PHYSICISTS FINALLY HAVE AN EXPLANATION TO AN URGENT QUESTION ON EVERY MILLENNIALS MIND, WHY DO MY EARPHONES GET TANGLED?
I mean even if nicely placed in your pocket or bag or even if your hands; they still get tangled and if you're unlucky you spend the entire walk to the bus stop or train station trying to get them fixed.
They found that “complex knots often form within seconds and that stiffer strings are less likely to get knotted up.
It is well known that a jostled string tends to become knotted; yet the factors governing the “spontaneous” formation of various knots are unclear. We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyze the knots. Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100%. This behavior differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100% with long, flexible strings. We analyzed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string. Remarkably, almost all were identified as prime knots: 120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed. The relative probability of forming a knot decreased exponentially with minimum crossing number and Möbius energy, mathematical measures of knot complexity. Based on the observation that long, stiff strings tend to form a coiled structure when confined, we propose a simple model to describe the knot formation based on random “braid moves” of the string end. Our model can qualitatively account for the observed distribution of knots and dependence on agitation time and string length.
I do not know if you made it through this story, but the bottom line is that annoying knot and tangle we have to forever deal with has a scientific backup story. Also guys below is the proper way to put your headphones on:


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- Bright Spots in Homeschooling
Home Schooling Works With Math Too!
It may have taken longer to start tapping into their potential in this area, but it is becoming more apparent that home schoolers are capable of excelling in mathematics, much as they have demonstrated they can in the liberal arts.
This is demonstrated in a number of ways, but perhaps none more visibly than recent high-level competitions that have seen home school students excelling.
At the recent USA Math Olympiad (USAMO), Alison Miller, 15, of Niskayuna, NY, and Anders Kaseorg, 15, of Charlotte, NC, both home schoolers, were among the 12 winners (out of 326 finalists). The 12 will participate in a summer training session at the University of Nebraska, after which six will be chosen to compete for the U.S. in the International Math Olympiad (IMO) in July at Glasgow, Scotland. Both students had made it through two regional qualifying competitions to get to the finals, as had Matthew and Nathaniel Ince, home schoolers from Chesterfield, MO who were named honorable mention in the final round.
They follow in the footsteps of Reid Barton. The Massachusetts home schooler won the USAMO four times and was a four-time gold medalist at the IMO. More recently, the MIT student was named a Putnam Fellow, the top honor of the prestigious William Lowell Putnam Mathematical Competition.
While these students are the highest profile examples of home schoolers excelling in math, the evidence abounds. There are numerous competitive math teams consisting of home schoolers, and many home schoolers also have done well in standardized testing.
Annette Bramsen, a home school mom from Wheaton, IL who coaches a competitive math team, said the elements of home schooling that have made it a helpful vehicle for students interested in the humanities, serve them well in mathematical pursuits as well.
Additionally, she said, math studies tend to be foundational.
"I think math serves as a great training ground for a student in any academic subject," Bramsen said. "You can't twist it. You can't make it mean what it doesn't mean. It's very important, especially for bright students, to learn to work hard on something, because if you don't learn that, life just gets tougher. You need that intestinal fortitude. It really aids in the study of any kind of logic. It helps with argumentation and debate. It teaches ordered reasoning. Math assumes there is an answer.
Bramsen, who said her children have surpassed her in their understanding of the subject, said it is important that home school teachers not be intimidated with mathematics.
"I think we have a tendency to want to teach subjects we are most comfortable with," Bramsen said. "Don't allow your own limits in math to define your child's future. I wanted all three of my children to do better in math than I did. Don't be intimidated by them exceeding you in math! When they exceed you, find a tutor if you need to."
More Bright Spots in Home Schooling...


The Mathematics program is designed for students to develop skills that can be used in everyday life as well as in other academic areas. The main objective of the Mathematics program is to prepare students to pursue degrees in computer science, business, electronics, and related fields. Courses are offered in both theoretical and applied mathematics to meet the needs of students from differing academic and professional areas.
The Mathematics program offers the following three options:
1. An Associate of Arts degree program in which a liberal arts education can be combined with a solid background in mathematics.
2. A Bachelor of Arts degree program with a major in mathematics which prepares the student for a mathematics-related career.
3. Specialized classes in mathematics which prepare students who major in other disciplines to increase their effectiveness in their own particular fields.
The Mathematics program at East-West University has three focuses.
The first focus is Mathematics. The second is Mathematics with Computer Applications, and the third is Mathematics with Digital Electronics Applications.
In addition, students are also prepared for graduate study leading to advanced degrees in pure and applied mathematics.


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KU Math Prize Competition winners announced
LAWRENCE— The University of Kansas Department of Mathematics held its 33rd annual KU Math Prize Competition earlier this month, providing undergraduates an opportunity to test their skills via a written exam that covers six questions to be completed within three hours. Cash awards were presented at the department’s honors banquet April 21.
The junior-level is open to all undergraduates of non-senior standing and assumes a knowledge of first-year calculus. The winners of the junior level:
First place: Christopher Mayo, a junior in mathematics from Clay Center.
Second place: Michael Zhou, a junior in mathematics and biomechanical engineering from Overland Park. Zhou also was the top first-year student.
Third place: Andrei Elliott, a junior in computer science and mathematics from Lawrence.
The senior-level is open to all undergraduates and covers a range of standard topics of undergraduate math. The winners of the senior level:
First place: Sean Holloway, a senior in electrical engineering from Mission.
Second place: Yujie Deng, a senior in computer science and mathematics from Wuhan, China.
Third place: Robert Winslow, a senior in computer engineering and mathematics from Olathe.
Hai Long Dao and Yasuyuki Kachi, associate professors of mathematics, were in charge of the competition.


The ROUNDDOWN formula in Microsoft Excel is the subject of this article. The function returns a number that has rounded down to a specified number of decimal places. Its unique qualities are what make it helpful. This function differs from ordinary rounding in that it decreases the value of all numbers.
For example, only numbers below five are rounded down in standard rounding, whereas values greater than five are round-up. All numbers are always rounded down when using ROUNDDOWN. It could be handy in a variety of situations.
The ROUNDDOWN function in Excel returns a number that has round-down to a specified number of decimal places. Unlike normal rounding, which only rounds down values less than 5, ROUNDDOWN rounds down all numbers. The ROUNDDOWN function in Microsoft Excel describes in this article, along with its formula syntax and usage.
Learn how to round down quickly and easily in Excel. Excel’s ROUND DOWN function ensures that data is always rounded-down to the specified number of decimal places. We’ll look at how to use this feature efficiently as a group.
What is the ROUNDDOWN formula in Excel?
This formula rounds a number down toward zero.
number: The amount you’d like to round down.
num_digits – The number of digits your specified number should round down.
In Excel, how to utilize the ROUNDDOWN formula.
This section explains how to utilize Microsoft Excel’s round-down feature. The methods below were created using the most recent version of Microsoft Excel for Windows 10 (version 2019). Don’t worry if you’re using a different version or platform; the guide will still work. The number and num digits arguments are the same for ROUNDUP and ROUNDDOWN as for ROUND.
We’ve created a table that shows how to use the ROUNDDOWN formula to link two numbers and return the desired number of decimal places.
1. Start Microsoft Excel and open or create a new document that you want to work with.
2. Choose an output cell to work with.
3. =ROUNDDOWN =ROUNDUP =ROUNDDOWN =ROUNDDOWN =ROUNDDOWN =ROUNDDOWN =ROUND (number,digits). If you wanted to round down the number 53.47364 to five digits, you’d enter in =ROUNDDOWN (53.47364,5).
4. You can also use cells as references in the formula. For example, you can use the =ROUNDDOWN(C4, E6) formula to round down the value in C4 to the matter in E6.
Excel Round-off Formula – Round down
In Excel, the round-off formula for rounding down will assist the user in rounding down the decimal value to the next lower whole number1.8630, for example, will be rounded up to the next most significant value of 1.8.
Now, calculate the round-off formula in Excel to round up the results by following the steps below. This example considers a student data collection in which you will attempt to round up the students’ percentage numbers.
Make a new column called “round-off % value” and rename it. To round-down down the first two decimal places, pick the first cell and type in the formula = ROUND(M2,2), as seen in the image below.
Choose the round-down option from the drop-down menu.
As seen in the image below, press enter and drag the cell throughout the column to apply the formula to the entire column.
Copy and paste the example data from the table below into cell A1 of a new Excel worksheet. To see the results of formulas, select them, press F2, and then Enter. You can alter the column widths to see all the data if necessary.
In Excel, how to ROUND DOWN to one decimal place.
Click in cell C3, type the equal sign, and then type the’ ROUNDDOWN’ function. Then we’ll move on to an opening bracket, which will require two things.
The first will be the cell containing the amount we want to round down, so click on B3, then insert a comma before typing in the second value – the number indicating how many decimal places in the result.
Type ‘1’, close the parenthesis and click ‘Enter’ to round down to one decimal place. Excel will display the result in C3, the value from B3 rounded to one decimal point.
In Excel, how to ROUND DOWN to two decimal places.
Use 2 in the function to round down to two decimal places, and the resulting integer will reduce down to two decimal places.
1, 2, 3, and so on are all positive numbers that can be used to round down to any number of decimal places.
What is the top way to round up a value to make it a whole number?
Enter a zero in the function to round the value down to a whole number.
And Excel will do precisely what you want – it will round down the original amount to a whole number, as shown below.
How to round a number to closest the tens or hundreds
Users must use negative numbers in the formula to round a number down to tens or hundreds, which implies shifting to the left of the decimal point; therefore, include the minus sign with the number in parentheses.
I’ll give you a handful of instances.
Enter ‘-1’ into the formula to round the number down to the nearest tenth, and here’s the result!
If you wish to round a number down to the nearest hundredth, type ‘-2’, and Excel will do the math.
That’s how it’s done! This function can be used to round any number to the nearest tenth.
We hope this article has supported your understanding of utilizing Excel’s ROUNDDOWN function to round down figures quickly. This understanding may help you do numerous computations more easily and quickly when working with spreadsheets that need mathematics.
Our Aid Center has hundreds of guides to help you if you need more assistance. Please revisit FastSoftwares helpful articles for more information on productivity and modern technology!


