We humans have always been fascinated by nature’s wonders and have always wondered how certain natural phenomena occur. The sunrise is one such phenomenon that has piqued our interest for centuries. It is a beautiful sight that marks the start of a new day, but have you ever wondered how the sunrise is calculated?
In this article, we will go over how the sunrise is calculated as well as the factors that influence it.
What is Sunrise?
Sunrise is the moment when the upper edge of the sun appears above the horizon in the morning. It is also known as the “dawn” or “daybreak” and is one of the most beautiful natural phenomena that can be witnessed. The sunrise occurs due to the rotation of the Earth around its axis, which causes the sun to appear above the horizon in the morning and disappear below it in the evening.
How is Sunrise Calculated?
The calculation of sunrise is based on the position of the sun in relation to the Earth’s horizon. It is influenced by various factors, such as the Earth’s rotation, the sun’s position, the observer’s location, and the time of year. The sunrise calculation involves the use of advanced algorithms and astronomical equations, which take into account all of these factors.
If you’re looking for a mathematical answer NASA defines the UTC time of sunrise using the following formula:
The Calculation Process
The calculation of sunrise involves the following steps:
- Determine the observer’s location: The first step in calculating the sunrise is to determine the observer’s location on Earth. The latitude and longitude of the observer’s location are crucial in determining the sunrise time.
- Calculate the solar position: Once the observer’s location is determined, the solar position is calculated based on the time of day and the observer’s location. This involves the use of complex mathematical equations that take into account the Earth’s rotation and the position of the sun in the sky.
- Determine the sunrise time: The final step in the calculation of sunrise is to determine the exact time when the sun will appear above the horizon in the morning. This is calculated using the solar position and the observer’s location.
Factors that Influence Sunrise Calculation
Several factors influence the calculation of the sunrise. The most significant factors are:
- Earth’s Rotation: The sunrise time varies from one location to another due to the Earth’s rotation. The time difference between two locations is approximately four minutes for every degree of longitude.
- The Sun’s Position: The position of the sun in the sky is also a crucial factor that influences the calculation of sunrise. During the summer solstice, the sun rises earlier, while during the winter solstice, it rises later.
- Observer’s Location: The observer’s location plays a significant role in determining the sunrise time. The closer the observer is to the equator, the earlier the sunrise, while the further away they are from the equator, the later the sunrise.
- Time of Year: The time of year is also an essential factor that influences the calculation of sunrise. The sunrise time varies throughout the year, with the shortest days occurring during the winter solstice and the longest days during the summer solstice.
To summarize, calculating the sunrise is a complex process involving numerous variables. The rotation of the Earth, the position of the sun, the location of the observer, and the time of year all play a role in determining the sunrise time.
To accurately calculate the time of sunrise, advanced algorithms and mathematical equations must be used. We hope that this comprehensive explanation has given you a better understanding of how the sunrise is calculated.


Catmull-Rom splines are interpolating, piece-wise cubic splines: a spline of this class passes through each of its control points, and restricted to each knot interval it is a cubic function.
How you choose the knot intervals has a significant effect on the spline’s quality. Long story short: you get the best results by setting them to the Euclidean distance between the two corresponding control points. Splines with such knot assignments are called centripetal splines.
For more information, this Wikipedia page has a nice summary and comparison plots for different choices of knot intervals. Cem Yuksel’s project page has more interesting details as well as many applications.
Computing a spline’s value at time is easy using a pyramidal formulation described here.
You can use the same pyramid structure to evaluate the tangent as well:
Here is a little MATLAB script that computes and plots a centripetal Catmull-Rom spline and its tangents.


Data Analysis & Probability
11. Mike and his parents went out for dinner. His dad ordered salmon for $9.99, his mom ordered pasta for $8.57, and Mike ordered a grilled cheese sandwich for $6.83. After dinner, Mike's dad paid the bill and included the tip. He paid a total of $30.00, after rounding up to the nearest dollar. What percent tip did Mike's dad leave (round to the nearest percent)?


From Oklahoma’s Education Standards Committee:
Mathematics Standards Writing Committee asking for help with online survey
The Mathematics Standards Writing Committee membership is being finalized.The first Writing Team meetings will occur May 1 and May 2, 2015 in Norman, Oklahoma. We are excited to begin this important work toward higher standards for mathematics in Oklahoma, and we would like to personally invite all teachers, administrators, parents, and community members to consider investing your valuable time to provide feedback on the current mathematics standards. Your input will provide a valuable lens for the Writing Team members as they carefully analyze and work to improve our mathematics standards.
The survey is divided by grade band so you can either answer the parts that matter to you most or fill out the entire survey pre-K through high school. Questions are designed to allow input on the nature of each standard in regard to whether it is “useful,” “realistic” and “challenging.” The standards are in two parts: the content standards (a list of topics to teach at each grade level) and the process skills (ways of using and applying the mathematics). Standards are shown side-by-side with previous or next-year standards to show how they build upon each other. There is space throughout the survey to make comments and recommendations.
While screenshots are provided when possible, we have also included links to PDF documents for each section embedded in the survey, allowing participants to download the entire document for easier viewing of the complete picture. Please do not rely on the screenshots alone. You can download each document within the survey or below:
– Primary (PK-2) Math Standards
– Intermediate (3-5) Math Standards
– Middle Level (5-8) Math Standards
– High School Algebra 1 and 2 Standards
– High School Geometry Standards
Thank you for your interest in this important work for mathematics education in Oklahoma.
Access the survey here: https://www.surveymonkey.com/s/GB7PNTZ


1. Turn off the air resistance. Making sure you change only one variable (ie. initial velocity) at a time, try to get some projectiles to hit the traget (at a range of 100 meters). Before firing each projectile, try to predict the range using:
where vo is the launch speed,
is the launch angle
(from horizontal), and g is the gravitational acceleration (9.8
Does your computed range match the one on screen? The final range you achieved appears on the status line at the bottom of your browser. (NOTE: Do not adjust the launch height).
2. Next, turn on the air resistance and vary the terminal velocity. Use the equation above to compute the expected range (without air resistance). Compare the expected range to the observed range. Explain why they are different.
3. Turn off the air resistance again. Now vary gravity and compare the trajectories (this is obviously something you could not do on earth, at least easily).
4. Now, turn on the air resistance one last time. Vary only the time step in incriments of 0.2 until you get to a time step of 1. What do you notice?
The time step is the incriment over which the equations are calculated. The smaller the time step the smoother, and more accurate the simulation. Of course, using smaller time steps also means many more calculations. If you had to do this by hand it would take a very long time, good thing you have a computer close by.


Is it possible to write more than 1 equation in LO Math? [closed]
Closed as off topic by Monica Cellio on Jul 11, 2021 at 22:31
This question is not within the scope of Linux Systems.
This question was closed; new answers can no longer be added. Users with the reopen privilege may vote to reopen this question if it has been improved or closed incorrectly.
I was using Libre Office Math. I thought I can write multiple equations in LO Math. But, I noticed I can't write more than one equation. I was trying to write multi-line. Unfortunately, I couldn't. Is it possible to write more than 1 equation in LO Math?


Applied econometrics using matlab james p lesage department of economics university of toledo october, 1999. I am currently reviewing econometrics by reading christopher baum's an introduction to modern econometrics using stata although linear regression is not discussed until chapter 4, chapters 1 to 3 (particularly chapter 3) are equally important (i finished chapter 3 last weeklong way to go given my current rate of 1 chapter a week. Econometric tools 2: marginal e ects in stata 1 introduction estimates are di erent, but in econometrics (and in general, in statistical analysis) we want. Econometrics and statistics teaches you how to use real world data to make good business decision you will learn to conduct quantitative analysis and testing of economic and business models.
Econometric tools 1: non-parametric methods some of the most basic tools for non-parametric estimation in stata non-parametric econometrics is a huge eld, and. Stata is the most widely used software in econometrics stata is a very powerful, full featured program and i will be explaining common stata commands as part of the class you can buy stata as an annual license or in perpetuity in several forms. Books about econometrics, including the latest additions to the bookstore, along with a subject index and search utility.
This article by american university faculty members kara reynolds and mahmud yesuf discusses how stata data analysis software is used in economics. Using stata for principles of econometrics, 4e by lee c adkins and r carter hill using stata for principles of econometrics 4e, (isbn 978-1-11803208-4 or wwwcoursesmartcom) by lee c adkins and r carter hill. Sayed hossain, econometrics, eviews, stata, spss, excell, data analysis answered dec 3, 2015 i have made few hundred videos on econometrics and statistical models using various software such as eviews, stata, r-package, spss etc and put it in hossain academy webpage.
Financial econometrics lecture notes professor doron avramov if you desire to use stata, sas, or other comparable tools, please consult with the ta. A practical introduction to stata by mark mcgovern. In econometrics, the seemingly unrelated regressions (sur): 306: 279: 332 or seemingly unrelated regression equations (sure): 2 model, proposed by arnold zellner in (1962), is a generalization of a linear regression model that consists of several regression equations, each having its own dependent variable and potentially different sets of.
Econometrics is the quantitative application of statistical and mathematical models using data to develop theories or test existing hypotheses in economics, such as stata, spss, or r. Have you ever wondered how to make regressions and tests of hyphotesis using stata if the answer is yes, read below. You can use the statistical tools of econometrics along with economic theory to test hypotheses of economic theories, explain economic phenomena, and derive precise quantitative estimates of the relationship between economic variables to accurately perform these tasks, you need econometric model.
Research working papers a quantile correlated random coefficients panel data model, accepted by the journal of econometrics web appendix stata do and. Econometrics with stata examples and exercises [maria perez] on amazoncom free shipping on qualifying offers this book is aimed at the presentation of both classical and modern econometric techniques, and treatment with stata software tool. Econometrics ii econ 6243 econometrics i i (econ 6243) is the second course in our phd level graduate econometrics sequence stata resources the stata.
Introduction to stata with econometrics in mind john c frain february 2010 abstract this paper is an introduction to stata with econometrics in mind. I have a panel dataset and i would like to estimate a linear equation in a fixed effects framework my question is: how should i implement a two-way clustering stata syntax and/or ado file necess. Stata is probably the most widely used statstical software for applied econometrics it already comes with an extensive library of functions and it is possible to easily download user-written functions.


