzzle, table game, gift for mom, gift for dad
This is a beautiful wooden version of the internationally popular Sudoku logic game. Our handcrafted and vibrantly Sudoku game can be played over and over, making it an amazing gift for every Sudoku enthusiast.
We provide three different levels (easy, medium and hard). On each level, there are 4 challenge patterns. What's really amazing about this sudoku set is that you can use any sudoku you find in a newspaper or online and in a few seconds set it up on your board for endless hours of entertainment.
The Sudoku game comes in a handcrafted wooden box for safekeeping.


Free 3-Day Introduction to Statistics & Related Careers
June 5 - 7, 2019 from 9 a.m. - 12 p.m.
Participants will work with UK experts to discuss what a statistician does, explore requirements to pursue higher education in statistics, and learn introductory statistical programming techniques.
Get a jump start in statistics!
The CCTS Biostatistics, Epidemiology & Research Design (BERD) Core is pleased to offer Statistics Facts & Snacks, a free statistics workshop for high school students of any grade level. No statistics or computer science experience is required.
This hands-on workshop will explore the fun of data analysis through basic statistical techniques taught using R, a free statistical programming language. Students will also learn about what a statistician does and what the requirements are to pursue higher education in statistics. The workshop will include visits from statisticians in a variety of different statistical careers, and students will have the opportunity to chat with them about their background and work life.
June 5 —7, 9:00am —12:00pm
University of Kentucky, MDS Building, Room 333
Participants must register to attend, and those under 18 years old must have a parent/guardian register for them. Space is limited, so register today!
“It was really fun and interesting. It really convinced me to want to be a statistician one day. I really liked the conferences with real statisticians.”
“The camp was great; the teacher and support staff were very kind, helpful, and knowledgeable.”
“It was a very fun and educational experience! I wasn't sure what to expect, but I enjoyed it and learned a lot.”


“Are there any proper IQ tests online..?” This is where the IAMX IQ Test was born.
IQ calculation is a difficult and complex process, so most online tests do not calculate IQ for every person.
In reality, most websites calculate with estimates, such as “the taker answered 90% of the questions correctly, so the score is 120,” which is not true IQ.
Because IQ is measured through calculation, incorrect calculation processes obviously do not represent correct scores… The IAMX IQ test continues to update your IQ scores from the up-to-date “current” statistical data.
Why would we do something high in cost and server load? That’s because we think that keeping the scores updated would be the best evidence to show that our scores are calculated from statistical data.
The IAMX IQ Test utilizes deviation IQ, which is measured from statistical data of all users.
We measure the average and deviation from the statistical scores of all IQ test takers. The IQ scores are then strictly calculated.
Also, the IAMX IQ Test recalculates your IQ test results every time the statistical data changes and updates your “current” IQ score in real-time.
The IAMX IQ Test adopts a real-time database.
This made it possible for us to measure accurate IQ scores through immediate statistical data updates of each test taker. Also, the rankings will be immediately updated and can be checked.
Our test is made from questions chosen through trial and error with IWASA, a MENSA member. Only the top 2% IQ can join the MENSA. Because its difficulty is set to MENSA level, many people take the test as a MENSA test prep.
If this test shows that you are in the top 2%, then you have a good chance of joining MENSA.
After finishing the IAMX Test, your dedicated page will be created and you will be able to see the following.
“Your IQ,” “What percentile you are in out of all users,” “The difference between the number of answers correct and the average,” “The average time,” “The standard deviation using the current data” can be seen.
Also, an IQ certificate will be issued, which can be downloaded from your page.


Sat Math Tutors in Shelbyville, TN
Find Private & Affordable SAT Math Tutoring in the Shelbyville Area!
-EE with a math and physics major from Rose-Hulman Institute of Technology -A few EE graduate credits from, Purdue University
Currently a doctoral student at MTSU in health and human performance with a 4.0 GPA.
Bachelor of Science in Physics - MTSU (2014) Minor in Mathematics Currently working on Master's in Computer Science.
Bachelor of Technology (Mechanical Engineering), BS in Recording Industry at MTSU
I am currently a full-time student at MTSU studying Computer Science, and I have a 3.5 GPA. I graduated from Brighton High School...
Honours Bachelor of Applied Science (1992) University of Waterloo - Systems Design Engineering Master of Science (1999) Vanderbilt...