If you had 10 billion $1 notes and spent one every second of every day, it would take 317 years for you to go broke.
Dorothy bought a watch, a blouse and a handbag. The watch cost $45, the blouse cost $33.70 and the handbag cost $44.20. How much did Dorothy spend?
Click here for the answer.
Sean saved $2,000. Then he paid for a car repair that cost $1,700 and some pop for $8.95. How much does Sean have left?
Tyler spent $35 on a bed for her dog. She also bought some chew bones for $15.60. How much did Tyler spend in all?


Bishundeo Saha* & Vijay Kumarb
aDept. of Mathematics, Marwari College, Ranchi University, Ranchi
bDept. of Mathematics, K.O. College, Gumla, Ranchi University, Ranchi, Jharkhand
Received : 12th May, 2015; Revised : 17th July, 2015
Abstract : This paper deals with some aspects of Struve transformation which has been extended to a class of generalized function.
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Topics include division facts, mental division, long division, division with remainders, order of … Improve your math knowledge with free questions in "Divide whole numbers - 2-digit divisors" and thousands of other math skills. Funny Talking Animals - Compilation. Tangram Stories. http://bg016.k12.sd.us/tangram.htm (Theme) General Math. Power Lines EZSchool's Grade 5 Math - Division: Learn to divide numbers. Start off by understanding how division is nothing but repeated subtraction and work your way up to … Whole Brain Teaching 3rd-5th has 7,101 members.
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I can explain how to divide a decimal number by a whole number and how
Math Worksheets · Student Sites · Quadrilaterals · Order of Operations · Long Division · Dividerama · Elapsed Time · Geoboards · Name the Rule Clones · Mixed
26 Nov 2017 Maths For Kids | Grade 4 | PeriwinkleWatch our other videos:English Stories for Kids: https://www.youtube.com/playlist?list=PLC1df0
Select the correct answer and score a goal. Dividerama Solve the long division problem with three-digit dividend. Division Facts for 4 · Division Facts for 5.
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MATH 1030Q: Elementary Discrete Mathematics
Three credits ($150). Offered Fall or Spring.
Topics chosen from discrete mathematics. May include counting and probability, sequences, graph theory, deductive reasoning, the axiomatic method and finite geometries, number systems, voting methods, apportionment methods, mathematics of finance, number theory.
Eligibility Guidelines: Successful completion of one year of pre-calculus is recommended. Not open for credit to students who have passed any math course other than MATH 1011, 1020, 1030, 1040, 1060 or 1070. UConn ECE Math 1030Q cannot be taken concurrent with or after UConn ECE Math 1131Q or 1132Q.
MATH 1070Q: Mathematics for Business and Economics
Three credits ($150). Offered Fall or Spring.
Linear equations and inequalities, matrices, systems of linear equations, and linear programming; sets, counting, probability and statistics; mathematics of finance; applications to business and economics.
Successful completion of one year of pre-calculus is recommended. Not open for credit to students who have passed Math 1132Q.
MATH 1131Q: Calculus I
Four credits ($200). Offered Fall only.
Limits, continuity, differentiation, antidifferentiation, definite integral, with applications to the physical sciences and engineering sciences. Suitable for students with some prior calculus experience. Substitutes for MATH 1151 as a requirement.
Eligibility Guidelines: Successful completion of one year of pre-calculus is required. A student must pass MATH 1131Q with a grade of a "C" or higher to continue on to MATH 1132Q. To receive credit for the MATH 1131Q – MATH 1132Q sequence a student must pass MATH 1131Q in the Fall with a C or higher and continue to MATH 1132Q in the following Spring. The sequence must be completed in one academic year. Students cannot receive credit for MATH 1131 and MATH 1151.
MATH 1132Q: Calculus II
Four credits ($200). Offered Spring only. Prerequisite: MATH 1131Q in the immediately preceding semester.
Transcendental functions, formal integration, polar coordinates, infinite sequences and series, vector algebra and geometry, with applications to the physical sciences and engineering. Substitutes for MATH 1122 as a requirement.
Eligibility Guidelines: Successful completion of one year of pre-calculus is required. A student must pass MATH 1131Q with a grade of a “C” or higher to continue on to MATH 1132Q. To receive credit for the MATH 1131Q – MATH 1132Q sequence a student must pass MATH 1131Q in the Fall with a C or higher and continue to MATH 1132Q in the following Spring. The sequence must be completed in one academic year.
MATH 2110Q: Multivariable Calculus*
Four credits ($200). Offered Fall only. Prerequisite: MATH 1132Q in the immediately preceding semester.
Two- and three-dimensional vector algebra, calculus of functions of several variables, vector differential calculus, line and surface integrals.
Eligibility Guidelines: Successful completion of MATH 1132Q with a grade of a “C” or better. MATH 2110Q can only be taken the following fall semester after completion of 1132Q.
Instructor Certification Requirements:
MATH 1030Q, MATH 1070Q*, MATH 1131Q**, & MATH 1132Q** The minimum degree requirement for instructors wishing to teach UConn ECE mathematics courses is typically a Master’s degree in Mathematics. In exceptional cases, a strong Bachelor’s degree in Math with evidence that the candidate is enrolled in a program to earn a Master’s degree may be considered. A candidate with a Master’s in Education may also be considered if coupled with a strong Bachelor’s degree in Mathematics.
ECE Instructors currently certified to teach MATH 1030Q, MATH 1131Q, 1132Q or MATH 2110Q will be eligible to add MATH 1070Q to their certification upon submission of an approved course syllabus.
New Applications for MATH 1070Q will take into account candidates who have a Master’s degree in Business or Economics, or a Master’s in Education with a strong bachelor’s degree in Business or Economics. Please note approval to teach MATH 1070Q may not lead to approval to teach additional course offerings without sufficient math coursework.
Interviews will be conducted before certification is granted. The Math Department will not certify candidates that have earned a degree completely through online coursework or who do not have a degree in an appropriate field.
MATH 2110Q To be eligible for certification in MATH 2110Q, instructors must first meet requirements to teach MATH 1131Q and 1132Q (possess a strong background as a math major and have a grade of at least a B in a Real Analysis I course). Instructors seeking to be certified in MATH 2110Q in addition to MATH 1131Q and 1132Q should have successfully taught each course at least twice. Additionally, to be certified to teach MATH 2110Q, instructors should possess a very strong background as a math major and have successfully completed at least four upper-level, proof-based courses (Real Analysis I & II, Abstract Algebra I & II, Abstract Linear Algebra, Complex Analysis, Differential Geometry, Number Theory, etc.) with a grade of a B or higher in each course. Exceptions may be made in extenuating circumstances at the discretion of the faculty coordinator.
Note: Core Questions are given to Instructors to include in final exams by the University's Mathematics Department.
**The transcript must include at least one course on the theory of calculus (i. e., Real Analysis or Theoretical Advanced Calculus) with a grade of B or better.**
MATH 1030Q Sample Syllabus (PDF)
MATH 1070Q Sample Syllabus (PDF)
MATH 1131Q Sample Syllabus (PDF)
MATH 1132Q Sample Syllabus (PDF)
List of Approved Math Textbooks
Math Department Resources for ECE Instructors
* Pilot course. Instructors, please contact the UConn ECE Program Office before applying for these courses.


