Touch Mathematics 10 Easy Arithmetic Tricks Technology Math can be terrifying for many people. This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head. 1. The 11 Times Trick We all know the trick when multiplying by ten – add 0 to the end of the number, but did you know there is an equally easy trick for multiplying a two digit number by 11? Take the original number and imagine a space between the two digits (in this example we will use 52: Now add the two numbers together and put them in the middle: That is it – you have the answer: 572. If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first: 1089 – It works every time. 2. If you need to square a 2 digit number ending in 5, you can do so very easily with this trick. 252 = (2x(2+1)) & 25 2 x 3 = 6 3. Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex – or does it? 2682 x 5 = (2682 / 2) & 5 or 0 4. 5.
Lots of Jokes - Funny Jokes, Pictures and Videos Hammack Home This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews. The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. Part I: Fundamentals Part II: How to Prove Conditional Statements Part III: More on Proof Part IV: Relations, Functions and Cardinality Thanks to readers around the world who wrote to report mistakes and typos! Instructors: Click here for my page for VCU's MATH 300, a course based on this book. I will always offer the book for free on my web page, and for the lowest possible price through on-demand publishing.
New Pattern Found in Prime Numbers (PhysOrg.com) -- Prime numbers have intrigued curious thinkers for centuries. On one hand, prime numbers seem to be randomly distributed among the natural numbers with no other law than that of chance. But on the other hand, the global distribution of primes reveals a remarkably smooth regularity. This combination of randomness and regularity has motivated researchers to search for patterns in the distribution of primes that may eventually shed light on their ultimate nature. In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad Politécnica de Madrid in Spain have discovered a new pattern in primes that has surprisingly gone unnoticed until now. “Mathematicians have studied prime numbers for centuries,” Lacasa told PhysOrg.com. Benford’s law (BL), named after physicist Frank Benford in 1938, describes the distribution of the leading digits of the numbers in a wide variety of data sets and mathematical sequences. “BL is a specific case of GBL,” Lacasa explained.
Contents, Interactive Mathematics Miscellany and Puzzles Since May 6, 1997You are visitor number E66B7E in base 20 Raymond Smullyan, a Mathematician, Philosopher and author of several outstanding books of logical puzzles, tells, in one of his books, a revealing story. A friend invited him for dinner. He told Smullyan that his teenage son was crazy about Smullyan's books and could not wait to meet him. The friend warned Smullyan not to mention that he is a Mathematician and that Logic is a part of Mathematics because the young fellow hated Mathematics. Having told this story, would it be wise to announce up front what this site is about? |Contact||Front page||Index||Store|
K-MODDL & Tutorials & Reuleaux Triangle If an enormously heavy object has to be moved from one spot to another, it may not be practical to move it on wheels. Instead the object is placed on a flat platform that in turn rests on cylindrical rollers (Figure 1). As the platform is pushed forward, the rollers left behind are picked up and put down in front. An object moved this way over a flat horizontal surface does not bob up and down as it rolls along. Is a circle the only curve with constant width? How to construct a Reuleaux triangle To construct a Reuleaux triangle begin with an equilateral triangle of side s, and then replace each side by a circular arc with the other two original sides as radii (Figure 4). The corners of a Reuleaux triangle are the sharpest possible on a curve with constant width. Other symmetrical curves with constant width result if you start with a regular pentagon (or any regular polygon with an odd number of sides) and follow similar procedures. Figure 1: Platform resting on cylindrical roller
9 Mental Math Tricks Math can be terrifying for many people. This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head. 1. Multiplying by 9, or 99, or 999 Multiplying by 9 is really multiplying by 10-1. So, 9×9 is just 9x(10-1) which is 9×10-9 which is 90-9 or 81. Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414. One more example: 68×9 = 680-68 = 612. To multiply by 99, you multiply by 100-1. So, 46×99 = 46x(100-1) = 4600-46 = 4554. Multiplying by 999 is similar to multiplying by 9 and by 99. 38×999 = 38x(1000-1) = 38000-38 = 37962. 2. To multiply a number by 11 you add pairs of numbers next to each other, except for the numbers on the edges. Let me illustrate: To multiply 436 by 11 go from right to left. First write down the 6 then add 6 to its neighbor on the left, 3, to get 9. Write down 9 to the left of 6. Then add 4 to 3 to get 7. Then, write down the leftmost digit, 4. So, 436×11 = is 4796. Let’s do another example: 3254×11. 3. 4. 5.
A Non-Mathematical Introduction to Using Neural Networks The goal of this article is to help you understand what a neural network is, and how it is used. Most people, even non-programmers, have heard of neural networks. There are many science fiction overtones associated with them. Most laypeople think of neural networks as a sort of artificial brain. Neural networks are one small part of AI. The human brain really should be called a biological neural network (BNN). There are some basic similarities between biological neural networks and artificial neural networks. Like I said, neural networks are designed to accomplish one small task. The task that neural networks accomplish very well is pattern recognition. Figure 1: A Typical Neural Network As you can see, the neural network above is accepting a pattern and returning a pattern. Neural Network Structure Neural networks are made of layers of similar neurons. The input and output patterns are both arrays of floating point numbers. Programming hash tables use keys and values. A Simple Example
Maths Online - Free Maths Tuition For All Australian High School Students Relplot: equation plotter Relplot constructs high-resolution PostScript or PDF plots of the solutions to equations on two variables. Unlike most other plotters, it can handle general equations and inequations, not just functions, and it can plot multiple equations at once. What can you plot? Multiple equations/formulas separated by commas: ,Logical operators for combining formulas: && & ||Relational operators: = < <= > >=Binary arithmetic ops: + * - / ^ modUnary arithmetic ops: |x| sqrt floor exp ln sin cos tan asin acos atan atan2 sinh cosh tanhBuilt-in variables: x y r thConstants: pi e 2 -.5 1.4e5 .7e01 πUser-defined function applications: f(e1,..., en)User-defined variables: a-z x^3 + y^3 = 3xy, r^2 = 9/2 Some interesting equations to try: Got feedback? Relplot was written by Andrew Myers at Cornell University.
An Introduction to Neural Networks Prof. Leslie Smith Centre for Cognitive and Computational Neuroscience Department of Computing and Mathematics University of Stirling. lss@cs.stir.ac.uk last major update: 25 October 1996: minor update 22 April 1998 and 12 Sept 2001: links updated (they were out of date) 12 Sept 2001; fix to math font (thanks Sietse Brouwer) 2 April 2003 This document is a roughly HTML-ised version of a talk given at the NSYN meeting in Edinburgh, Scotland, on 28 February 1996, then updated a few times in response to comments received. Please email me comments, but remember that this was originally just the slides from an introductory talk! Why would anyone want a `new' sort of computer? What is a neural network? Some algorithms and architectures. Where have they been applied? What new applications are likely? Some useful sources of information. Some comments added Sept 2001 NEW: questions and answers arising from this tutorial Why would anyone want a `new' sort of computer? Good at Not so good at Fast arithmetic
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