I have accomplished my BSc and MSc in Mathematics and Physics at the University of Warwick in the United Kingdom and I’m a researcher at the world leading company in lightfield camera technology Raytrix.
My current and future research interests include respectively analysis and modelling of point spread functions for lightfield cameras and will developing an elaborate mathematical distortion model for enhanced metric calibration.
The point spread function (PSF) of an optical system gives fundamental insight into the imaging performance of a camera. So modelling and understanding this optical property of the imaging system is significantly advantageous in a number of ways.
One major complication however is that in a lightfield camera, there is not a single PSF, but rather an array of them formed behind the microlenses imaging the object point relayed through the main lens.
Having an accurate PSF simulation model at hand allows for faster computational imaging and scene rendering for synthetic data, (as intensity images form from a convolution of the PSF with the object profile). From this, one can then test the performance of depth estimation algorithms of pixel matching and how these change with the optical setup. Thus we can ultimately optimise the system’s configuration to achieve the most accurate depth maps.
Furthermore, by knowing the depth dependent PSF, we can construct our lightfield cameras better. This is because with knowledge of the PSF, we can attain the relationship between the intensity PSF spot size at the sensor with respect to the microlens array (MLA) to sensor distance.
As lightfield camera already provides us with a depth map of our scene, then for a corresponding object depth, we can determine an initial estimate on the defocus parameter. As a result, one can then apply an iterative algorithm which alternates between estimating depth from disparity and deconvolution for image restoration of lightfield images.
As a result we obtain enhanced lateral resolution in our final microimages and therefore improved depth/3D scene reconstruction.
Mehdi Daniel Ardebili


Short Biography of Kurt Gödel
A known mathematical genius even before he received his doctorate at the age of 25, Kurt Gödel published his Incompleteness Theorems at the University of Vienna in 1931. Additionally, he came up with a system of working with proof theories that clarified the distinctions between different types of logic, namely modal logic versus classical logic.
Growing up, Kurt Gödel was always becoming one citizen or another because of the area of the world he lived in. He always claimed he was Austrian, even after the Czech Republic was formed. Even though he was gifted in languages from an early age, he refused to learn the new Czech tongue. He later became a German Citizen before the break out of World War II. While studying at the University of Vienna, he did not pay much attention to the politics of the day, but concentrated more on physics, philosophy, and mathematics.
As he went off to university, his family had always called him ‘Mr. Why’ because of his extreme curiosity in everything he experienced. Within six years, he had already earned a doctorate and within ten years, he had already published more mathematical marvels than any of his professors. His work was understood and possible for even the lesser mathematicians of the time. In essence, his work proved that some formulas are impossible to prove in a formal system of understanding. But, if one used another system of logic and labeling, then some of the theorems could be solved.
By the mid-1930s, Gödel had already been to the United States and often lectured at Princeton University. It was at Princeton that he became very good friends with Albert Einstein. In 1938, when Austria became a part of Germany, Gödel knew he was at the prime age and fitness for military service, so he escaped by railway and made it to Japan, where they then flew into San Francisco. With the influence and help of the universities where he worked and of his friend Einstein, Gödel was able to become a naturalized American citizen. Gödel would add to Einstein’s own theories and even came up with some points that showed that time travel would be possible if Einstein’s ideas of rotating universes were correct. Later in his career, he was awarded the Albert Einstein Award and the National Medal of Science. With his old age, paranoia got the best of him and he often believed there was a conspiracy to kill him. As a result, he died of malnutrition in a hospital.