students, and many others take some version of calculus or discrete math or both. The book relates discrete math ideas to other parts of mathematics and. full solution (which in the pdf version of the text can be found by clicking on the exercises number—clicking on the solution number will bring. Notes on Discrete Mathematics So why do I need to learn all this nasty mathematics? edu/homes/aspnes/classes//ininenzero.tk
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The study of mathematical proof is particularly important in logic, and has applications to automated theorem proving and formal verification of software.
Logical formulas are discrete structures, as are proofs , which form finite trees  or, more generally, directed acyclic graph structures   with each inference step combining one or more premise branches to give a single conclusion. The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e.
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Concepts such as infinite proof trees or infinite derivation trees have also been studied,  e. Partially ordered sets and sets with other relations have applications in several areas. In discrete mathematics, countable sets including finite sets are the main focus.
The beginning of set theory as a branch of mathematics is usually marked by Georg Cantor 's work distinguishing between different kinds of infinite set , motivated by the study of trigonometric series, and further development of the theory of infinite sets is outside the scope of discrete mathematics.
Indeed, contemporary work in descriptive set theory makes extensive use of traditional continuous mathematics. Main article: Combinatorics Combinatorics studies the way in which discrete structures can be combined or arranged.
Enumerative combinatorics concentrates on counting the number of certain combinatorial objects - e. Analytic combinatorics concerns the enumeration i. In contrast with enumerative combinatorics which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae.
Design theory is a study of combinatorial designs , which are collections of subsets with certain intersection properties. download paperback This is the new 3rd edition of the book.
The previous version is available at the 2nd edition's site. Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach.
Since Spring , the book has been used as the primary textbook or a supplemental resource at multiple universities around the world see the partial adoptions list. This 3rd edition brings many improvements, including nearly new exercises, a new section on trees in the graph theory chapter, and improved exposition throughout, as well as many corrections to previous errors.
GATE CS Notes according to GATE 2020 syllabus
Previous editions will continue to be available indefinitely. Please contact the author with feedback and suggestions, or if you are decide to use the book in a course you are teaching.
Get the book The entire book is available for free as an interactive online ebook. This should work well on all screen sizes, including smart phones. Hints and solutions to examples and exercises are hidden but easily revealed by clicking on their links.
Some exercises also allow you to enter and check your work, so you can try multiple times without spoiling the answer. Discrete Mathematics, Second Edition. Discrete Mathematics: An Open Introduction, 2nd Edition. Foundations of Combinatorics with Applications.
Foundations of Computation, Second Edition. Foundations of Computer Science: C Edition. Lecture Notes in Discrete Mathematics. Toggle navigation FreeTechBooks.
Discrete Mathematics The study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. All categories Follow Books under this sub-category 20 books.
About this book
A Course in Discrete Structures Post date: Publication date:If you prefer a physical copy, an inexpensive print version of the text is available on site. Partition theory studies various enumeration and asymptotic problems related to integer partitions , and is closely related to q-series , special functions and orthogonal polynomials.
DP of interest and practice problems on that topic. Automata theory and formal language theory are closely related to computability.
What Is Discrete Math?
Back Matter Pages All in all, one would indeed learn and improve tremendously here. Additionally, every contest provides immediate helpful tutorials usually written by the authors themselves.
It draws heavily on graph theory and mathematical logic. It's home to many classic problems from the Chinese IOI scene.


Crags Mathematics Curriculum
The National Curriculum for Maths aims to ensure that all children:
- Become fluent in the fundamentals of Mathematics
- Are able to reason mathematically
- Can solve problems by applying their Mathematics
In order to meet these aims at Crags Community School, these skills are embedded within Maths and Arithmetic lessons and developed progressively over time using a mastery approach supported by documentation from recognised providers such as Mathematics Mastery, White Rose Maths and NCETM.
We are committed to ensuring that children are able to recognise the importance of Maths in the wider world and that they are also able to use their mathematical skills and knowledge confidently in other subject areas and contexts. We want all children to enjoy Maths and to experience success in the subject, with the ability to reason mathematically.
The programmes of study are taught in distinct domains, however where possible links are made allowing connections across ideas to help develop fluency, Mathematical reasoning and competence in solving increasingly sophisticated problems. Children should also apply their Mathematical knowledge to other subjects such as Science, ICT, Geography and P.E.


You don’t have to be an expert at math to be a good cook, but it certainly helps to commit a few essential measuring equivalents to memory. For those less-used measurements, however, there are some helpful lists you can keep on hand in the kitchen. Bookmark these two websites of cooking measurement conversions for easy reference.
- Measure Equivalents [USDA]
Find any metric to U.S. conversion on this chart along with cups to teaspoons, tablespoons, and ounces. You can use this website to convert gallons to quarts, quarts to pints, and pints to cups.
- Cooking Measure Equivalents [Info Please]
This website provides a quick reference for converting table- or teaspoons to cups. It also has the essential conversions for the metric system to the American system of measurements. So if you're ever wondering how many grams are in an ounce or milliliters are in a tablespoon, check out this page on Info Please.


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The Joy of Thinking: The Beauty and Power of Classical Mathematical Ideas.
By Edward Burger, Michael Startbird
Reviewed by: Darrell
Summary: This set of 24 lectures on DVD based on the author’s book “The Heart of Mathematics: An Invitation to Effective Thinking”. The authors review many of the most important concepts of classical mathematics and show how these concepts can be applied to help us improve our everyday thinking.
Review: This is another wonderful set of lectures from “The Teaching Company”. This particular course is a great example of what has made their courses so popular: They take complex topics and make them simple to understand, fun to learn and easy to apply. This course boils some very difficult concepts (e.g. the fourth dimension) and presents them so lucidly that even people with math anxiety can gain a better appreciation of these ideas. One great example of Burger and Starbird’s gift for explanation is their treatment of the famous “Monty Hall Problem” (lecture 20). I’ve heard many explanations of this problem – most of them incorrect. Their treatment of this counter intuitive problem was so clear I now feel like I finally understand the right answer! Learning math concepts is fun with this course.


Fourth class are piloting Mathletics, an interactive maths programme. Children are assigned tasks by class teacher and progress is monitored throughout the school year. The programme has proven very successful worldwide fostering a greater understanding and interest in numeracy. World Maths Day is on the 1st of March this year and we look forward to pitting our wits against classes all over the world!
What the Pupils Think:
"Mathletics is an Australian math progamme online and people from all over the world go on it! Your teacher might assign tasks for you to do in the week, When you are finished your tasks you could play a range of different games on Rainforest Maths or you could play Live Mathlethics which means you play people from all over the world.
In Mathletics you get points - for every answer you get five points, if you get one thousand points in a week you get a bronze certificate, if you get five bronze certs you get a silver cert, if you get five silver certs you get a gold cert!
On world maths day Mathletics is crazy - you can get a gold cert on that day alone! But remember you can only get one cert a week! I love mathletics and you should too!"
By Ellen Smith 4th class
"My name is James Nugent,and I am in Mr. Corry's 4th Class. Our class is doing an online Maths programme called Mathletics. It is an Australian programme but Kids all Around the world use it. Mr. Corry assigns tasks every Sunday and we are meant to complete them before the next sunday. You get points for getting sums correct and if you get 1000 points you get a bronze cert. If you get 5 bronze certs you get a silver cert. if you get 5 silver certs you get a gold cert. when you are finished all your tasks you can play a game called online Mathletics. There are 5 levels, each one harder than the next - 1 being the easiest, 5 being the Hardest.
My record in level one is 74 questions in a minute. There is a bar at the side that tells you how well you are doing The best being Human Calculator, the worst being Raging Rookie. You can play against kids all over the world ranging from America to Australia, Qatar to Ireland, England to South Africa. I have 1 Silver Cert and 2 Bronze Certs. (You can only get 1 cert a Week and you can get more than 1000 points a week). Mathletics is a great Website and I like it a lot. Signed James Nugent Mr. Corry's 4th class."
By James Nugent
"Hi my name is Shauna . My class and I are doing a computer programme called mathletics. It is a very fun programme where you can play people from all over the world in a tables competition.
.You have to get tables right but if you don't you will get a strike out but if you do there is a blue line ahead of your picture (which is at the left) which
moves.There are other things other than that, there are tasks you have to do that teacher sets for you to do.As you do you get points and if you get a 1000 points you get a bronze cert.
If you get 5 bronzes, you get a silver and if you get 4 silvers, you get a gold.I spend at least a half an hour on it and try to get a cert for the week.There is a rocket at the left hand of the screen and it tells you how many points you have.There is a face maker where you can make your own person and save up credits to buy accesories at the shop.You can buy backgrounds and other things too."


My old 27" TV is about to die. I came across this site while trying to figure out what size of TV to replace it with.
To find the HDTV screen size (diagonal measure) that gives the same height as your old television, take the screen size of the old TV and multiply by 1.22. So if you want an HDTV with a screen that's the same height as your old 34-inch TV, for example, the chart below shows that you need to buy an HDTV with a 42-inch screen, and that they will both have a height of 20.4 inches.
More size conversions on the screenmath.com website.