- T: +31 10 741 08 04
- M: +31 6 518 69 705
- E: email@example.com
Willemijn Smit specialises in liability and insurance matters. She completed her master's degree in Liability and Insurance cum laude at Erasmus University Rotterdam and obtained her master’s degree Mathematics summa cum laude at Radboud University Nijmegen.
During her studies Willemijn interned at a large insurance company in Rotterdam and a law firm in Amsterdam. She tutored first-year law students and supervised tutorials in mathematics. She was president of the Mathematics Study Association.
Willemijn joined VanNiekerkCieremans in September 2022 and has been admitted to the Rotterdam Bar as a lawyer.
Patrick van der Vorst
Bas van der Ent
Martijn van Rijen
Antje de Groot
Eric van Niekerk


Imagine guiding a bunch of chipmunks through a math exam. It is Ridiculous hard. It takes years of experience to execute. And it’s incredible hard to master.
It feels like the most challenging task in the world. It is frustrating in every step of the way. And even in the best possible scenario, it is extremely time consuming.
But once executed, you get the satisfaction of… well, having a bunch of chipmunks with a math degree. Congratulations!
And did you know: Leading a interdisciplinary task force at the office accomplishes exactly the same.


We all know that the purpose of investment is to make money. The extra money you make on your investment is called Interest.
So today, let’s talk about the Interest on your investment.
Interest can either be simple or compound.
Simple interest is calculated using the following formula:
Simple Interest=P×r×nwhere:P=Principal amountr=Annual interest raten=Term of loan, in years
For example, if you invest $5,000 at a simple interest rate of 10%, for 30 years.
At the end of 30 years, you will have:
I = P X R X T = ($1,000 X 0.1 X 30) = $3,000
Your total balance = P + I = $4,000
Imagine that $3,000 in 30 years.
I don’t know about you, but that is not good enough for me.
Let’s check what the big brother – Compound interest can do for you.
Compound interest has been called the eighth wonder of the world because it not only lets your money works for you, but also ensures that the accumulated Interest you earn on your money works as hard. It lets you earn Interest on Interest, and if you understand and embrace this principle of reinvesting Interest, you will be able to build wealth quicker.
Let’s go with the same principal investment of $1,000, earning annual Interest of 10%, compounded annually. After 30 years, how much will you have?
Don’t worry….I have a formula for you.
Compound Interest=P × −P
r=Annual interest rate
t=Number of years interest is applied
Compound Interest = $1,000 X – $1,000
= $1,000 X 17.5 – ($1,000)
= $17,500 – $1,000
My knowledge of math tells me that, I’m getting a bigger bang for my buck on compound interest. What do you think?
Same amount invested, simple interest earns me $3,000 after 30 years. And my good friend, compound interest gave me more than five times that amount, $16,500.
I love math, so let’s play around with some other figures.
For example, if you invest $5,000 every year and generate a return of 10% on your investment per annum. In the first year, you investment will generate a return of $500. For some people, that is not a significant amount; they may choose to quit and look for another form of investment. They lost focus.
But for a consistent individual, if he continues with the $5,000 yearly investment, and provided that he is still getting the same rate, at the end of year two, the interest is not going to be $500, but $1,550. The power of compounding is showing up.
After five years, the balance in the account will be $33,578, that’s a total interest of $8,578 ($33,578-$25,000). I’m sure you are noticing the effects of staying focused and being consistent with your investment plan.
But wait, why on earth would you just do a one-time investment?
Let’s say you did not stop after the first year, but you continue to invest $5,000 every year for thirty years. Do you know how much you will have in your account after 30 years?
Give it a guess….
You will have $904,717. That’s almost a million dollar.


Dear Parents/Guardians & Students,
PolyUp is a software application where students all over the world can come together to build and share 3D creations through fun activities underpinned by mathematics, computer science, robotics, data science, sustainable energy and more. It is a novel software that could have particular application in mathematics teaching and learning.
Glanmire Community College has been invited and has agreed to participate in a study of “PolyUp and its Impact on the development of TY students’ Algebraic and Problem-solving Skills”.
Please click on the link below to view the Information Sheet for Parents/Guardians of Children & Young People Participating in the study:
GCC Senior Management
Ronan McCarthy (Principal), Gertie Cahill (Deputy Principal), Seamus Kennefick (Deputy Principal), Sean McGrath (Deputy Principal)


Kid’s math game is the complete package for kids math learning. This application covers math learning of preschooler’s kids to 3rd grade students. Game is prepared in such a way that kids learn math briskly and very effective. For this proper research has been done on kids. So, we can simply say it surely help your kids to learn math very quickly. App is designed in such a way that kids will enjoy playing application, colorful graphics in math exercises increase efficiency of preschool kids’ math games.
Best Kids Math Games for Preschool:
Best part about preschool kid’s math game is; it includes vast variety of math lessons and exercises. Main exercises of preschools kid’s math games are;
Read and trace 123 exercises will help kids memorize 123 numbers and trace exercises will help kids writing 123 numbers.
Addition and subtraction exercises will help kids solve small equations containing addition and subtraction of numbers. Addition and subtraction of things is one of the most basic learning of kids.
Dots and sequences games help kids make pattern by connecting dots. Math numbers are used for patterns. Kids love this game and it gives learning too so not a bad bargain.
Min and Max number exercises is designed in a way that kids have to identify the smallest and biggest numbers on screen. Kids love this exercise.
Surely you will like this application. It is one of the best kid’s maths learning applications available. Share your valued comments about the game on http://goo.gl/q0Gryg.


Working on differentiating math instruction? Trying to plan small math groups? Need independent math activities? Read on!
Full disclosure: yes, I am a reading specialist. I have years of experience as a departmentalized upper elementary reading and writing teacher. However, I have been a self-contained second, third, fourth, and fifth grade teacher—I have had to teach math! I also taught virtual fifth grade math during the Covid-19 quarantine. During that time, I made a LOT of independent math activities for students to do when they were not in meetings with me.
How do my ideas work in your math classroom? This article about managing small groups is a great place to start—it works for both reading and math. From there, here are a few ideas you can implement to keep your students learning independently while you work with differentiated groups
Practice Math Facts
Independent work time is a great opportunity for students to work on their math facts. There are many ways to do this for addition, subtraction, multiplication, and division. Practice sheets would be an option.
A fun way to practice math facts is to let your kids team up to play Kaboom! To create one of these games, grab 20 thick popsicle sticks like these. Write math facts on 15 of them. Write “Kaboom” on five of them. Color code each of your sets by marking the end of your popsicle sticks in a different color. Place each set in its own container. During independent time, students can grab their assigned cup. They take turns drawing sticks. If they solve the fact correctly, they get to keep the stick. If they draw a “Kaboom” stick, they have to return their sticks to the container. The student with the most sticks at the end of the game wins.
Another method for working on those facts is to use these cool math fact calculators. We had a set when I was self-contained in fourth grade, and the kids liked using them. This is a much quieter, albeit expensive, option for independent math practice. Your school may have some of these hidden away in a classroom or lab. Definitely ask around before you buy some.
Use Technology for Independent Math Activities
Our district has instructional programs for independent practice like Freckle by Renaissance, Xtra Math, or IXL. This is a great way for you to assign specific skills to each student group for practice.
If your district doesn’t have a subscription to a big learning site like these, you could try Blooket.com. I love this site, and it is super popular with kids. With a free teacher account, you can create question sets for whatever skill you’re learning. The program will turn your questions into a variety of fun games. In addition to the questions you make, you can find hundreds of premade question sets on every subject. You host the games and invite students to play different ones on their devices. You could actually host differentiated games for your groups. During Covid, I had students playing Blooket after they left my virtual meeting. These kids loved these games so much that they begged to play them each day. I would assign the game by giving the kids the code as they were leaving my meeting. That way, I could monitor the game from a different tab on my computer while I met with my next group. Even though I couldn’t guarantee that they would do the work I assigned when they left my group, I could tell they were still interacting with my material through these games. Blooket is an excellent incentive!
There are several free math websites for you to check out as well. These sites appear to change hands often, so make sure you go through them carefully. As of fall of 2022, they are free, however.
- Multiplication.com At this moment, the site teaches multiplication facts with stories and other brain-friendly ways. Teachers can create an account and monitor a class.
- Cool Math Games: This site has a variety of games your students can play, and it is a bit harder to monitor or control what skills they are practicing. The site also has ads. It’s a great idea to monitor this one carefully to make sure the ads that pop up are appropriate.
- Math Blaster: This site has games for logic and computation. It has a fun storyline. The game is free, but you may have to register.
Math Task Cards
Scoot games or math problems on cards held on a ring are a great independent center for kids. You could even project a few of the cards onto your white board or screen. Kids could work the problems on an answer sheet or separate sheet of paper for a classwork grade.
Digital task cards are another great activity. You can assign these activities on your school’s learning management system or your own digital classroom. Students can work through them on their own or with a partner. These are a little time consuming for you to put together so here are few options for you from my own Teachers Pay Teachers Store.
Helpful Independent Math Activities
- Giraffe Themed PDF Task Cards for Primary Students: You can use this set of math task cards in guided math groups, centers, or for a whole class game of Scoot. The cards will allow students to demonstrate their understanding of simple addition, subtraction, and multiplication. The accompanying answer key can make these activities perfect for a self-checking center if you so choose. There is also a corresponding giraffe-themed reading set that’s included in this bundle!
- Word Problems: Estimation and Computation Digital and PDF Task Cards Bundle: These task cards will give students the opportunity to practice addition, subtraction, multiplication, and division estimation and computation. I included answer keys and sheets.
- Factors and Multiples Digital Task Cards and PDF Activities: These activities will help students practice finding factors and multiples using digital task cards and PDF activities and games. Instructional charts come with this as well.
- Fractions, Decimals, Mixed Numbers Digital and PDF Task Cards: Students can practice finding equivalent decimals and fractions as well as solving differentiated problems with mixed numbers with this set of digital and PDF task cards. You can find answer sheets there as well.
- Even, Odd, Prime, and Composite Numbers Digital Task Cards and PDF Sorts: This product has multiple ways for students to practice these skills independently. Instructional charts are included.
Hopefully, all these ideas will help you plan your math groups and keep everyone on task. You can implement these activities immediately to expedite your planning and make your small group math life generally easier.