Parallel Functional Arrays. Ananya Kumar, Guy E. Blelloch and Robert Harper. Principles of Programming Languages (POPL) 2017. Accepted with review grades of A/A/A/B/C. Conference acceptance rate was 23%
The goal of this paper is to develop a form of functional/persistent arrays that can be used in parallel. We allow operations on “old” arrays to be more expensive than on “new” arrays. The key difficulty is 1. Providing a functional interface while safely dealing with concurrent effects under the hood, and 2. Giving a deterministic way to bound the costs even though the actual costs depend on the interleaving of execution threads.
Advised by Guy Blelloch and Bob Harper.
SCS Alumni Award for Undergraduate Excellence, and second place in Math Competition at Meeting of the Minds 2017.
Given a set of points P, an approximate convex hull is a subset of points in P that approximately covers the original set. More formally, every point in P is within distance epsilon from the convex closure of the subset. The optimal approximate convex hull is the smallest such subset. Approximate convex hulls are intimately tied to the notion of coresets, which are used in computational geometry, machine learning, and approximation algorithms.
Existing streaming (one-pass) algorithms for this problem give bounds that only depend on epsilon but that ignore the structure of the data. A natural question is whether we can do better than state-of-the-art when the data is well structured, in particular, when the optimal approximate convex hull is small.
We show lower bounds for this problem to justify that it is hard. We then propose two interesting relaxations of the problem. In the first relaxation the data is randomly permuted before the algorithm runs. In the second relaxation our approximation only needs to be correct in “most” directions. We come up with new streaming algorithms and theorems for these relaxations.
Advised by Avrim Blum and collaborated with Lin Yang, Harry Lang, Vladimir Braverman.


I was born in what is now called Thunder Bay (originally Fort William), Ontario, Canada. I was educated there at Confederation College with an engineering degree and worked for a consulting firm for six years. Lakehead University made me an offer I couldn't refuse and I returned there to major in mathematics, and then followed that up with a degree in education. After that, I received my certification to teach high school calculus from the University of Toronto. I also have a masters degree from the University of St. Thomas in education. I have a daughter and a son and, nowadays, enjoy spending as much time as possible with them as adults. My summers are spent keeping up with current tech, reading, riding my bicycle, and playing a little disc golf!


“RoboSurv” is intended to calculate and optimize a bunch of quantities and metrics that are related to Markov chains. It is motivated by the use of Markov chains in robotic applications where one or a group of robots randomly move on a graph to perform surveillance tasks. These stochastic surveillance strategies for the quickest detection of anomalies or intelligent intruders in network environments. To solve this problem, different algorithms have been proposed. In this package we implement five different algorithms to calculate and optimize related quantities and metrics: mixing time, hittingtime probability, Kemeny constant, entropy rate and return time entropy.
In the optimization part, for solving non-convex optimization problems, we use “fmincon” with SQP solver in Matlab and JuMP with Ipopt solver in Julia. Users also are provided with to solve semidenite programming (SDP) with CVX in Matlab and Convex.jl in Julia. For details of the optimization solver, the users are referred to the above references.
Documentation can be found here


Mathematics is an art well understood when well exercised. It is an elementary base for all the subjects from various streams. To enrich the interest of students in the field of mathematics, a one day workshop was being organized successfully at Career Point University where an expert session was delivered by the eminent speaker Dr Harish Nagar, from Sangam University.
This proficient session was witnessed by all the first year students of University from different courses and departments. Dr Nagar very efficiently kept the students captivated with his variety of contents that he covered in the session which started with a humorous video depicting a little child who was afraid of mathematics as he was growing up and then got motivated by the thought “brain works as much we exercise it”. Moving forward with the session, he explained the basics of Vedic Mathematics and different techniques which are used to solve the regular mathematics. He introduced the students with many short and tricky methods for solving the problems.
In the second part of the workshop, Dr Nagar taught some new tools and techniques to develop the derivations and matrices by using fingers and solve the trigonometric equations and problems easily.
He encouraged the students not to fear from mathematics but develop an interest in it. Mathematics is easier if you start playing it as a game with an intention to win the hurdles in the form of problems. He motivated the students to practice more and keep revising the methods and contents in order to learn the subject efficiently.