Baccarat cards counting strategy. No need to be a mathematical genius, as the count strategy is easy as it. From time to time the question of card counting in baccarat comes up. Because baccarat is dealt from a shoe, it follows that the odds for the. Baccarat Strategy - Will counting cards in baccarat give you an edge over the casino? Read our simple guide to find out.
Baccarat counting cards Video
Card Counting at Baccarat Notify me of follow-up comments by email. While you have a running count with what's described above, you'll actually want to divide that by the number of decks that are left in the shoe to find the true count. With a payout of 8-to-1, the counter can earn 0. Card counting in live blackjack tables not using any automatic shuffle machine is definitely a possibility regardless of the number of decks used and it is profitable. While card counting is a well-known phenomenon in blackjack, few players realize that affair amount of study has been done of the subject of card counting in baccarat as well. Why the James Bond Roulette Strategy Fails? A bet hits zero house edge at the following true counts:. Things You Should Know Before You Play 5 Ways to Play Double Double Bonus in Video Poker 7 Silly Mistakes Made While Playing Craps 7 Tips to Avoid Rookie Mistakes at the Casino 8 Craps Tips That Will Make You a Better Player 8 Habits of Smart Casino Players 8 Things to Know Before Entering the Casino 8 Tips on How to Win at Baccarat 8 Tips on How to Win at Roulette Advanced Card Counting: For example, a card counter who makes the banker wager whenever the true count is 30 or higher will make the wager about once every hands, and will be playing against a house edge of about 0. Please remember that this table assumes the player is able to keep a perfect count and the casino is not going to mind the player only making a bet once every hands of less. A high running count for the banker would mean a corresponding low count for the player, and vise versa. What do you Need beste spieleseite im internet Know to Have an Edge? While a running count brettspiel casino 16 or below is optimized for a Player snooker german masters 2017 and a card counting above 16 is optimized for a Banker bet, the real numbers are actually a lot higher. Http://www.compasshealthgroup.com/vulnerability-and-addiction-treatment/ Things Smart Heimarbeit texte schreiben Poker Casino games to play Should Do Game Theory in 10 Easy Steps Hit or Stand: Using this system, players will be begriffe erraten spiel to measure which of the two bets wolf quesr more likely to pay off on an individual hand. Casino deutschland poker is possible to make a wager in baccarat with online casino ch edge over the house, using baccarat counting cards card counting. Therefore, in magix online world, it is reasonable to wonder if card counting can be used to beat the game. Are you Ready for the Best Game in Town? A true count of 30 is the lowest true count that yields an edge over the casino. In order for any given bet to become advantageous the player should divide the running count by the ratio of cards left in the deck to get the true count. How to Become a High Roller? He gathers all the information he can by watching the first round without making a bet. Find us on Facebook.
Baccarat counting cards - Ihrer
So toss that thinking out the window. The next table shows the ratio of hands played, based on a sample of million, in which the true count passes the break even points above. In baccarat chemin de fer and baccarat banque players can make choices, so skill has a role. The cards that decrease the chances of the player bet being better include fives, sevens and eights, and you'll subtract one from the count for all three of them. A high running count for the banker would mean a corresponding low count for the player, and vise versa.


Year 4 MTC
Calling all Year 4 parents and carers...
Your children will be sitting the Multiplication Tables Check in June 2023. Whilst they are busy working on their times table recall and fluency in class, any additional practice you can do in this area at home would be of great benefit to your child.
https://ttrockstars.com/ is a great resource to use as is simply chanting times tables facts.
Further information will be sent out in Spring Term but the Government 'Information for Parents' document can be found here: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/1116420/2023_Information_for_parents_Multiplication_tables_check_Nov_22_PDFA.pdf


AQE Transfer Test 3 book bundle.
This bundle contains: -
AQE Transfer Test Papers. ISBN 978-1873385-395
English Preparation – Ideal for AQE Tests. ISBN-13: 978-1-873385-14-2
Mathematics Preparation – Ideal for AQE Tests. ISBN-13: 978-1-873385-13-5
This bundle will provide everything to get you started on the AQE Transfer Test journey.
The AQE Transfer Tests require that your child has a very sound understanding of both maths and English. Most of this content will have been taught in school but they will need to revise this work both in school and at home.
The Maths and English books provided in this bundle offer structured practice that is essential to aid your child in preparing for this important exam.
Having worked through the English and maths books your child will then be ready to tackle the AQE practice tests.
These tests have been written to replicate the actual AQE Transfer Tests and will give your child practice in an exam situation in the comfort and security of their own home.
AQE, English and maths 3 book bundle.
At a glance
*Save almost £4.50 on this bundle* which gives you all the content needed to help prepare for the AQE Transfer Tests.
Delivery & Returns
World wide postage and packing is just £2.95 per order. Orders are sent by first class Royal Mail and usually take from 1 - 3 days for delivery.
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We accept returns up to 7 days after dispatch if the goods are still in marketable condition. If you would like to return goods, contact email@example.com
Postage on returned goods will be borne by the customer, unless we were at fault. Print-on-demand titles are not eligible for return.


What is Celsius?
Celsius is a temperature scale that uses the degree Celsius (°C) as the base unit. The Kelvin scale, which is also used in science, uses a different set of base units.
How to Convert 32 Celsius to Fahrenheit
To convert Celsius to Fahrenheit, multiply the Celsius temperature by 1.8. For example, if the temperature is 32 degrees Celsius, the conversion would be: 3200 x 1.8 = 4692 degrees Fahrenheit.
What is Fahrenheit?
Fahrenheit is a temperature measurement that is different from Celsius. Celsius is based on the temperature of water, and Fahrenheit is based on the temperature of mercury.
One degree Celsius is equal to 100 degrees Fahrenheit. To convert Celsius to Fahrenheit, subtract 32 from the Celsius number. For example, if someone measures 95 degrees Celsius, their Fahrenheit temperature would be 38 degrees Fahrenheit.
How to Convert Celsius to Fahrenheit
To convert Celsius to Fahrenheit, divide the Celsius temperature by 9.5. For example, if the temperature is 32 degrees Celsius, the Fahrenheit temperature would be 2.6 degrees Fahrenheit.
How to Convert Farenheight to Celsius
To convert Fahrenheit to Celsius, divide the Fahrenheit temperature by 9:5. For example, if the temperature is 32°F, then the Celsius temperature would be 0.5°C.
If you’re ever in a situation where you need to convert temperature measurements from Celsius to Fahrenheit, there’s no need to worry. This simple guide will walk you through the steps needed.


See also Alphabet and Numbers/Counting Books on the picture book page.
Math in Children's Literature (Nancy Padak, Ohio Literacy Resource Center, Kent State University): Author, title and publication info for more than 100 books in these categories: addition, counting, estimating, fractions, geometry, graphing, measurement, money, multiplication and division, and number sense. Updated Oct. 2006.
Children's picture books that teach mathematics concepts (Christchurch City Libraries, NZ): Recommended for children aged 4 - 6. Lists about 65 books, with author, title, and summary for each, in these categories: Addition, Counting, Division, Fractions, Geometry, Measurement, Multiplication, Sets, Size, Subtraction, Time, and Other Concepts.
Suggested Children's Books that Relate to Mathematics (Janice L. Flake): Author, title, publication info for about 40 children's books useful for teaching math concepts, in alpha order from Dinosaurs are different by Aliki to More incredible true adventures by D.L. Wulffson.