The Downside Risk of Help Me Solve This Math Problem
Business, obviously, is about problems. Currently Alcumus is free of charge. Internet is the perfect place to have a superior knowledge on algebra.
While the issue solving materials don’t always have a focus on one specific strand of wisdom and understanding, they’ve been grouped in the tabs below in the strands that have the larger focus. Put simply, particles cannot be of zero masses even when they’re analogous to massless photons. In addition, it would supply you with clues that may hint at a proof of the presence of one-way functions.
The usage of an easy to comprehend language can assist the student feel at ease and take the next step towards solving the issue. Students sometimes make the error of sticking to types of problems they understand how to solve well. Explicitly teach royalessays.co.uk and review the language used in mathematics so that they understand what is being asked in a problem and how the problem should be solved.
As a result of fixed center face, you just need to be worried about the remainder of the eight faces on each side. With the internet available, you truly have countless possibilities. As an extension, challenge your student to make their own puzzle for another person to fix.
You can trust our math help using these difficult times! There are lots of riddles in English poetry too, which are a fantastic quantity of fun to fix. 20 children wish to share 12 lbs of beads so that everyone receives the same quantity.
Key Pieces of Help Me Solve This Math Problem
In case you have data about your small business, they can probably help you to find valuable information within it. With the info available, you can calculate which loan is the ideal option for you. Creating an account While trying to find the proper webpages for your maths problems, you’ll discover that lots of them asking you to make an account.
To receive your child comfortable with the practice of solving math word issues, you and your little one may talk through how to fix the problem before he or she attempts to come across the response. It will be helpful if you’re ready to talk about your problem with your tutor. What’s more, a great tutor needs to be in a position to summarize the concept quickly and succinctly.
By solving a system, you’re finding where the 2 relationships are true at the identical time, to put it differently, the point at which the 2 lines cross. Frankly speaking, there are plenty of students around who are in desperate need of assistance by using their math tasks, and their number keeps growing exponentially with each passing day. There’s a simple way to find the last answer here.
The Man at St. Ives is among the oldest riddles in history, look it over. Dating it’s about math. Questions at the end are usually harder, and so you will learn faster.
Life After Help Me Solve This Math Problem
All you have to do is search for the mathematics and lots of different characteristics of your life. First and foremost, maths isn’t taught strategically with a concentration. Begin by finding out the scenario the problem would like you to address.
If You Read Nothing Else Today, Read This Report on Help Me Solve This Math Problem
Together with the progression of mathematical abilities, children may also learn about various tasks of an agriculturist. Then once you encounter an issue, you are going to know which tricks, or rules, you will want to address the algebraic issue. There are frequently several methods to work the exact issue.
Enrolled students of the course are eligible for a temporary matlab license. Math tutoring isn’t only an enjoyable approach to do and understand concepts but likewise an affordable and time-saving learning procedure. In the same way, Math tutors may be in a position to give trigonometry help, but a Math coach also seeks to comprehend why the student demands trigonometry help.
Sign uphereto get INSIDER’s favourite stories right to your inbox. Dating it’s about math. Start from the easiest thing possible.
The New Fuss About Help Me Solve This Math Problem
In the event you don’t know the best places to start or have some questions, don’t hesitate to speak to our customer support via live chat! With the info available, you can calculate which loan is the ideal option for you. Creating an account While trying to find the proper webpages for your maths problems, you’ll discover that lots of them asking you to make an account.
Preface It is just feasible to have a good comprehension of applied mathematics and theoretical physics by spending a lengthy time solving a wide number of problems. Then once you encounter an issue, you are going to know which tricks, or rules, you will want to address the algebraic issue. Look over the kinds of problems you’ll be working.
Of course there are lots of other means to address this issue too. It’s these problems which make the subject mesmerizing. In order to be sure you have solved the issue correctly, plug your answer back into the original issue.
On-line math help is fast and simple to utilize for students. Now, a conventional middle school math class is a somewhat hostile environment to attempt to nurture a community of vertical learners. Nope The real-life math isn’t fully introduced by the majority of teachers.
Characteristics of Help Me Solve This Math Problem
You’re able to attempt breaking the issue into simpler parts. For instance, a man would like to pack 100 watermelons into boxes. You’ve got a barrel of oil, and you have to measure out just a single gallon.


Easy. Firstly calculate the total square metres of the concrete slab and then divide this figure by 12.5. This will give you the number of sheets required. (Calculation based on standard mesh sheet size of 6 metres x 2.4 metres)
Firstly calculate the total lineal metres. For a single layer of trench mesh, divide this figure by 5.5. You now have the total number of trench mesh (6 metre lengths) required for the job. If a double layer of trench mesh is required, then double this figure.


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Chose any two digit number.Follow the instructions and "Mind Reader" will know what number you've chosen!
-Choose any 2 digit number (example:54)
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- Subtract the result of the summation from the first number ( 54-9 )
- Find the corresponding image of your result from the list
- Concentrate and tap the Magic Crystal Ball
- Magic Crystal will read your mind and find the image
Share the app and amaze your friends too.
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*Application has advertisements, those are not virus. We try making free applications and using some advertisements to develop more free apps.Thank you for your understanding..


What You Should Do To Improve Mathematics Skills For Your Child.
In this age and era, students in schools have been performing lowly and poorly in the mathematics subject and this has been accelerated by as number of factors that make the either hate the subject or find it difficult with a lot of tricks to unravel. There are numerous tricks and methods of passing and excelling in mathematics that you should be aware of in your high school life and this article will guide you in knowing some of them so that you can shift from bottom to top in mathematics performance.
First, you need to have advanced knowledge of using the logarithm calculator that has been advanced with mathematics tools and tactics of doing some calculations and its pivotal to ensure in every mathematics session, you carry with you this important mathematics equipment as most of the calculations you will encounter rotates around it. In mathematics,. There are tables that details operations for conducting basic operations on logarithm calc and you need to be verse on them and be able to do any simple tangent, cosine or sin operations and tabulations that may be asked.
The presence of your course books and mathematics revision and logarithm booklets are a step forward in the knowledge of mathematics and you need to avail them for you to get numerous calculations and past questions with their responses that will guide you in coaching yourself. When you have vital interests in advancing your mathematics levels, it’s essential to have a valuable tutor that will equip you with more knowledge and introduce you to the various mathematics operations and guide you as you go wrong so that you can perfect your understanding in every calculation you encounter.
Better learning of mathematics occurs when a dedicated and committed team of learners come together with deep passion to learn and know mathematics as they are able to exchange ideas that will aid their fellows and this is superb help that any learner for mathematics can get. For you to be an ardent mathematics reader and learner with insight, it’s vital to have a dedicated heart full of positive mind so that you can see every operation as easy and therefore grasp them instantly that will save your time and enable you to excel.
There are numerous online tools that you can use for you to succeed in mathematics and know what mathematics requires and this therefore calls for browsing relevant internet mathematics help pages that are often updated by mathematics experts. Combine all those tricks with excess practice on logarithms and you will get superb grade in mathematics.
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The “Present Worth Interest Element of an annuity” (PVIFA) is a variable that can be utilized to work out the current worth of a series of annuities when it is duplicated by the common uses. The underlying store procures revenue at the financing cost (r), which
adequately funds a progression of (n) continuous withdrawals. PVIFA resembles the variable utilized while assessing the current worth of a customary annuity.
What is PVIFA utilized for?
The current worth interest variable of an annuity is valuable while recognizing whether to keep up a singular amount installment now or acknowledge an annuity installment in ongoing periods. Controlling assessed paces of return, you can estimate the worth of the annuity income to a single amount. The (PVIFA) possibly be determined on the off chance that the annuity installments are for a foreordained sum traversing a foreordained period.
Look at this, the closely guarded secret PVIFA
How to utilize (PVIFA)?
We should assume that you have put resources into a startup that conveys 3D printers. The speculation of the startup will bring about you getting eight installments of $3,000 – one every year. The loan fee, as currently referenced above, is comparable to 4%. What can be the current worth of this annuity?
1_Distinguish the no.of periods and loan cost. For this situation, we have n= 8, and r= 4% = 0.04.
2_Calculate PVIFA as per the PVIFA recipe:
4 What might be the installment esteem, then? The all-out worth of these 8 installments won’t be equivalent to just 8 * $3,000. Rather, we need to draw out the result of the installment esteem and the PVIFA:
6.73 * $3,000 = $20,198
5_The present worth of this annuity is identical to $20,198.
Make a point to open the high-level method of the PVIFA number cruncher, In the event that you like to compute the current worth of the annuity.
PVIF number cruncher or RFM?
Though, on the off chance that you like to compute your overall fat mass, you can make the most of the rfm adding machine, which is the best reasonable for this work. RFM mini-computer (or Relative Fat Mass number cruncher) predicts muscle-to-fat ratio mass utilizing just two body estimations – the boundary of weight and level. This action is more helpful than the notable weight file (BMI) weight list, which frequently misclassifies corpulence
The greatest benefit of utilizing PVIFA is that it empowers you to settle on your installment. It shows whether you ought to take a decent sum back now or acknowledge an annuity installment framework over years.
As referenced over, the PVIFA equation has a financing cost that can assist you with checking what you will get toward the finish of the annuity installment period. By utilizing the loan fee, you can get a last sum that you will move past a timeframe in annuities. To get more data than you can visit here calculator bag.
Presently, you can contrast this sum and the proper one that you are proposing to take right now. Along these lines, you can have a thought of what will be more gainful for yourself and which technique you ought to acknowledge for your installments.
However, remember that you ought to have the loan cost and the annuity period to compute PVIFA from a manual as well as a PVIFA mini-computer. It can’t be determined without these terms or values. I have