@lavender I'm sorry, I didn't understand. Probably I'm being dense and am missing a joke; can you rephrase that? Thanks!
@sam peano numerals are this esoteric way to represent whole numbers. you define something special (usually called Z) to mean zero, then you have a special "successor" function (usually called S) to mean "the number after".
so, S(S(S(Z))) is 3.
the joke is that you can have Z=op and S=co- to get an op (0), a co-op (1), a co-co-op (2), a co-co-co-co-co-op (5)...
it's not actually that funny don't worry
@lavender hah, I actually should have gotten that. I didn't know the name but am familiar with the counting system; nice.
A Mastodon instance for the hypnosis community; 18+, queer, and getting very sleepy.


My way of thinking, once i began to write, try like – ‘it is really not my personal job, however, should i exercise in any event?’
My personal genetics Against My personal jeans
It’s my the newest thing; to get posts on the web that all certainly aren’t necessities. I think it’s partially good lockdown-founded procedure, in me searching for you to searching boost someplace. Especially given that I’m refusing so you’re able to queue to consult with stores that we extremely might take otherwise get off! Partly although, when it comes to clothes, it’s because quite a few of my latest clothes was snug to say the least!
In any event, this type of jeans have been terrible! I attempted her or him on the (in terms of they might go) and i pulled her or him of – almost harming myself in the process.
six.step 1 and you will 6.step 3 Test
Explanation: SV = VU 2x + 11 = 8x – step 1 8x – 2x = eleven + 1 6x = a dozen x = dos Uv = 8(2) – step 1 = 15
Explanation: 5x – 4 = 4x + three times = seven ?JGK = 4(7) + step three = 30 yards?GJK = 180 – (30 + 90) = 180 – 121 = 59
Explanation: Bear in mind that the circumcentre away from a good triangle was equidistant regarding vertices off an effective triangle. Next PA = PB = Desktop computer PA? = PB? = PC? PA? = PB? (x + 4)? + (y – 2)? = (x + 4)? + (y + 4)? x? + 8x + 16 + y? – 4y + cuatro = x? + 8x + sixteen + y? + 8y + sixteen 12y = -a dozen y = -1 PB? = PC? (x + 4)? + (y + 4)? = (x – 0)? + (y + 4)?