Cbse mathematics chapter 10 straight lines class 11 notes mathematics in pdf are available for free download in mycbseguide mobile app cbse guide notes are the comprehensive notes which covers the latest syllabus of cbse and ncert it includes all the topics given in ncert class 11. Cbse class 11 mathematics maths straight lines, access study material for mathematics maths straight lines, students can free download in pdf click on tabs below for class 11 mathematics maths straight lines worksheets, assignments, syllabus, ncert cbse books, ncert solutions, hots. Cl provides cbse math prep material for class 8 students get free key notes, mcqs, tests, sample papers, ncert solutions, ncert solutions, hots questions for 8. Motion in a straight line ncert solutions class11 physics acid base salt ncert solutions master class 12 maths and be successful in examshere find class 10 maths notes, assignments,ncert solutions concept maps and lots of study material for easy learning and. Straight lines a coordinate geometry note :- if two vertex a(x1, y1), b(x2, y2) are given then third vertex of equilateral triangle c is ncert textbook chapter 10 - straight lines, mathematics, class 11.
11 of maths subject includes detailed answers of all the questions in chapter 10 - straight lines provided in ncert book which is prescribed for class 11 resource: national council of educational research and training (ncert) solutions class: 11th class subject: maths chapter: chapter 10. Maths : class 7 ncert / cbse revision notes tet success key provides free mathematics cbse revision notes, ncert revision notes , maths ncert solutions for class 7, summary of chapters as per ncert text book syllabus , free mcqs test. We'll be learning different types of equation of lines, the general form and various formulae related to slopes, angle between the lines, and distance point formulae of a line.
Exercise 2straight lines question 1: write the equations for the x and y-axes answer : the y-coordinate of every point on the x-axis is 0 therefore question 5: find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope -2 answer : it is known that. Mathematics revision notes nobody can undermine the importance of revision we at askiitians understand this need and have concocted an ultimate set of revision notes of mathematics covering almost all the important facts and revision notes on straight lines given two points. Notes of ncert cbse 11th maths chapter-10 straight lines on this link - https maths straight lines part 1 (introduction to lines, slope of line) cbse class 11 mathematics xi - продолжительность: 14:59 examfear education 148 505 просмотров. Ncert-xi-maths-chap-101-gradient, slope of a line- straight line, angle between two lines, cbse ncert xi maths class 11 ncert chapter 10 straight lines exercise 103 question 18 (important for cbse) if p is the length of perpendicular from origin to the line whose.
Learn cbse ncert solutions for class 6, 7, 8, 9, 10, 11 and 12 q-5 what is the slope of a line passing through the origin and, the mid- point of the line- segment joining the two points o (0, -5) and a (9, 0. Cbse class 11 mathematics ncert solutions: chapter 10, straight lines get the ncert solutions for cbse class 11 mathematics to access detailed and accurate answers to all questions of start your preparation for class 11 maths by accessing the ncert solutions for chapter 1, sets. Hi friends, on this page, i am sharing the class 11th maths ncert solutions on the topic straight lines this pdf file for 11th class maths subject contains solutions for all questions in the ncert text book the solutions are detailed for your easy understanding and easy to download in a pdf file. Download free pdfs of ncert class 11 maths solutions chapter 10 straight lines with examples, tips & more at byju's thus, by our observation, the coordinates of the point y are (0, b), while the coordinates of the point z is (0, -a) we know that, the line joining the vertex of an equilateral triangle.
Cbse notes class 11 maths chapter 10 straight lines pdf free download the best educational study material pdf for cbse class 6, 7, 8, 9, 10, 11, 12 for better exam result ncert books, cbse notes and ncert exemplar solutions are also available here. Learn chapter 10 straight lines of class 11 for free with solutions of all ncert questions for cbse maths chapter 10 class 11 straight lines. Ncert class 9 maths notes, summary, solution & guide, number system, polynomials, coordinate geometry, linear equation in two variables notes & formulas notesfun ncert class 9 maths print this page.
1 in fig 613, lines ab and cd intersect at o if ∠aoc + ∠boe = 70° and ∠bod = 40°, find ∠boe and reflex ∠coe answer given, ∠aoc + ∠boe = 70° and ∠bod = 40° a/q, ∠aoc + ∠boe +∠coe liked ncert solutions and notes, share this with your friends:: class9maths facebook comments. Straight lines coordinate geometry the branch of mathematics in which geometrical problem are solved through algebra by using the coordinate the angle e between two lines having slopes m1 and m2 is wwwncerthelpcom (visit for all ncert solutions in text and videos, cbse syllabus, note and. Cbse maths notes, cbse physics notes, cbse chemistry notes question 8: if one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles to show points a, o and b are collinear ie, aob is a straight line proof since, od and oe bisect.
Maths - maths : cbse ncert exercise solutions for class 11th for straight lines ( exercise 101, 102, 103, miscellaneous, miscellaneousmiscellaneous ) will be available online in pdf book form soon the solutions are absolutely free soon you will be able to download the solutions. Go back to class viii maths all chapters solutions posted in cbsetagged class 8 mathematics solutions, class 8 maths solutions, class 8 solutions, maths solutions, ncert maths solutions, ncert textbook solutions. Free pdf download of ncert solutions for class 11 maths chapter 10 - straight lines solved by expert teachers as per ncert (cbse) book guidelines all straight lines exercise questions with solutions to help you to revise complete syllabus and score more marks.
Extra questions on straight lines on shifting the origin to (p, q), the coordinates of point (2, -1) changes to (5, 2) find p and q [answer: p = -3 find the equation of a line with slope -1 and whose perpendicular distance from the origin is equal to 5 [answer: x + y + 5√2 = 0 and x + y - 5√2 = 0. Straight lines cbse class 9 mathematics sa1 2011 question paper (8) so k θ is the angle made by the line with positive direction of x-axisncerthelpcom (visit for all ncert solutions in text and videos y2) is given by m = tan θ = y2 - y1 / x2 - x1.


In mathematics, there are various types of numbers such as real numbers, natural numbers, whole numbers, negative and positive numbers, and so on. Similarly, irrational numbers are the type of numbers that can be written or expressed in the form of a simple fraction. Irrational numbers can also be defined as real numbers which cannot be written or represented in the form of p/q or a/b where q or b is not equal to zero. The opposite of irrational numbers is rational numbers. Those numbers can be expressed in the form of simple fractions i.e., real numbers or in the form of p/q where q is not equal to the number 0. Some examples of rational numbers are as follows: ¾, ⅚, 4, 8, etc. Some examples of irrational numbers are as follows: √5, √8, √3, etc. In this article, we will try to cover some basic aspects of irrational numbers such as properties of these numbers, comparison from rational numbers, and do a brief analysis about them.
As mentioned above, irrational numbers are the type of numbers that can be written or expressed in the form of a simple fraction. Let us look into the properties of these numbers. Some of them are mentioned below:
- If we add an irrational number and a rational number, the resultant value will always be a rational number. For example, ‘x’ is an irrational number, and ‘y’ is a rational number, then x + y = z which is a rational number. Therefore, the sum of a rational and irrational number is equivalent to a rational number.
- The arithmetic operation of multiplication with a number that is irrational and with a rational number that is non-zero in nature will provide you with an irrational number.
- The least common divisor or multiple of a number that is irrational may exist or may not exist.
- If we add or multiply two irrational numbers, the resultant value always comes as a rational number. For example, when two irrational numbers such as √5 and √5 are multiplied the answer comes = 5 which is a rational number.
- You may observe that the set of the number which is rational may be closed during the process of multiplication. But, in irrational numbers, the contrary happens.
In the next few points, we will carry out the comparison of rational and irrational numbers.
- Irrational numbers are the type of numbers that can be written or expressed in the form of a simple fraction whereas rational numbers can be represented in the form of a simple fraction.
- The irrational numbers cannot be expressed in the form of a/b or p/q where b or q is not equal to zero whereas the rational numbers can be written in the form of p/q where q is not equal to zero.
- Some examples of rational numbers are as follows: ¾, ⅚, 4, 8, etc. Some examples of irrational numbers are as follows: √5, √8, √3, etc.
In order to excel in mathematics, one should practice more and more. There is a very famous quote, ‘practice makes a man perfect. This quote is totally correct and implies mathematics. Therefore, to practice math from math worksheets, visit Cuemath. There are various other perks that are facilitated by the team. The teachers are highly experienced in their domains. Not only the teachers, but it also provides you with various different kinds of math puzzles so that studying math becomes fun. Thus, visit the Cuemath website for one-one live sessions, doubt clearing classes, and book a free session now.


Sir Isaac Newton, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)
Printed in London by Joseph Streater for the Royal Society, 1687
Newton’s Principia is generally regarded as the greatest work in the history of science. Building on the achievements of Copernicus, Galileo and Kepler, Newton explained the underlying universal laws and showed that a single mathematical law could explain the motion of objects on earth as well as the phenomena of the heavens.
The book was bought by the Library from the London bookseller Samuel Smith on 28 November 1690 for the sum of 7s 6d. Its low cost is an indication of the fact that the book was not an immediate success. In order to rid himself of some of the many unsold copies, Newton resorted to donating copies to university and college libraries, including the library of his own college, Trinity College Cambridge.
At the same time he ‘made over a portion of the edition’ of the Principia to Samuel Smith who supplied it to Chetham’s Library some three years after it was published.


Time-varying effect modeling (TVEM) allows scientists to understand the way associations between variables change over time. TVEM is an extension of linear regression that allows the association between two variables to be modeled without making assumptions about the nature of the association. For example, TVEM does not force an estimated curve to be linear.
TVEM was developed for use with intensive longitudinal data (ILD), but it has been expanded to be used with a broad variety of data types. The examples on this page use panel data and ILD, but TVEM has also been applied to cross-sectional data and historical data.


BECAUSE for over 50 years the Federal and State Departments of Education have failed to influence changes in teaching methods and strategies to address the steadily declining test scores identified by A Nation at Risk, ACT tests, and a variety of other testing tools, and
BECAUSE for over 50 years the National Council of Teachers of Mathematics continued to advocate the implementation of teaching methods and strategies which resulted in those declining test scores, and
BECAUSE the negligence perpetrated by the Federal and State Departments of Education, the National Council of Teachers of Mathematics, and other responsible agencies represents a dereliction of duty and a blatant disregard for the taxpayers’ expectation that school children receive a quality education, and
BECAUSE it is the responsibility of the people to protect each child’s right to a quality education,
THEREFORE math instruction must include memorization of basic math facts, formulas, theorems, rules and standard methods of computation, and
THEREFORE each student’s mastery of math skills and formulas appropriate for his grade level be assessed through yearly testing.


Decimal nature of the metric system
1795-1995 Bicentenary of the Decimal Metric System
On 7 April 1795 the National Convention of France decreed the new "Republican Measures" to be legal measures in France. The units of measurement included the meter, are, liter, and gram; and the prefixes centi, deci, deca, hecto, and kilo. This was the decimal system of measurement units or the decimal metric system that has survived practically unchanged as the basis of the modern International System of Units, or SI for short.
"A TOUS LES TEMPS; A TOUS LES PEUPLES"
["FOR ALL TIME; FOR ALL PEOPLES"]
Take the following tests to see why the decimal system is simpler:
Question: Which column would you rather add?
|Inch-pound units||Metric units|
|1 yard, 2 feet, 3-1/4 inches||1.607 meters|
|1 foot, 11-3/16 inches||0.589 meters|
|2 feet, 5-1/2 inches||0.749 meters|
|3 yards, 1 foot, 6-5/8 inches||3.216 meters|
|? yards, ? feet, ? inches||? meters|
Hint: The two sums are the same.
Answer: 6 yards, 2 feet, 2-9/16 inches; or 6.161 meters
A room measures 15 ft. 3-3/4 in. by 21 ft. 7-1/2 in. (4.667 m by 6.591 m).
What is its floor area in square yards?
What is its floor area in square meters?
36.79 sq. yd., or 30.76 m2
In designing a calendar you wish to divide an area of 7-1/4 in. by 11 in. (184 mm by 279 mm) into 35 rectangles;
that is you wish to divide 7-1/4 in. by 5 and to divide 11 in. by 7.
What are the dimensions of each rectangle in inches?
What are the dimensions of each rectangle in millimeters?
1-29/64 in. by 1-37/64 in., or 36.8 mm by 39.9 mm
The above information was compiled by the late Joseph B. Reid, President Emeritus, Canadian Metric Association.
A PDF version of the this page is available at: decimal-nature.pdf.
Back to USMA home.
Copyright © 1996-2013, U.S. Metric Association (USMA), Inc. All rights reserved.
Web hosting courtesy of Colorado State University.
Website maintained by USMA Webmaster


Have gone through any of the following curriculum with marks as prescribed below:
(a) The candidate should have passed 10+2 scheme of Examination with 50% marks in Physics, Chemistry and Mathematics and also 50% marks in aggregate of the 10+2 level examination.
(b) 10+3 Diploma (any stream) recognized by Central/State Govts. with 50% aggregate marks with a pass in Mathematics as a compulsory subject of examination;
(c) International Baccalaureate Diploma passed/appearing, after 10 years of Schooling with 50% marks in aggregate and with a pass in Mathematics as compulsory subject of examination.