Instruction format: G02/G03 X(U)___Z(W)___I___K___F___;
1. Judgment of arc reversal
Circular interpolation instructions are divided into a clockwise circular interpolation command G02 and a counterclockwise circular interpolation command G03. The forward and reverse of circular interpolation can be judged according to the direction given in Fig. 2-1: When viewed along the negative direction (-Y) of the vertical axis of the arc (such as the XZ plane), the clockwise direction is G02. Clockwise direction is G03.
The CNC lathe is a two-coordinate machine with only the X-axis and the Z-axis, and the Y-axis is also added to the right-hand rule. The observer makes the positive direction of the Y-axis point toward himself (ie, looking in the negative direction of the Y-axis), and standing in such a position can correctly judge the arc of the XZ plane along the anti-clockwise direction.
Figure 2-1 Judgment of Circular Arc Inverse
1 When programming in absolute value, the arc end point coordinate is the coordinate value of the arc end point in the workpiece coordinate system, which is represented by X and Z. When programming with incremental values, the arc end point coordinate is the incremental value of the arc end point relative to the arc start point, which is represented by U and W.
2 Center coordinates I and K are the vector of the vector from the starting point of the arc to the center of the arc in the direction of the X and Z axes (the vector direction points to the center of the circle). The system I, K is an incremental value with a "+" sign, and the "-" sign is taken when the direction of the division vector and the direction of the coordinate axis are not the same.
3 When only the center of the circle is specified by the radius, because there is a possibility of two arcs from the starting point of the arc to the ending point in the case of the same radius, when the center angle is determined to be less than or equal to 180Â°, use " +R" indicates. If the arc center angle is >180Â°, use â€œ-Râ€.
4 When specifying the center of the circle with a radius, the entire circle cannot be described.
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Beneish M-Score- A Tool To Find The Manipulation Of The Earnings.
The extent to which earnings are manipulated has long been a question of interest to analysts, regulators, researchers, and other investment professionals. To address this issue, Professor Messod Beneish developed the Beneish M-score model and published it in a paper in June 1999 called The Detection of Earnings Manipulation.
Beneish M score is a Mathematical model designed to find out the manipulation in the company’s earnings. Beneish’s M-Score model uses eight variables weighted by coefficients to identify whether a company has manipulated its profits.
How is it calculated?
1.Days’ Sales in Receivables Index (DSRI)-
DSRI is the ratio of days sales in receivables in a year to the previous year. If the value of DSRI > 1, it is an indicator of revenue inflation. An increase in the value of DSRI indicates that the company has followed the lenient credit policy or allowed the higher credit period to increase the sales.
DSRI = (Net Receivablest / Salest) / (Net Receivablest-1 / Salest-1)
2. Gross Margin Index(GMI)-
GMI is the ratio of gross margin of a year to the previous year. When GMI is greater than 1, it indicates that gross margins have deteriorated. A firm with a declining gross profit margin is more likely to manipulate earnings.
GMI = [(Salest-1 – COGSt-1) / Salest-1] / [(Salest – COGSt) / Salest]
3. Asset Quality Index (AQI)-
Asset quality in a given year is the ratio of non-current assets other than property plant and equipment (PPE) to total assets. If AQI > 1, it indicates that the firm has potentially increased its involvement in cost deferral.
AQI = [1 – (Current Assetst + PP&Et + Securitiest) / Total Assetst] / [1 – ((Current Assets t-1+ PP&E t-1 + Securities t-1) / Total Assets t-1)]
4. Sales Growth Index (SGI)-
SGI is the ratio of sales of a year to the previous year. The value of SGI > 1 indicates that the company’s sales have increased compared to last year.
High sales growth does not imply manipulation, but high growth companies are more likely to commit financial fraud because their financial position and capital need pressure managers to achieve earnings targets.
SGI = Salest / Salest-1
5. Depreciation Index (DEPI)-
DEPI is the ratio of the rate of depreciation in the previous year to the current year. The value of DEPI higher than 1 indicates the company has revised the life of its useful asset to provide a better picture of its profits.
DEPI = (Depreciation t-1/ (PP&E t-1 + Depreciation t-1)) / (Depreciation t / (PP&E t + Depreciation t))
6. Sales, General, and Administrative Expenses (SGAI)-
SGAI measures the ratio of Sales, General, and Administrative expenses to the prior year. The value of SGAI > 1 indicates that SGA expenses as a percentage of sales increased in the current year. An increase in the SGA expenses leads to a reduction in the operating profits. Management may try to cover up this through manipulation.
SGAI = (SG&A Expense t / Sales t) / (SG&A Expense t-1/ Sales t-1)
7. Leverage Index (LVGI)-
LVGI is the ratio of total debt to total assets in a year relative to the corresponding ratio with the previous year. An LVGI greater than 1 indicates an increase in leverage. Increased leverage results in an increase in the interest expenditure, Thus affecting the company’s net profits. Increased leverage increases the chances of manipulation of earnings.
LVGI = [(Current Liabilities t + Total Long Term Debt t) / Total Assets t] / [(Current Liabilities t-1 + Total Long Term Debt t-1) / Total Assets t-1]
8. Total Accruals to Total Assets (TATA)-
Accruals measures the difference between the accounting Profit/(loss) and the cash profit/(loss). Larger discrepancies in the accounting profits and cash profits increase the probability of manipulation of the earnings.
TATA = (Income from the Continuing Operations t – Cash Flows from the Operations t) / Total Assets t
Based on the above eight variable M-score can be calculated as follows:
M Score = -4.840 + 0.920 x DSRI + 0.528 x GMI + 0.404 x AQ + 0.892 x SGI + 0.115 x DEPI – 0.172 x SGAI – 0.327 x LVGI + 4.697 x TATA
We can draw two possible conclusions using the M score:
- Beneish M Score < -2.22: the company is not likely to have manipulated its earnings
- Beneish M Score > -2.22: the company is likely to have manipulated its earnings.
Let us find out the M-score of Apple with the MarketXLS template.
Limitations of the model-
- Beneish’s M-score model uses to find the manipulation of the overstated profits. We cannot use it to find the understated profits.
- The Beneish model does not apply to financial firms like banks and insurance companies.
- The Beneish model is a probability theory model and doesn’t guarantee fraud detection in a company.
Successful Application of Beneish Model-
In 1998, a group of Cornell University business students used the Beneish model and correctly identified that the Enron Corporation was manipulating its earnings. At that time, Enron’s stock was trading at $48. Noticeably, Wall Street’s financial analysts didn’t pay heed to this and still recommending a buy for the stock. Eventually, the stock went up to $90. In 2001, when Enron filed for bankruptcy, it was found out that Enron manipulated its earnings, and it results in a $74 billion loss to the shareholders.
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Fortune’s Shawn Tully recently looked at the Shiller P/E model (developed by Yale University professor Robert Shiller), which calculates the P/E ratio of the market using ten years worth of earnings (vs. just the earnings of the last 12 months). Currently, the market P/E based on the Shiller model is around 15, which is lower than it’s been in 20 years. The bottom line is the lower the P/E is when you invest the higher returns you will most likely get in the future.
On his Yale web page, Shiller has posted the historical data he uses to calculate the market’s 10-year P/E. He periodically updates the calculations, but you can also download the data in Excel spreadsheet form and (with a bit of digging), find and plug in newly available earnings and price data to update it yourself.