Table of Contents
Begin the introduction of teen numbers by focusing on quantity, which is essential. In Montessori education, golden ten-bead bars and Short Bead Stair are used to introduce quantity. When children are already familiar with number words through rote counting, they can readily associate the words with their respective quantities. You can also use alternatives like Lego, blocks, or any other connectors as well. Once the child grasps the concept of quantity for teen numbers, proceed to introduce the symbols. In Montessori, the Seguin Board/Teen Board apparatus is utilized for this purpose.”
I use a blend of Montessori materials and DIY materials to introduce and practice teen numbers. If you do not have real Montessori materials, the following DIY materials work just as fine.
Printable DIY Teen Number Activities
Teen Number Activity for Circle Time
This is the easy DIY version of the Montessori Teen Board. All you have to do is Print, Cut and Laminate. The bead bars are also printable. You can use sticky tac, velcro or agents to post this activity on the blackboard. When my children are ready for teen numbers, I post them on the blackboard. and build the teen numbers(quantity and symbol) and build the teen number with the children during circle time.
Teen Number Self Activity with Velcro
This is a great addition to your math centers when your children are ready for teen numbers. The colours of the beads are the same as real Montessori beads. Golden ten-bead bars and the coloured Short Bead Stair. Print, cut and laminate the quantity cards and the number cards separately. Use velcro dots for children to match the team number quantities to the correct number.
Teen Number cards for the wall
Print, cut and laminate these Teen Number symbols with their quantities. Post them on the wall. You can go through them with the children during circle time. The children also can use these wall cards as a reference when they do their teen number worksheets.
⭐ 1-100 Number Tracing and Writing Worksheets
⭐ 1-19 Teen Number Tracing with Short Bead Stair Worksheets
⭐ 1-20 Number Sense – Sequence & Skip Counting
⭐ 1-10 Subtraction – Static
⭐ 1-10 Quantity with Short Bead Stair Worksheets –
Montessori way to teach Teen Numbers
Teen Numbers – Quantity
The children must be familiar with the golden bead bar. They should already know that the golden bead bar represents 10. Because it is 10 golden beads attached to each other.
The Short Bead Stair has 9 beads, each representing a number from 1-9. Each bead bar has a unique colour. Before you introduce teen numbers, the child should be familiar with the colour of each bead bar. This will help the child to pick the right number without counting them over and over again. One is always red. Two bar is green, three is pink, four is yellow, five is sky blue, six is purple, seven is white, eight is brown and nine is dark blue.
When introducing the quantity, review about ten bead bars. Then show them how to take one bead bar at a time from the Short Bead Stair, add to a ten bar and count them altogether.
Teen Numbers – Symbols
The Montessori Sguin Board or the Teen Board is a wooden box with nine 10s printed below each other. There are 9 separate wooden cards numbers 1-9.
First, ask the child to make a number line with the unit cards. Then show them how to take one unit card at a time and place them over the zero of each 10. Do this in order. Unlike in language, it is crucial to follow the 1, 2, 3 order than to take it randomly. Start by taking the 1 unit card and placing it over the zero of the first 10. Then tell the child that it is eleven. Continue until you complete till 19.
Teen Numbers – Combination of Quantity & Symbols
At this stage, the child should be well familiar with the quantities and symbols of teen numbers separately. Now it’s time to match them.
First, ask the child to lay all the materials on the carpet, build the Short Bead Stair, and make the number line with the unit cards. Now ask the child to build 11 with the beads and place them next to the first 10 of the Teen Board. Then ask the child to make 11 with the symbols by placing 1 over the zero. continue until you reach up to 19 with beads and number symbols.


grinding mill calculation in
grinding capacity calculation of ball mill Mining Calculate and Select Ball Mill Ball Size for Optimum Grinding 2 Aug 2013 In Grinding, selecting .
GRINDING PARAMETERS CONVERSION CALCULATOR
CALCULATING SFPM The performance of grinding wheels and quality of the finished workpiece is affected by how fast the abrasive grains sweep over the workpiece
Grinding Calculation Formulas - Practical Machinist
Firstly, I'm new to the grinding industry (IT Deptartment) I am writing a new program that does our calculations for us I am stuck on figuring out Qprime The .
Cylindrical Grinding Calculator
In the equation of Time for Cylindrical Grinding Cut Length of Cut = Length of job + Over-Travel where, Over-Travel equals to 05 cm And Feed/Rev = w/2 (for rough .
Grinding Time Calculation – Grinding Mill China
time calculation formula for surface grinding - Grinding Mill , Grind time (from above calculation) 120 » More detailed Throughfeed One Machine Grinding Calculations
calculation in grinding process - Newest Crusher, Grinding ,
calculation in grinding process - Crusher|Granite , This page is provide professional calculation in grinding process information for you, we have livechat to .
GRINDING FEEDS AND SPEEDS
QUESTION: Why can’t I find speeds and feeds tables for grinding? I’m not interested in any fancy grinding process I just want the most common speeds and feeds for .
grinding time calculation - ZCRUSHER
machining time calculation for grinding - Grinding Mill China Cylindrical Grinding 鈥?Cost Estimating Software and 鈥?Cylindrical Grinding Calculation for time is .
Calculate and Select Ball Mill Ball Size for Optimum Grinding
In Grinding, selecting (calculate) the correct or optimum ball size that allows for the best and optimum/ideal or target grind size to be achieved by your ball mill .
Crushing and Grinding Calculations New | Mill (Grinding ,
This paper presents a summary of equations useful in crushing and grinding calculations, starting with the Third Theory Each equation is explained briefly, but in .