How to calculate investment interest for a job search
The Investment Interest Calculator allows you to see the investment interest you would need to earn before you can start earning interest on your money.
In order to calculate the interest you need to make, simply multiply the annual rate of return of your investment by the amount of money you will need to invest.
For example, if you want to earn an interest rate of 0.5% per year on your investment, you need $1,000,000 to invest in a 10% equity interest rate.
This means that you will have to invest $3,000 in your investment account to reach this investment interest rate, which will mean you will only earn interest on $3.5 million of your money!
How much interest you’ll need to payIn order for you to be able to earn interest, you will also need to keep track of the amount you are expected to pay out in interest each month.
The interest calculator also allows you the ability to see your current savings, as well as the expected amount of interest you will be earning on your investments.
It will also tell you if you are overspending on your savings.
The amount you needTo calculate your investment interest, simply take the annual interest rate you are earning and divide it by the total amount of your investments, in this case $3 million.
How much money you needWhen it comes to determining your investment amount, the Investment Interest calculator is great for those who want to understand their investments more quickly, but do not want to have to worry about their finances.
There are a couple of other ways to calculate your investmentsinterest, which you can read about in more detail in the Investment Income calculator.
The Calculator gives you a total amount you have to pay into your investment accounts each month, so if you’re a student or have little money saved, you can use the calculator to work out how much you will spend each month to earn a given interest rate on your account.
The calculator allows you both the annual and monthly rate of interest.
If you are a student, the annual number is your interest rate per year and is calculated as the difference between the interest rate the average investor earns on the year and the average rate you would have to earn on a typical investment.
If you are an individual, the monthly rate is the rate of change in the amount the investor earns each month on their investment account.
If the investor makes a large gain, you could earn a higher monthly rate and therefore pay more in interest, but if they lose the investment and don’t make any gains, the interest they will be paying out will be lower.
If both the monthly and annual rate are higher than you want, you might need to look into other investment options.


Analemma and equation of time
One thing makes sundials absolutely different from all other clocks: they are based on very complex movement of the Earth in the space. Although this movement has a lot of regularities (like day-night and annual seasons), it is very complex and can not be expressed in one formula. The difference between true and mean time is called equation of time (EOT). Its value varies within ±15 minutes.
The inverse problem of showing true time by mechanical clocks is considered to be one of the most complex watch complications. On the left picture you can see Notos model of Martin Braun's watches with indication of the date, EOT and Sun's declination.
Mean time and phantom Sun
If we imagine an "ideal" Sun moving in accordance with our mean time,
it would have to revolve around the Earth with constant speed in a circular orbit,
located in the plane of the equator. We may call such Sun phantom, and mark it with gray color and letter
f on the following drafts.
All our mordern clocks are based on the constant speed of such phantom Sun.
However, the real orbit of Sun is elliptical and it is inclined to equatorial plane at an angle of about 23.5°. These two factors make the real Sun (t) to behave differently. This real movement of the Sun defines local Sun time.
There are two Sun's trajectories shown on the above draft. Phantom Sun f always moves in equatorial plane with constant speed 24 hours per turnover. Local mean time is defined by angle hf, delayed from the South direction. Local Sun time corresponds to angle ht. In general, these angles are not the same, and the equation of time can be recorded as ht - hf. Such mismatch between mean and sun time has a 6-month period and equals to zero four times a year: in the days of equinox and solstice. During the year the Earth's axis tilt contributes to the equation of time the value of ±9.9 minutes.
Elliptical orbit and Kepler's laws
The second essential component of the equation of time is an elliptical orbit of real Sun.
In the early XVII century a German astronomer Johannes Kepler has discovered the three laws of planetary rotation.
The first two of them are relevant to origin of EOT.
The first law describes all possible orbits of the motion of celestial bodies relative to each other. According to it, the Earth is located in one of the foci of the Sun's elliptical orbit, as shown in the figure on the left. Point 1 corresponds to the maximum removal of the Sun from the Earth and is called the apogee. The minimum distance between the Earth and the Sun is reached at the point 2. Such position is called perigee. Annual perigee happens on January 3, while apogee occurs on 4 June.
For those who prefer to consider the rotation of the Earth around the Sun, it should be noted that the closest to the Sun point of the Earth's orbit is called the perihelion, and the most distant point - aphelion.
The second law states that the speed of the Sun on elliptical orbit will not be constant, but will increase when approaching perigee and decrease at the point of apogee. The dependence can be illustrated graphically. Sun passes areas of AB and CD for one and the same time, if areas of the relevant shaded sections are equal.
The figure on the left shows the positions of phantom Sun(f) and true Sun (t). Phantom Sun that determines mean time moves around the Earth in a circular orbit with constant speed. The real Sun, on the contrary, accelerates at perigee point 2 and slows down at apogee 1. Accordingly, phantom and real longitudes will be different. This difference is expressed by the formula Lt - Lf. Twice a year, at apogee and perigee, the difference becomes zero. The rest of the time it changes within ±7.7 minutes.
The graph of EOT
The resulting graph of the equation of time is a composition of
two factors described above: Earth's axis tilt and ecliptical Earth's orbit.
Equation of time takes on a positive value when real Sun
crosses the local meridian before it would make a phantom Sun. A negative value
means that the real Sun is late compared to phantom Sun, e.g. mean time.
The value of EOT is zero four times a year:
on 15th of April, 13th of June, 1st of September and 25th of December.
In some books a graphical image of the equation of time is inverted. In this case EOT is expressed as mean time minus true.
Sometimes the equation of time is depicted in the form "analemmatic eight". In the Internet you can find pictures similar to the photo. If you set the camera on a tripod and make multiexposition shooting every day at the same mean time during the whole year, the Sun will form the shape which is similar to digit eight. Such 8-like figure is called analemma. Depending on the place and shooting time the curve can have a different shape and slope.
Sometimes an analemmatic curve is drawn on the dial at noon hour mark. Near noon time such curve helps to know the equation of time at certain day of the year.
If one wants to make sundials showing mean time, he has to take EOT into consideration. Therefore, the hour-lines of such sundials will always be in the form of analemma curves. Another method to display mean time by sundials is shown on the photo. The usual equatorial sundials have a gnomon in the form of a slotted analemma eight. On the curved dial two times are presented: civil time on the top, and local sun time at the bottom scale.


MAX JONESíS TOP TEN TIPS FOR CALCULATING YOUR MARATHON TIME
by Max Jones
first published in
Valley Striders News
I have referred to before, but not set out in full, my Top Ten Tips for calculating marathon times. They are:
- The par time is 2 hours plus your age in minutes, plus another 10% if you are female.
- This will be achieved, after a year or so of effective training, if, in the last 13 weeks before the race - excluding the week of the race but counting the miles in all 13 calendar weeks prior to that - youíve recorded an average of 55 miles per week.
- More mileage than that contributes nothing. But for every mile per week less than 55, add one minute to your race time.
- Provided, though, youíre not overweight. Par weight for men is 2 lbs per inch of height minus 5 lbs; for women 2 lbs per inch minus 15. Every pound over these weights adds 2 seconds per mile to your pace, say a minute to your marathon time.
- Weather: add 2 seconds per mile for every degree (Celsius) by which shade temperatures exceed 18 deg C.
- If itís humid as well as hot, add 1 second per mile for every percentage point the relative humidity exceeds 65%.
- On a windy day, add 1 second per mile for every mile per hour that the headwind exceeds 10mph : deduct 1 second per mile for every 2mph that the tailwind exceeds 20mph.
- If the race director describes the course as "testing", "undulating", or more honestly "hilly", add anything up to 5 minutes. e.g. the Sheffield course carries a handicap of 3 minutes for the 3 hour runner.
- Now the positive bit. If you average, over the 13 weeks (see 2), one (short) hill times 10 repetition session or one (short) speed session per week, take off 4% from whatever 1 to 4 calculates to. For an average 1Ĺ sessions per week, take off 8%. For 2 hill/speed sessions per week, take off 12%.
- Thatís it. But you can throw it all away by going faster at the start than the calculated pace and trying to put "minutes in the bank". Remember minute banks charge at least 4 times as much for overdrafts as they allow on deposits, every second per mile you run too fast in the first 10 miles will cost you at least 4 seconds per mile in the last 10 miles.
But, I hear you say, "Iím not into running marathons". I guess youíre not into running 100km either, but use the following table to calculate your race pace - and by extension, your finishing time - at distances other than marathons:
Distance Mile 5km 10km l0mi Ĺmar 20mi Mara 100km
Distance (miles) 1.00 3.11 6.21 10.00 13.11 20.00 26.22 62.10
Mile Pace Ratio 1.00 1.05 1.10 1.12 1.15 1.18 1.20 1.37
Use the Top Ten Tips, using just items 1,2,3,4 and 9 to work out what your marathon time would be if you trained for it properly and had no adverse conditions. Divide by 26.22 to give your mile pace for the marathon. Then divide by the "Mile Pace Ratio" 1.2 to tell you what pace you could run a (track) mile if you trained properly for that. Now, select your distance, multiply the track mile pace by the distance in miles and the mile pace ratio, press the buttons on the calculator and youíve got your answer.
E.g. if your marathon time, using the Top Ten Tips, calculates to 3hr 3min, then your 10 mile time calculates as follows
183 * 1.12 * 10.00 = 65.14 mins = 65min 9secs