What happened to subtraction?
You know. Good old subtraction. You have 12 pencils, and you take 5 away, how many do you have left?
I always knew the answer to be 7. Mostly because my Dad was really smart and he showed me how to SIMPLIFY math. He happened to be an accountant, so he had that going for him, too. He and all of my teachers in school physically showed me exactly how to utilize basic math skills and work through the process of elimination. They would put out 12 pencils, or coins, or Cheerios, or balls, or marbles, or whatever was lying around – and then like magic, would remove 5 of them. At that point, you could very easily count what was left on the table and come to the simple conclusion that 12 – 5 = 7.
7 pencils. Figured it out in less than 5 seconds.
And the best part about this type of learning, it could work with pretty much any number! You could take 247 gummy bears, and eat 114 of them, and you would be able to figure out there would be 133 of them left. And with practice, and a piece of paper and pencil, even big numbers like 13,688 minus 10,359 would yield results of 3,329, just like this:
My oldest son Ben came home from 2nd grade on Friday with some homework, including a math problem. Or should I say, “Strategies for Subtracting to 100”. Now, I have an open mind when it comes to learning, and even more so when it comes to children and learning. I truly believe every individual “learns” differently. I happen to learn when I hear and see something at the same time. Ben is great at memorizing dates. He knows every single birthday of everyone in our family. Some children and adults need to read things first, then do it themselves.
One thing is for sure.
I truly do not believe in complicating and adding steps to processes in order to show multiple ways of working the same issue.
There is a name for that. Redundancy.
Enter what I can only assume is our first adventure into Common Core.
I have been hearing about this for years now through social media, blog posts, and even more so from my 2 nephews and a frustrated sister-in-law. It is now becoming apparent my wife and I are embarking into the unknown world of COMPLETELY useless thought processes.
Here is a picture of 5 different ways to subtract 67-34…
Does my son REALLY need to learn all five ways to jump to the 10, and count blocks, and have friendly numbers that add multiple steps to a somewhat straightforward math problem?
What if we just started with the algorithm way (which if I am not mistaken has worked for THOUSANDS OF YEARS), and test our children on whether the vast majority of them, “get it?”
If that does not seem to work, let’s move on to the number line, which does a dandy job of visualizing the numbers, but drastically increases the amount of writing, space, addition and subtraction. Just in that one problem, I made 39 different marks on one piece of paper! How is this making subtraction easier!?
Does anyone else agree with me?
Practicing and working hard to understand the basic principles of mathematics is important. Our children need to understand math and be able to do basic computations WITHOUT the use of a smart phone or calculator. But I do not see the point in COMPLICATING anything. And of all things, basic arithmetic.
That is why I named this blog “The Deconstructed Dad”. I believe it is incredibly important to have the skills of looking at complicated issues and understanding how to deconstruct or simplify them. This is not an easy task, as our incredibly complicated world continues to increase in speed and complexity. I believe this will be a skill in high demand in the future, and you better believe I am teaching my children how to solve problems by simplifying them.
So after it took 27 minutes for my 7-year-old son to show me how to do ONE math problem, I asked him which one of the 5 “Strategies for Subtracting to 100” he “liked” the best. Do you know which one he chose?
Yup, the one which has been around for a thousand years, and his old man can even understand. That is right folks, the apple doesn’t fall too far from the tree. His “Pop” accountant will be proud.
I also told him the next time his teacher asked him to show his work, in order to understand his process – Daddy will not be mad if he forwards his teacher this classic clip from Abbott & Costello…
Just because you show your work, doesn’t always make it right!
PS. If you have a common core story – share it with us! Misery loves company. Reply below in the comments section now. I would love to hear it!


This is the last week of classes at my school before the Christmas Break! I always find it a difficult week to keep the kids focused and productive so I have tried to write some math problems to embrace the theme and help them to see there there is math every where we look!
Christmas Math Problems
1. The wrapping station in the mall can wrap 3 gifts every 5 minutes. For each gift they receive a donation of $2. How much money could they raise in 2 hours?
2. Walmart is open 24 hours a day for the month of December, excluding Chirstmas Day when they are closed, and Boxing Day they are open from 7:00 am – 11:00 pm. How many hours is Walmart open during the month of December?
3. Miss Lewis would like to put lights around 4 windows on her house. Each window is 1.25 m tall and 0.75 m wide. How many meters of lighting does she need?
4. Mr. M would like to purchase a 2.5 m tall Christmas tree for the dining hall. Which of these trees is a better buy?
a. All trees $49
b. $18 per meter tall
c. First 2 meters $40; each additional 10 cm $2
55. There are 180 students in Lower School. Mr. Nagy needs to gingerbread cookies to lunch on Wednesday. Each batch makes 36 cookies and takes 22 minutes to bake. If each student can have 2 cookies. How many batches will he have to prepare? How long will it take to bake all of the cookies?
(Some questions adapted for metric units from: http://www.fi.edu/school/math/merry.html)


After writing my post yesterday, I did some reading and found this article from The Times Online about the creator of the KENKEN puzzles. He has some very interesting ideas about math and education in general.
Mr. Myamoto offers special math classes on weekends, and parents flock to him for a chance to have their children attend. In these classes, children solve the puzzles with minimal guidance. They are encouraged to work on their own, using trial and error, which differs greatly from fact memorization, a common theme in education around the world.
Mr Miyamoto’s theory is that the brain – of a child or adult – is failed by conventional teaching. By concentrating on a “third way” of problem-solving, he believes that the mind becomes a more potent tool for dealing with the rest of life, from main-stream education to the challenges of the workplace.
Last night I introduced my own children to KENKEN. Together, they solved a 4X4 and a 5×5 puzzle. Tonight, they want to try the next size. They are working on their math without any reminder to please finish their homework. I agree with Mr. Myamoto who says, the puzzle “draws out the primal, self-starting learning instinct of human beings.”


2 Year Olds
Two year olds are introduced to the preschool program's circle time, cooperative play, sharing and taking turns, all in a foreign language with lots of support and reassurance. They learn to make appropriate choices in a classroom setting. Fine motor coordination is honed with drawing time, ginger play, pounding and squeezing clay, and shaking rythmn instruments. Large motor coordination is developed with fun activities like rolling, crawling, creeping, walking, running, jumping and climbing. Highly interactive story time helps the two year olds develop a love for books and reading. We encourage emerging logical reasoning by tackling shape-sorting, simple puzzles, and ring stacking. Basic math concepts are introduced with numbers one and two. Ball time helps with hand eye coordination. Music time helps our two year olds gain control over their voices.


By Richard Lustig
I gotta tell you… it makes me SO MAD when people say I’m “lucky” because I’ve won the lottery grand prize 7 different times.
I’m sorry, you don’t win 7 Lottery Game Grand Prizes by luck.
That would be like saying I’m going to get struck by lightning 7 times in my life.
Winning 7 times at ANYTHING, whether it’s a game of checkers, chess, or the lottery isn’t from luck.
It’s from following a system, a set of rules that help to reduce the odds of losing.
When you stack the odds in your favor and stick with the things that have worked, THAT is when patterns emerge.
After 7 Lottery Game Grand Prize wins… I’ve cracked the code to winning the lottery and can show you how to win it too.
My biggest win to date was $842,152 playing Mega Money in Florida. I recently won a $98,000 Fantasy Five Grand Prize.
All of these are verified on the Florida lotto website.
So how have I been able to come up with my winning strategies?
Well, I’ve been able to win over $2 million in cash and prizes from the lottery by doing this…
1. Write down the previous winning numbers for each of the games you want to play.
2. Once you have the winning numbers for at least seven previous drawings… plug them into the simple formula I teach inside Lotto Dominator.
This formula is based on an algorithm that goes to work scanning statistics and giving you the probability of certain numbers hitting when you want them to.
See, by scanning through thousands of winning combinations, this algorithm can track and see the statistical probability of certain numbers coming up.
The formula inside Lottery Dominator does all the heavy lifting… you just need to add and divide a couple of numbers.
Use a calculator if you want – but it’s simple math. Again, the formula does the heavy lifting.
3. Purchase your tickets based on the winning numbers my formula gives you.
Practically every single lottery game in the world is based on the same mathematical statistics and probabilities.
This means that the formula you get inside Lottery Dominator works for all lottery games.
And the reason why this formula works?
The numbers don’t lie, so when you take out ALL emotional attachment… you increase your odds of winning.
In other words, let the numbers and statistics do the work… don’t let your emotions get in the way.
Since winning is all about probability and patterns… you’ll be astonished at the long-term stability of using statistical formulas when playing, versus using your emotions.
All lotto games in the world have the same principles, which are based on math, numbers, and statistics.
No where is any lotto based on your feelings or emotions.
So get rid of those, use the formula in the Lottery Dominator system, and your probability of winning even $200, $500, or $1,000 will go up dramatically.
If you’re ready to grab the same formula I’ve used to win 7 grand prize lottery games… it’s inside your Lottery Dominator private site…
Best of luck,
P.S. Remember how I said winning the lottery is all about stacking the odds in your favor?
And remember how I said it’s all based on statistics and probabilities?
This is something I just read from a lottery study…
“Certain numbers DO come up more often than others in lottery draws.
The top seven numbers to pop up since the National Lottery launched in 1994 have been 23, 40, 44, 38, 30 and 33.
If you want to learn more of the proof that will skyrocket your odds of winning… head here now…


Trajectory Optimization in Convex Underapproximations of Safe Regions
Jerry Ding and Claire Tomlin
Air Force Office of Scientific Research
This project is concerned with a computationally efficient method for optimizing an aircraft trajectory in a two-aircraft conflict scenario, under a noncooperative setting. It is assumed that the future trajectory of the uncontrolled aircraft is unknown, but that deterministic input bounds are given. The only sensor information available is assumed to be readings of the position of the uncontrolled aircraft at regularly sampled discrete time instants. Safety is ensured through the computation of unsafe reachable sets in a game theoretic framework. The reachable sets are then employed as constraints in a convex trajectory optimization program at each time step. We prove the safety property of the optimization program, and address the errors introduced by model linearization through a robustness analysis. Simulation results demonstrate that the trajectories generated by the proposed algorithm provide a tight bound on the feasible trajectories in the presence of uncertainties.