In this lesson, we will look at how to draw an heart in stages with a pencil.
Draw a rectangle with very thin lines so that its height is slightly less than its width and now mark the middle of each side with dashes.
Next, divide the middle half in half, as shown in the picture. We draw a smooth line from a point that starts just above ¼ of the height and is located in the middle of the rectangle, then connects to certain points that we previously put down.
Draw the same line on the other side. To make it more even, you can draw a line in the middle of the heart and measure the distance from this middle to the line of the heart with a ruler and set aside the same distance on the other side. Do this several times going down, and then connect these points.
We erase all auxiliary lines and paint our hearts red.


We discuss an example of statistical efficiency vs. computational efficiency in the context of shrinkage priors in some high dimensional problems. Most of the material is from the author’s recent joint work (Bhattacharay et al., 2012). The author takes this opportunity to thank his collaborators Anirban Bhattacharya, Debdeep Pati and David Dunson for sharing their valuable insights. He also thanks Andrew Gelman, Eric Laber, Abel Rodriguez and James Scott for helpful discussions, but is solely responsibility for the contents of this blog.
Penalization methods in high dimensional problems, being the flavor of the last decade, have enjoyed much attention resulting in a rich
theoretical literature establishing their optimality properties. There
are also fast algorithms and compelling applied results underlining the
success story of these methods. The overwhelming emphasis has been on
rapidly producing a point estimator with good empirical and theoretical
properties. However, to the best of this author’s knowledge, a
satisfactory theory for uncertainty quantification for penalized
estimators is not yet in place.
Given that most shrinkage estimators correspond to the mode of a
Bayesian posterior, it is natural to ask whether we can use the whole
posterior distribution to provide a probabilistic measure of
uncertainty. The hope is to be able to choose a default shrinkage
prior that leads to similar optimality properties to those shown for
penalization and other approaches, but with the added advantage of the entire posterior distribution concentrating at the
optimal rate, instead of just focusing on the point estimate. Furthermore, taking a Bayesian perspective has distinct advantages in terms of tuning parameter choice, allowing key penalty parameters to be marginalized over the posterior distribution instead of relying on cross-validation. Of course, for the Bayesian methods to be useful for uncertainty quantification, there should exist fast Markov Chain Monte Carlo (MCMC) algorithms to explore these gigantic model spaces. As life would have it, there are theoretically efficient priors for the MCMC algorithm which are slow in high dimensions, and conversely, there are priors for which there exist fast computational algorithms but are not theoretically efficient. The
point is further detailed in a concrete example below.
Point mass priors vs. Shrinkage Priors
For a high-dimensional vector , a natural, time-tested way to incorporate sparsity in a Bayesian framework is to use point mass mixture priors, (1)
where , is the prior guess on model
size (sparsity level), and is an absolutely continuous
density on . It is common to place a beta prior on ,
leading to a beta-Bernoulli prior on the model size, which conveys an
automatic multiplicity adjustment (Scott and Berger, 2010). Let us also
take the model to be, the popular Normal means model (though the
discussion here holds in more generality):
For the model above, Castillo and van der Vaart (2012) established that the posterior corresponding to the prior (1) with an
appropriate beta prior on contracts at the frequentist minimax
rate. Thus at least theoretically, the prior given in
(1) is “hard to beat”. Unfortunately, to simulate
posterior draws corresponding to such priors is not an easy task as the MCMC algorithm has to explore a model space of dimension . This is not feasible even for moderate .
Shrinkage priors (there is an amazing variety of them), often constructed as continuous scale mixtures of Gaussians, are appealing alternatives as they can potentially lead to dramatically more efficient posterior computation. They also allow separate control of the level of sparsity and the size of the signal coefficients. Thus, one formulation of the million dollar question is: What family of shrinkage priors achieves the theoretical efficiency of the point mass priors?
In the recent preprint (Bhattacharya et al., 2012), we give a reasonably satisfactory answer for the above question. One of the main results is that a broad class of Gaussian scale mixture priors, including the
Bayesian Lasso and other commonly used choices such as ridge regression, are sub-optimal for the normal means model, i.e., they do not achieve the same theoretical efficiency as that of the point mass priors.
The key insight obtained in Bhattacharya et al. (2012) is that, the sub-optimal performance of shrinkage priors is due to the lack of borrowing information across coordinates apriori. Indeed, as Polson and Scott (2010) noted, essentially all such shrinkage priors can be represented as global-local (GL) mixtures of Gaussians,
where controls global shrinkage towards the origin while the local scales allow deviations in the degree of shrinkage. Thus the local scales are i.i.d from ; this lack of borrowing from other coordinates hurts the performance.
This is a well documented phenomenon in a related context. Indeed, the famous James-Stein estimator is an example of a superior estimator constructed by borrowing information across coordinates. Recall that this estimator can be considered as the posterior mean of a Bayesian model. Similarly, a high dimensional shrinkage prior which does not impose sufficient dependence across coordinates is not expected to perform well. There is ample evidence of this in Bhattacharya et al. (2012). Note that because of the global scale $\tau$, marginally the coordinate are not independent, but it turns out that the dependence induced by is often weak.
Inspired by the idea of inducing dependence, a new class of priors, called Dirichlet-Laplace (DL) priors, were proposed in Bhattacharya et al. (2012). These priors seem to achieve both optimal theoretical efficiency and efficient posterior simulation. Initial results for DL priors relative to a variety of competitors show promise, though much remains to be done. The DL prior can be written as
where is a suitable density (say the half-Cauchy; see Gelman (2006)). Clearly, the DL prior induces a much stronger dependence at the local scale via the Dirichlet distribution. There
is also an efficient Gibbs sampler which leads to fast posterior simulation. Let me also add that, among the existing shrinkage priors, the horseshoe prior Carvalho et al. (2010) stands out and is very similar in performance to our DL prior. But the horseshoe seems much harder to analyze theoretically.
Have we answered the $1,000,000 Question?
Not yet! What we have done amounts to constructing a shrinkage prior which seems to achieve the same theoretical efficiency as of the point-mass priors. However, the second piece of the puzzle-computational efficiency – is not rigorously studied in the Bayesian shrinkage prior circles. The key reason for this, in my opinion, is the lack of availability of easy to use criteria to measure computational efficiency. For instance, statistical efficiency can be measured in terms of minimax rate, posterior convergence rate, various loss functions etc. On the other hand, for measuring computational efficiency of MCMC algorithms, the only prevalent notion is that of effective sample size (ESS). For most MCMC algorithms, to get exact ESS theoretically is almost impossible for real problems; but even obtaining reasonable bounds is out of reach using state of the art methods.
My point here is that to rigorously answer the efficiency trade-off, some quantitative notion of computational efficiency should be part of the equation. For instance, with in a fixed computational budget, how do the effective sample sizes corresponding two different shrinkage priors with the same statistical efficiency compare? Fortunately, this can be done by simulation and is a low hanging fruit. Again, this question is not often seriously pursued because the notion of fixed computational budget is artificial for moderate sized problems. But for really gigantic problems, which seem to be the flavor of the next decade, I believe the notion of analyzing algorithms with a fixed computational budget and incorporating them into the balance sheet of efficiency for Bayesian procedures will be an important one.
 Anirban Bhattacharya, Debdeep Pati, Natesh S Pillai, and David B Dunson. Bayesian shrinkage. arXiv preprint arXiv:1212.6088, 2012.
 C.M. Carvalho, N.G. Polson, and J.G. Scott. The horseshoe estimator for sparse signals. Biometrika, 97(2):465–480, 2010. 4
 I. Castillo and A. van der Vaart. Needles and straws in a haystack: Posterior concentration for possibly sparse sequences. The Annals of Statistics,
 A. Gelman. Prior distributions for variance parameters in hierarchical models (comment on article by browne and draper). Bayesian analysis, 1(3):515–534, 2006.
 N.G. Polson and J.G. Scott. Shrink globally, act locally: Sparse Bayesian regularization and prediction. In Bayesian Statistics 9 (J.M. Bernardo, M.J.
Bayarri, J.O. Berger, A.P. Dawid, D. Heckerman, A.F.M. Smith and M. West, eds.), pages 501–538. Oxford University Press, New York, 2010.
 J.G. Scott and J.O. Berger. Bayes and empirical-bayes multiplicity adjustment in the variable-selection problem. The Annals of Statistics, 38(5):2587–2619,