Imagine an ideal gas, for example hydrogen, contained in a container of volume V, which has a temperature T and exerts a pressure on the same P. With the aim of the radio anlizar hydrogen atoms with the average velocity of its molecules, the following will Desarrolo below: From PV = nRT, mam dividing by Avogadro's num N: PV / N = nRT / N, the term V / N = a , would the apparent volume of a molecule if we neglect the average distance between these: PA = nkT, where K = R / N, Boltzmann constant. If concideramos atomic volume, a / 2 = Q, where Q is the preload of the hydrogen atom, therefore, PQ = NkT / 2. Solving for T, T = 2PQ/nK. Given the equation of the kinetic-molecular theory of gases: T = IU * 2.M/3R, IU * 2 is the mean square speed of the molecule and M is the molar mass. T Equating the last two equations: ui2.M/3R = 2PQ/nK, solving and simplifying is: IU * 2.m / P = 6Q. The hydrogen atom orbital is spherical symmetry, so that Q = 4 (pi) r * 3 / 3. Replacing: IU * 2.m / P = 8 (pi) r * 3, where m is the unit mass of a proton, and r is the atomic radius of spherical symmetry (for a quantum level n = 1). Solving Re is: Re = (ui * 2.m / 8 (pi) P) * (1 / 3), allowing to calculate the atomic radius root of the average velocity of the gas. These results show that, depending on the energetic state of the particles may be variations in the relative distances of electron-proton in the hydrogen atom, ie the orbital energy is not constant, but varies depending on the thermal and kinetic state of its neighboring molecules.


Tesseracts and Tessellation:
Understanding the Fourth Dimension without Mathmatics
The top figure is a tesseract which is a fourth dimensional analog to a cube. The cube is a three dimensional analog to the square. Underneath we see a hexagon and next to it a honeycomb which is a tessellation of the hexagon. A tessellation is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps. It is an extension of the hexagon into two dimensional space.
When we talk of the other dimensions we are not talking about a separate reality with no relationship to our own. Such “other worlds” are tessellations of a three dimensional space out into the fourth dimension. Thus, every dimension is related to our dimension as the hexagon is to the honey comb.
Now here is an interesting little twist. When I was in college before I knew anything about tesseracts or tessellation I participated in a peyote ceremony. While I was under the influence of this powerful substance I saw intricate three dimensional patterns extending out into space in all directions. I saw a tesseract of a tessellation of my own three dimensional reality.
☯ Samsaran ☯


The National Benchmark Test (NBT) could be see as a meanstest used by Universities to check the mathematics and literacy proficiency of future students. Many Universities require students to complete the NBT’s before they can be admitted to the institution.
Before you sit down to write the NBT test, you need to be registered. Here’s all you need to know about the NBT registration.
Read more: https://www.careersportal.co.za/high-school/grade-12/how-to-register-to-write-the-national-benchmark-tests
Where to find Careers Portal:


#include <random> std::mt19937 rng; // engine std::normal_distribution<> dist; // distribution // rng()で生成される値は全処理系で同一 // dist(rng)で生成される値は処理系依存
The algorithms for producing each of the specified distributions are implementation-defined.
N1398 A Proposal to Add an Extensible Random Number Facility to the Standard Libraryより根拠箇所を引用（下線部は強調）。
C. Separation of Engines and Distributions
This proposal attempts to specify the engines precisely; two different implementations, with the same seed, should return the same output sequence. This forces implementations to use the well-researched engines specified hereinafter, and users can have confidence in their quality and the limits thereof.
On the other hand, the specifications for the distributions only define the statistical result, not the precise algorithm to use. This is different from engines, because for distribution algorithms, rigorous proofs of their correctness are available, usually under the precondition that the input random numbers are (truely) uniformly distributed. For example, there are at least a handful of algorithms known to produce normally distributed random numbers from uniformly distributed ones. Which one of these is most efficient depends on at least the relative execution speeds for various transcendental functions, cache and branch prediction behaviour of the CPU, and desired memory use. This proposal therefore leaves the choice of the algorithm to the implementation. It follows that output sequences for the distributions will not be identical across implementations. It is expected that implementations will carefully choose the algorithms for distributions up front, since it is certainly surprising to customers if some distribution produces different numbers from one implementation version to the next.


Sentiment analysis is especially valuable when acting on social media data sources.
Deep learning is another technology that’s growing in popularity as a powerful machine learning technique that learns multiple layers of representations or features of the data and yields prediction results.
The paper also focuses on the precedents of these classes of models, examining how the initial ideas are assembled to construct the early models and how these preliminary models are developed into their current forms.
Recent Advances in Recurrent Neural Networks Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data.
RNNs consist of a stack of non-linear units where at least one connection between units forms a directed cycle.
A well-trained RNN can model any dynamical system; however, training RNNs is mostly plagued by issues in learning long-term dependencies.Deep Learning: An Introduction for Applied Mathematicians As a mathematician myself, I like to see tutorials that represent data science topics in light of their connections to applied mathematics.This paper provides a good introduction to the basic ideas that underlie deep learning from an applied mathematics perspective.Along with the success of deep learning in many other application domains, deep learning is also finding common use in sentiment analysis in recent years.This paper provides an informative overview of deep learning and then offers a comprehensive survey of its current application in the area of sentiment analysis.A New Backpropagation Algorithm without Gradient Descent We’ve all been taught that the backpropagation algorithm, originally introduced in the 1970s, is the pillar of learning in neural networks.In turn, backpropagation makes use of the well-known first-order iterative optimization algorithm known as , which is used for finding the minimum of a function.Against a background of considerable progress in areas such as speech recognition, image recognition, and game playing, AI contrarian Gary Marcus of New York University presents ten concerns for deep learning, and suggests that deep learning must be supplemented by other techniques if we are to reach the long-term goal of .The Matrix Calculus You Need For Deep Learning This paper is a wonderful resource that explains all the linear algebra you need in order to understand the operation of deep neural networks (and to read most of the other papers on this list).On the Origin of Deep Learning This paper is a comprehensive historical review of deep learning models.It covers the genesis of artificial neural networks all the way up to the models that dominate the last decade of research in deep learning like convolutional neural networks, deep belief networks, and recurrent neural networks.


I did not realize until reading Michael J. Bradley’s book, Age Of Genius: 1300 to 1800, just how recently the Base-60 Numbering System of the Egyptians remained in at least partial use in mathematics.
Thanks to the Indians and the Arabs, the world long ago replaced the okay number system of the Romans with the superior base-ten place-value system we use today for whole numbers. However, as recently as Shakespeare’s time, mathematicians were still using the Base-60 system for fractions.
Today, fractional values are most scientifically rendered using the Decimal system– which as the name implies– is a Base-10 system. As the Decimals system also utilizes place-value, it integrates perfectly with our whole number system. Truly, it’s a beautiful thing, and mathematics surely ranks as one of the most sublime inventions of mankind.
Base-60 fractions were commonly in use before being supplanted by the decimal, and the system was called the “Sexagesimal” system (or so I’m told, although I wonder how many people using it actually called it that at the time; I’ve never to my recollection heard the term come up before in my historical or epistolary readings).
In a recent post, I talked of the intricate connection between Astronomy and the development of Mathematics, so I won’t go into detail here about how the Base-60 system of fractions ultimately derives from the fact that the year-measurement used by Egyptians divided into 360 days, which is a multiple of 60. This is also where the (otherwise arbitrary) idea came from that a circle is comprised of 360 degrees.
As I said in that same recent post, many of the developments in Mathematics originated from work being done with circles. That means… when Mathematicians were calculating, they were often dealing with degrees. Therefore, when they went to express a fractional amount, they were speaking of partial-degrees. By tradition, degrees had long been divided into “minutes,” with each degree containing sixty minutes (and I’m sure with each minute containing sixty seconds since this is precisely where we get our clock measurements of today).
Knowing this background, it becomes clearer why mathematicians would have ever bothered with a Base-60 Fractional System.
To use Bradley’s example from Age Of Genius, if a mathematician in the days of the Sexagesimal system were to write the decimal fraction…
…he likely would have expressed it as:
0: 1, 2, 49, 43, 11, 14, 44, 16, 20, 17
This was a shortcut way of writing: 1/60 + 2/60^2 + 49/60^3 + 43/60^4… and so on.
One of the earliest exponents (no math pun intended) of the Base-10 system over the Sexagesimal system was al-Kashi, who lived 1380 to 1429. He used fractions with denominators of powers of 10, not 60, which means he was basically using a proto-decimal system.
Nearly a hundred years later, Francois Viete [vee ET] (1540- 1603) was still trying to convince stubborn mathematicians to switch to decimal fractions.
It wasn’t until the 1590s that G.A. Magini and Christoph Clavius introduced the “decimal point.”
And it was the Scotsman John Napier [NAY pee yur] (1550 – 1617), a slightly older contemporary of Shakespeare’s, who finally convinced the world to begin adopting the decimal system with his book, Constructio.


The study explores what happens when a regular wave pattern has small irregularities, a question that scientists have been trying to answer for the last 50 years.
Researchers have long known that in many cases such minor imperfections grow and eventually completely distort the original wave as it travels over long distances, a phenomenon known as "modulational instability." But the UB team has added to this story by showing, mathematically, that many different kinds of disturbances evolve to produce wave forms belonging to a single class, denoted by their identical asymptotic state.
Biondini, a professor of mathematics in the UB College of Arts and Sciences and an adjunct faculty member in the UB physics department, says the first great success in using math to represent waves came in the 1700s. The so-called wave equation, used to describe the propagation of waves such as light, sound and water waves, was discovered by Jean le Rond d'Alembert in the middle of that century. But the model has limitations.
"The wave equation is a great first approximation, but it breaks down when the waves are very large — or, in technical parlance — 'nonlinear,'" Biondini said. "So, for example, in optical fibers, the wave equation is great for moderate distances, but if you send a laser pulse (which is an electromagnetic wave) through an optical fiber across the ocean or the continental U.S., the wave equation is not a good approximation anymore. "Similarly, when a water wave whitecaps and overturns, the wave equation is not a good description of the physics anymore."
Over the next 250 years, scientists and mathematicians continued to develop new and better ways to describe waves. One of the models that researchers derived in the middle of the 20th century is the nonlinear Schrödinger equation, which helps to characterize wave trains in a variety of physical contexts, including in nonlinear optics and in deep water.


use circumference in a sentence.
The 20k figure is an approximate circumference of the Earth.
Isn't the circumference of the waistline a better measure?
So you can have two versions of a circle, one with circumference = pi, and one with circumference = wtf?
Whether pi or 2pi or 4pi is more convenient depends on whether you're working with circumference, area, or solid angle.
Have they ever explained why Pi is the ratio of a circle's circumference to its diameter?
I think you mean the circumference of geostationary orbit is 265000km.
Wow, mixing up circumference and diameter is pretty bad journalistic mistake.
As a circle expands, its area grows proportional to its circumference.
Corners don't get caught on crap and slashes are deflected tangentially around the circumference rather than cleaving the shield itself.
The circumference of the earth is ~40k km, which would make "the other side of the earth" ~20k.
I don't know if this visualization is really useful for those who know that circumference = diameter * pi
Also BMI is getting phased out in favour of ratio between circumferences of hips and belly.
I know it's just a saying, but taken literally, "coming full circle" would mean the circumference.
I wasn't actually talking about the circumference per se, just that Balsamiq has come "full circle" which I represented using pi.
Waist circumference and BMI together give a decent measure...
In fact, wait circumference is pretty important, especially for me.
On top of that, you don't even an ocean to measure the Earth's circumference.