I received offer from company that just raised Series A round. I'm trying to determine a method of finding out how much my stock options are worth.
They gave me multiple offers with varying salaries at different options amounts. The problem is that they gave me the options in form of value rather than percentage. For example, 200,000 + 50K options.
I asked for what percent 50K is of the company, but (and yes I know it's not a good sign when a company doesn't share this) but said they can't tell me the percentage of the company the 40K would represent.
They did tell me the strike price (~.65 cents) and the valuation they raised after series A (50 million)
Does this mean that I can calculate my percentage of the company by dividing 50,000/50 million (0.1%)?
At least this is what I was thinking... but then I remembered (from startups I formed in past) that stock options usually come from an option pool (usually around 15-20% of a company).
I'm just trying to figure out the percent I would own (after the vesting). If I know that, I can play around with dilution estimates for future raises and acquisition hypotheticals


You might find yourself in a situation where you need to know how many feet are in 42 inches. You could be working with a designer on a project that requires specific measurements, or perhaps you’re trying to figure out if those old jeans will still fit you. Either way, this article can help you understand everything you need to know about 42 inches in feet.
Every unit of length has its own special name and significance. While it may seem like nothing more than a string of numbers and letters, the beauty of units of measurement is that they are universal across every profession and trade.
The first step towards understanding How Many Feet Are In 42 Inches is learning about the different units of measurement that are available for measuring length.
When you are measuring your body for clothing, it’s helpful to understand how many inches and feet your measurements represent.
This article explains how many feet are in 42 inches so that you can accurately measure your body and compare clothes in the future.
There are multiple units of measurement used to measure height and weight. Depending on where you live and what type of measuring device you use, one unit may be more common than another. It is important to understand the differences between these units of measurement when recording your stats or shopping for new clothes.
What is the definition of an inch?
An inch is a unit of length or distance in several systems of measurement, including in the US Customary Units and British Imperial Units. One inch is defined as 1⁄12 of a foot and is therefore 1⁄36 of a yard. According to the modern definition, one inch is equal to 25.4 mm exactly.
What is the definition of a foot?
A foot is a unit of length defined as 0.3048m exactly and used in the British imperial system of units and United States customary units. It is subdivided into 12 inches and is called an international foot.
How Many Feet are in 42 Inches?
To calculate an inch value to the corresponding value in feet, just multiply the quantity in inch by 0.083333333333333 (the conversion factor). Here is the formula:
Value in feet = value in inch × 0.083333333333333
Suppose you want to convert 42 inches into feet. Using the conversion formula above, you will get:
Value in feet = 42 × 0.083333333333333 = 3 1/2 feet
So that we can say that 42 inches is equal to 3.5 feet.
Relationship between Inches to Feet:
The relationship between Inch to Ft is quite a straightforward one. They are 12 inches in a foot. This means that to convert inches to feet, you just need to divide the value in inches by 12.
Formula: divide the value in inches by 12 because 1-foot is equals to 12 inches.
So, 42 inches = 42/12 = 3 1/2 or 3.5 feet.
If anyone is always confused by math which involves the conversion and measurement units, this article is the best option for her/him for a better understanding of inches to feet conversion. We understand how important it is to know the conversion process for different units nowadays. But unfortunately, it is not always that easy. Therefore, we are making your life easier with this article by explaining the process of conversion, and other factors related to the same.


One of the most frequently used functions in machine learning and data science algorithms are polynomials or functions involving powers of x. It is therefore, important to understand how the derivatives of such functions are calculated.
In this tutorial, you will discover how to compute the derivative of powers of x and polynomials.
After completing this tutorial, you will know:
General rule for computing the derivative of polynomials
General rule for finding the derivative of a function that involves any non-zero real powers of x
Let’s get started.
This tutorial is divided into two parts; they are:
The derivative of a function that involve integer powers of x
Differentiation of a function that has any real non-zero power of x
Derivative of the Sum of Two Functions
Let’s start by finding a simple rule that governs the sum of two functions. Suppose we have two functions f(x) and g(x), then the derivative of their sum can be found as follows. You can refer to the definition of the derivative, in case you need to review it.
Here we have a general rule that says that the derivative of the sum of two functions is the sum of the derivatives of the individual functions.
Derivative of Integer Powers of x
Before we talk about derivatives of integer powers of x, let’s review the Binomial theorem, which tells us how to expand the following expression (here C(n,k) is the choose function):
(a+b)^n = a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + … + C(n,n-1)ab^(n-1) + b^n
We’ll derive a simple rule for finding the derivative of a function that involves x^n, where n is an integer and n>0. Let’s go back to the definition of a derivative discussed in this tutorial and apply it to kx^n, where k is a constant.
Following are some examples of applying this rule:
Derivative of x^2 is 2x
Derivative of 3x^5 is 15x^4
Derivative of 4x^9 is 36x^8
How to Differentiate a Polynomial?
The two rules, i.e., the rule for the derivative of the sum of two functions, and the rule for the derivative of an integer power of x, enable us to differentiating a polynomial. If we have a polynomial of degree n, we can consider it as a sum of individual functions that involve different powers of x. Suppose we have a polynomial P(x) of degree n, then its derivative is given by P'(x) as:
This shows that the derivative of the polynomial of degree n, is in fact a polynomial of degree (n-1).
Some examples are shown below, where the polynomial function and its derivatives are all plotted together. The blue curve shows the function itself, while the red curve is the derivative of that function.
What about Non-Integer Powers of x?
The rules derived above extend to non-integer real powers of x, which can be fractions, negative numbers or irrational numbers. The general rule is given below, where a and k can be any real numbers not equal to zero.
f(x) = kx^a
f'(x) = kax^(a-1)
A few examples are:
Derivative of x^(0.2) is (0.2)x^(-0.8)
Derivative of x^(𝜋) is 𝜋x^(𝜋-1)
Derivative of x^(-3/4) is (-3/4)x^(-7/4)
Here are a few examples, which are plotted along with their derivatives. Again, the blue curve denotes the function itself, and the red curve denotes the corresponding derivative:
This section lists some ideas for extending the tutorial that you may wish to explore.
Rules for derivatives of the product of two functions
Rules for derivatives of rational functions
If you explore any of these extensions, I’d love to know. Post your findings in the comments below.
This section provides more resources on the topic if you are looking to go deeper.
Additional resources on Calculus Books for Machine Learning
Thomas’ Calculus, 14th edition, 2017. (based on the original works of George B. Thomas, revised by Joel Hass, Christopher Heil, Maurice Weir)
Calculus, 3rd Edition, 2017. (Gilbert Strang)
Calculus, 8th edition, 2015. (James Stewart)
In this tutorial, you discovered how to differentiate a polynomial function and functions involving a sum of non-integer powers of x.
Specifically, you learned:
Derivative of the sum of two functions
Derivative of a constant multiplied by an integer power of x
Derivative of a polynomial function
Derivative of a sum of expressions involving non-integers powers of x
Do you have any questions?
Ask your questions in the comments below and I will do my best to answer.
The post A Gentle Introduction to Derivatives of Powers and Polynomials appeared first on Machine Learning Mastery.
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Benefits Of Using an Online Calculator.
Calculator is one of the devices that has really made calculations very simple. Different types of calculators have been invented and for example we have the online calculators and also the physical ones. Online calculators are being used widely nowadays due to the changing technologies in the world. Online calculators are also different for example we have the online calculators used for fractions and we calling online fraction calculator.
Online fraction calculator is greatly being utilized by many people nowadays and this is as a result of the calculation of fractions being very hard for a normal person. Online fraction calculator is a very helpful device in such cases as it makes fraction calculations easier for the people. There are different sites that provide the online fraction calculator for free because what is only needed for a person to have is a good Internet connection.
There are many benefits that the online fraction calculator offers to those people who use them. To start with on the list of the online fraction calculator pros is that it helps in the multiplication, division, addition and subtraction of the various fractions in a very easy way. That being made easy, then all the stresses that people experience when working out fractions are eliminated. There is a need to validate the answers that you get from your calculations and the online fraction calculator provides an option for this.
Online fraction calculator is also beneficial in that you are able to get a step by step on how you will be able to obtain your results in a very easy format. Therefore, you are able to get a very good understanding of how you did all your fractions calculations and also you can easily explain how you arrived at all your answers at ease. This also provides one of the simplest and easiest ways of doing all the fractions calculations that may be hard at sometimes. Another important quality of the online fraction calculator is that it provides examples of how you fractions calculations are done.
To make sure that you learn this very fast and easily, these examples are always very well explained and also I detailed forms. The one who provides numerous illustrations of doing these calculations should be the best. Another distinguishing factor is that you should look for the one that has been providing this service for the longest duration of time and being used by very many people as they are the most reliable one.


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