%* tutor.m: Tutorial for beginning MATLAB users.
%* Written by: Kyle D. Dippery
%* 473 Anderson Hall
%* (606) 257-3893
%* Last updated May 20, 1997
%* Copyright 1997 by Kyle D. Dippery
%* Reproduction of this document is permitted for
%* noncommercial use only, provided the entire document,
%* including this copyright notice, remains intact.
% WELCOME TO MATLAB!
% The purpose of this tutorial is to familiarize the
% user (that's you) with the basics of MATLAB.
% In the screens to follow, lines preceded by a percent
% sign ('%') are comment lines, and are ignored by the
% MATLAB interpreter. All other lines are actual MATLAB
% commands, which will be executed before your very eyes.
% Press a key to continue...
% Probably the first useful thing you need to know is
% how to enter data from the keyboard. You can do this
% by assigning values directly to variables. For example,
% to assign the value 5 to the variable 'a', we enter:
% That first line ("a=5") is what we entered. MATLAB
% then shows us that it understood what we said, by
% echoing the value of a (5).
% Press another key...
% MATLAB doesn't particularly care whether the value
% we enter is a scalar, vector, or matrix. The syntax
% for the assignment is mostly the same, regardless.
% The only difference for vectors or matrices is that
% we need square brackets () to tell MATLAB that the
% input is an array. So, to enter a row vector, let's
% call it 'b', we type:
b=[1 3 4 5 8 9]
% Here we've separated the elements of the array by
% spaces. Commas would have worked just as well, but
% we tend to think commas make the line look a bit more
% cluttered than it really needs to.
% Column vectors, like 'bc', are entered as:
bc=[1; 4; 3; 5; 3; 5];
% Notice the dual use of the semicolon in the last
% example. First, it separates the rows of column
% vectors (or other multi-row arrays). (Spaces after
% the semicolons aren't necessary, but we think they
% help make the line more readable.)
% Second, when a semicolon ends a command it tells
% MATLAB not to echo the results of the command to
% the screen.
% Another key to continue...
% If we want to look at a variable after it is assigned,
% we can use the 'disp' command.
% Colons have special uses in MATLAB, too - they can
% be used to build vectors of evenly-spaced numbers:
% Notice that the last element of the vector is 3.0, not
% 3.4. This is because the next element of the specified
% sequence is 3.5, which is greater than the upper limit
% (3.4) we assigned.
% Notice also that, in this case, we didn't need the
% square brackets. That's because MATLAB expects a
% vector input when the colon notation is used. Still,
% the brackets can be used if there's any doubt; there's
% nothing wrong with a little redundancy.
% If the increment (the second number in that last
% assignment statement) is omitted, it defaults to 1:
% Matrices can be entered as a sequence of row vectors,
% separated by semicolons.
A=[1 3 5 7; 2:2:8; 1 2 4 9]
% Or as a sequence of column vectors, separated by commas
% or spaces:
% Complex numbers also receive no special treatment:
C=ones(3,3) + i * A(:,1:3)
% Some notes about this last command:
% C=ones(3,3) + i * A(:,1:3)
% 1. 'i' is implicitly recognized as sqrt(-1).
% So is 'j'.
% 2. 'ones(m,n)', where m and n are positive integers,
% generates an mxn array of 1's, in this case used for
% the real part of C. Some other 'special' matrices can
% be generated by 'zeros', 'eye', 'rand', 'randn', or
% 3. Submatrices can be extracted from matrices by
% using indices. In this case, the imaginary part of
% C is a submatrix of A, consisting of the first three
% columns of A (the same matrix A we used before, still
% in memory for us to use.)
% A bit more about:
% C=ones(3,3) + i * A(:,1:3)
% The first index into an array always indicates the rows
% to be used, the second index indicates the columns.
% Indices may be scalars or vectors. A colon, by itself,
% means "use 'em all". Hence, A(:,1:3), A(1:3,1:3), and
% A([1 2 3],[1 2 3]) would all give the same result (since
% A, in this particular case, has only three rows).
% 4. Multiplication of a matrix by a scalar is
% accomplished by the '*'. Matrices, scalars, and
% vectors are all added by '+'.
% Addition and subtraction act the same for scalars,
% vectors, and matrices. a+b, where a and b are scalars
% adds a and b together.
% If a and b are vectors,
% or matrices, with the same dimensions, then a+b adds each
% element of a to its corresponding element in b:
% Notice that, if an operation is not assigned to a
% specific variable, it is assigned to the temporary
% variable, 'ans'.
% Scalars can be added to (or subtracted from) anything:
% See if you can follow what just happened, there...
% Order of operation is pretty standard - exponents are
% evaluated first, multiplication and division next,
% addition and subtraction last; operations are evaluated
% left to right, except when parentheses are used to group
% things together. The usual stuff...
% Multiplication and division are slightly different:
% they are assumed to be matrix operations:
B=[8 2 1; 2 2 1; 5 3 7]
% If what we want is an array whose elements are the
% elements of A times the elements of B, we need to
% use a 'dot-multiply', or '.*':
% This is called 'array multiplication', to distinguish
% it from 'matrix multiplication'.
% Let's look again at our matrix product, for comparison:
% Division with matrices is similar to multiplying
% one matrix by the inverse of the other:
% A/B is almost A*inv(B) (where inv(B) is the MATLAB
% command which finds the inverse of B).
% A\B is almost inv(A)*B.
% (The reason it's "similar to" and not "the same as" is
% that A and B don't have to be square matrices for the /
% or \ operations, but do for the inv() operation.)
% For more precise definitions of / and \, try
% 'help /' or 'help slash'.
% Array division is accomplished by the 'dot-divide'
% operations, './' and '.\'.
% A./B yields an array whose elements are the elements of
% A divided BY the elements of B.
% A.\B yields an array whose elements are the elements of
% A divided INTO the elements of B (or, the elements of B
% divided BY the elements of A).
% Note that A.\B is the same as B./A, but A\B is NOT the
% same as B/A.
% Matrices may be multiplied by scalars without using the
% '.*', but division requires a bit of care.
% For instance, 2*A and A*2 will both yield
% A/2 gives us an array whose elements are the elements of
% A divided by 2, but 2/A does _not_ give us an array whose
% elements are 2 divided by each element of A (unless A
% happens to be a scalar).
% Exponents are kinda ugly. Usually, what you'll probably
% want is every element of a vector raised to a certain
% power, or a certain base raised to the power of every
% element in a vector. These would be accomplished by the
% '.^' operator:
% The '^' operator by itself has more to do with matrix
% powers, and either the matrix or the exponent, but not
% both, must be a square matrix. 'help arith' will give
% more information on this.
% The '.' means something a bit different when dealing
% with transposes.
% Normally, a transpose is denoted by a single quote, '.
% When the matrix is complex, this is actually a complex
% conjugate ("Hermitian") transpose operator. A
% "straight" transpose is denoted by a dot-transpose, .'.
% Note: for real-valued matrices, there is no difference
% between a transpose (') and a dot-transpose (.').
% Some examples, using our matrix C
% For an example of why we like array multiplication,
% let's try to draw a spiral.
t=0:720; % angle, in degrees, twice around
x=t.*sin(pi/180*t); % x coordinate
y=t.*cos(pi/180*t); % y coordinate
% Notice that mathematical functions can operate on
% arrays. sin(pi/180*t) takes the sine of every element of
% the vector, pi/180*t. (pi is 3.1415etc., implicitly defined.)
% t*sin(pi/180*t) would try to multiply a 1x721 matrix by
% another 1x721 matrix, which doesn't work. Instead,
% t.*sin(pi/180*t) multiplies the ith element of t by the
% ith element of sin(pi/180*t), which is what we really
% Notice also that the input to the sin and cos functions
% is converted from degrees to radians. Trig functions
% in MATLAB always operate on radians.
% Notice also how the array operations neatly reduce
% the need for 'for' loops.
% gives the same result as:
% for ii=1:721,
% (We like to use 'ii' and 'jj' instead of 'i' and 'j'
% for loop counters, because 'i' and 'j' already mean
% sqrt(-1) to MATLAB, and we'd hate to try to build a
% complex array out of something, only to find out that
% i=17.2 or j=150 suddenly, because we used them for
% something else beforehand...)
% Now let's look at our spiral.
% This is the simplest method of obtaining a graph. We
% can label this graph,
title('Wow, It Worked!')
% Input to the 'xlabel', 'ylabel', and 'title' commands
% must be a string argument. Strings in MATLAB are
% delimited by single quotation marks (').
% Strings are concatenated (stuffed together) with square
% brackets. ['Hi' ' there!'], for instance, yields the
% string 'Hi there!' (see 'puzzle(2)' for another example).
% Functions exist for turning numbers into strings, which
% can then be used in figure titles or labels:
text(0,max(y),['Max y value = ' num2str(max(y))]);
% If, for some reason, we don't like yellow lines,
% we could ask for the plot in some other color (we
% like green, ourselves):
% Notice that all of our nice labels are gone.
% Successive 'plot' statements generally erase
% anything that was set by earlier ones. (This
% can be changed by playing with the 'hold'
% Or we could ask it to plot the data as red plusses:
% For a list of possible linestyles and colors,
% enter 'help plot' from the command prompt (when
% you get it back, that is).
% Multiple plots can be placed in a single window by
% using 'subplot'.
subplot(212), plot(t,y,'Color',[1 0.5 0],'linestyle','-.')
title('It Doesn''t Look Like a Spiral...')
% Look carefully at the second 'title' command, above, and
% compare it to the actual title. Look again. There is a
% difference - where the apostrophe appears in the title,
% there are two in the command. This is how you get
% single apostrophes to appear in MATLAB strings, since
% one by itself would mean the end of the string.
% Alternate methods of specifying line colors and styles
% are also illustrated above.
% Did you notice how nothing happened in the figure window
% until all the commands for building all of the plots had
% been executed? MATLAB doesn't like to update figures
% until it absolutely has to (who does?), or when it runs
% out of commands to execute, or when it runs into a
% 'pause' statement (as it did, here). The 'drawnow'
% command will force MATLAB to display graphs before it
% reaches the end of the command stack:
drawnow % just like this
subplot(212), plot(t,y,'Color',[1 0.5 0],'Marker','.')
title('It Doesn''t Look Like a Spiral...')
% Or we could look at multiple plots on a single set
% of axes:
title('There''s Something Fishy Here...')
% We can add gridlines:
% Or turn just some of them on or off:
% Or even zoom in some,
% but that's getting a bit fancier than we generally
% need. Still, if you want to play with lots of figure
% or axes properties, you can look into the 'set' and
% 'get' commands, later. There's lots of fun to be had,
% in there...
% Figures can be cleared by 'clf'. Empty figure windows
% can be opened by entering 'figure'. Figure windows
% can be closed by entering 'close(n)', where n is the
% number of the window to close. (The figure number is
% usually displayed in the window's title bar.)
% 'close all' closes all figure windows.
% Hardcopies of plots are obtained through the 'print'
% command. 'print -deps filename' would print the
% current figure to filename.eps, in encapsulated
% PostScript format. The file could then be printed
% on a laser printer, or imported into documents, or
% whatever. 'print', by itself, sends the plot to the
% default printer. You may want to be careful of this, if
% your printer has a page quota, or if you're just trying
% not to be wasteful, or some such...
% MATLAB also supports formats besides Encapsulated
% PostScript. Enter 'help print' to find out about
% We've played with quite a few arrays, so far: a, b,
% bc, A, B, t, x, y, and maybe one or two more we don't
% remember. Right now, they're all still sitting in
% memory. What if we've lost track of what we've done?
% Is there a way to find out what we have in memory?
% Maybe.... Try entering 'who':
% This shows all the variables currently residing in
% Or we could type 'whos'. This shows all the variables
% in memory, along with their sizes and some other neat
% things about them. Let's first introduce the 'more'
% function, though: this forces screen display to pause
% each time the screen fills up. 'more on' and 'more off'
% are used to control this paging routine.
% When 'more' is 'on', the spacebar pages ahead one full
% screen, 'q' quits the pager (it probably would not be a
% good idea to press 'q' just now, however... it likely
% would also quit the tutorial at this point) and just
% about any other key moves forward one line.
% Let's get rid of some of this baggage:
clear Aprod Mprod a a2 a3 ans b bc t x y
% 'clear', by itself, or 'clear all', would get rid of
% everything. But I wanted to keep some things...
% What if we only want to know the size of one array?
% 'size' returns a two-element vector, containing the
% number of rows (1st element) and the number of columns
% (2nd element) of an array. 'size(ans,1)' will return
% just the number of rows. 'size(ans,2)' will return
% just the number of columns.
% 'length' returns the maximum element of the 'size'
% vector (useful for dealing with vectors)
% We could use the 'tic' and 'toc' commands to find
% out how much time it takes to calculate that inverse.
% The 'elapsed_time' is shown in seconds.
% If we just wanted to know what time it is, we could
% look at the 'clock' (since some of us don't wear watches):
% This tells us, in order, the current year, month, day,
% hour, minute and second (just multiply that '1.0e+03'
% factor through each element to get the right values).
% (And no, we don't know what's going to happen at the end
% of the millenium...)
% Hardcopy of any MATLAB session can be obtained by
% using the 'diary' function. If 'diary' is on ('diary
% on' is the command), then anything that prints on the
% screen also prints to a file called 'diary'.
% 'diary filename' sends all output to the specified file.
% 'diary off' turns the diary function off.
% That's it for this tutorial. If you want to look
% at it again, without pressing all those carriage
% returns, set 'more on', then 'type tutor'.
% To quit MATLAB when you're done (or ready for lunch),
% type either 'exit' or 'quit'.


The Yellow Brick Road is a wonderful project that is intended to mix up two stories about the Wizard of Oz and Alice in Wonderland. Each story is set in a fantasy land and has a young heroine and an evil woman antagonist. For the mathematics in this project I plan to use an Archimedes spiral that defines the start of the Yellow Brick Road. I will set Alice in Wonderland on the road as my bronze figure, and there will be a copper witches hat for the wicked witch of the East, and a brass Queen of Hearts card for the other nasty woman.
The mathematics of this work relates to an Archimedes spiral. This type of spiral is drawn by continually moving outwards from the center as you draw a circle. The spiral is the set of points that correspond to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation
with real numbers a and b. Changing the parameter a will turn the spiral, while b controls the distance between successive turnings. There is a video describing how to draw an Archimedes Spiral.
Yellow Brick Road
Alice is a curious figure. She will be standing on the Yellow Brick Road looking somewhat apprehensive or pensive about her pending journey. On the other side of the road I will set the witches hat and the Queen of Hearts card to portray each of the evil antagonists in the tales.
Alice in Wonderland
Alice in Wonderland
The witches hat is another interesting mathematical construction. The hat is essentially a cone that fits inside a brim that must be fabricated at the correct size. For a 1/8 scale figure we can measure that the hat size must be a 3/4 inch diameter circle. A full brim would be 1 1/2 inches in diameter, and this would also be the height of the cone.
If we drop a perpendicular down from the top of the cone we will have a right triangle from which we can calculate the length of the hypotenuse, or the cone side.
Now, if you have a cone and cut it by a line perpendicular to the circular base and then lay it out flat, you will have a sector of a circle.
We know the length of the cone side or the radius of the sector is 1.55 from above. And we know that the cone circle or brim has a radius of 0.375. And we also know from our high school math that the circumference of a circle is 2Πr.
If we now multiply by 180 / Π to convert radians to degrees, this gives 87 degrees. So we now draw an arc with a radius of 1.55 and measure an angle of 87 degrees. If this segment is cut out and formed into a cone it will have the correct height and circumference to fit the hat brim.
The next step is to draw out the Archimedes spiral on paper and the witches hat, too, and fabricate the design. We can then build a model of the work.