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RF Cafe - Mathematical References

RF Cafe - Mathematical References

How to Read Mathematics This article is part of my new book Rediscovering Mathematics, now in paperback! How to Read Mathematics by Shai Simonson and Fernando Gouvea Mathematics is “a language that can neither be read nor understood without initiation.” 1 A reading protocol is a set of strategies that a reader must use in order to benefit fully from reading the text. Mathematics has a reading protocol all its own, and just as we learn to read literature, we should learn to read mathematics. When we read a novel we become absorbed in the plot and characters. Novelists frequently describe characters by involving them in well-chosen anecdotes, rather than by describing them by well-chosen adjectives. Mathematical ideas are by nature precise and well defined, so that a precise description is possible in a very short space. What are the common mistakes people make in trying to read mathematics? Don’t Miss the Big Picture Don’t assume that understanding each phrase, will enable you to understand the whole idea. P: Ok.

Nerd Paradise : Divisibility Rules for Arbitrary Divisors It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number. Here are the rules for 2 through 11... The last digit is divisible by 2. The sum of all the digits in the number is divisible by 3. The last 2 digits are divisible by 4. The last digit is 5 or 0. The number is both divisible by 2 and divisible by 3. Cut the number into 2 parts: the last digit and everything else before that. The last 3 digits are divisible by 8 The sum of all the digits in the number is divisible by 9. The last digit is a 0. Break the number into two parts (like you did for the division by 7 rule). Also there is a quick way for determining divisibility by 11 for 3-digit numbers: If the inner digit is larger than the two outer digits, then it is divisible by 11 if the inner digit is the sum of the two outer digits. Rules for all divisors ending in 1... User Comments: 9 Dividing By 12

Ians Shoelace Site - Shoe Lacing Methods Mathematics tells us that there are more than 2 Trillion ways of feeding a lace through the six pairs of eyelets on an average shoe. This section presents a fairly extensive selection of 50 shoe lacing tutorials. They include traditional and alternative lacing methods that are either widely used, have a particular feature or benefit, or that I just like the look of. 50 Different Ways To Lace Shoes Criss Cross Lacing This is probably the most common method of lacing normal shoes & boots. Over Under Lacing This method reduces friction, making the lacing easier to tighten and loosen plus reducing wear and tear. Gap Lacing This simple variation of Criss Cross Lacing skips a crossover to create a gap in the middle of the lacing, either to bypass a sensitive area on the instep or to increase ankle flexibility. Straight European Lacing This traditional method of Straight Lacing appears to be more common in Europe. Straight Bar Lacing Hiking / Biking Lacing Quick Tight Lacing Ukrainian Lacing- New!

How To Analyze Data Using the Average The average is a simple term with several meanings. The type of average to use depends on whether you’re adding, multiplying, grouping or dividing work among the items in your set. Quick quiz: You drove to work at 30 mph, and drove back at 60 mph. What was your average speed? Hint: It’s not 45 mph, and it doesn’t matter how far your commute is. Read on to understand the many uses of this statistical tool. But what does it mean? Let’s step back a bit: what is the “average” all about? To most of us, it’s “the number in the middle” or a number that is “balanced”. The average is the value that can replace every existing item, and have the same result. One goal of the average is to understand a data set by getting a “representative” sample. The Arithmetic Mean The arithmetic mean is the most common type of average: Let’s say you weigh 150 lbs, and are in an elevator with a 100lb kid and 350lb walrus. Pros: Cons: The arithmetic mean works great 80% of the time; many quantities are added together.

Weierstrass functions Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere". Here is an example of one: It is not hard to show that this series converges for all x. In fact, it is absolutely convergent. Here's a graph of the function. You can see it's pretty bumpy. Below is an animation, zooming into the graph at x=1. Wikipedia and MathWorld both have informative entries on Weierstrass functions. back to Dr.

Lucid Dreaming/Using Dream stabilization[edit] Once you are able to dream lucidly, you may find that it is difficult to stay in the dream; for example, you may wake instantly or the dream may start “fading” which is characterized by loss or degradation of any of the senses, especially vision. Alternatively, a new lucid dreamer could easily forget that they are in a dream, as a result of the shock of the sensation. Don't worry if you wake immediately after becoming lucid. You can avoid more gradual fadings by stimulating your senses. Ideally you should be able to use the techniques below to stabilize your dream before it starts to fade (or “black out”). If you still can’t stabilize your dream, you may decide to try and wake up with the aim of remembering your dream as accurately as possible while its still fresh in your mind. Hand Touching[edit] Rub your hands together and concentrate on the rubbing. Spinning[edit] You spin around in your dream much as you would if you suddenly want to feel dizzy in real life.

6174 (number) 6174 is known as Kaprekar's constant[1][2][3] after the Indian mathematician D. R. Kaprekar. This number is notable for the following property: Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.Subtract the smaller number from the bigger number.Go back to step 2. 9990 – 0999 = 8991 (rather than 999 – 999 = 0) 9831 reaches 6174 after 7 iterations: 8820 – 0288 = 8532 (rather than 882 – 288 = 594) 8774, 8477, 8747, 7748, 7487, 7847, 7784, 4877, 4787, and 4778 reach 6174 after 4 iterations: Note that in each iteration of Kaprekar's routine, the two numbers being subtracted one from the other have the same digit sum and hence the same remainder modulo 9. Sequence of Kaprekar transformations ending in 6174 Sequence of three digit Kaprekar transformations ending in 495 Kaprekar number Bowley, Rover. "6174 is Kaprekar's Constant".

- StumbleUpon The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of sides is The total length of the spiral for an -gon with side length is therefore Consider the solid region obtained by filling in subsequent triangles which the spiral encloses. -gons of side length , is The shaded triangular polygonal spiral is a rep-4-tile. Physics Flash Animations We have been increasingly using Flash animations for illustrating Physics content. This page provides access to those animations which may be of general interest. The animations will appear in a separate window. The animations are sorted by category, and the file size of each animation is included in the listing. In addition, I have prepared a small tutorial in using Flash to do Physics animations. LInks to versions of these animations in other languages, other links, and license information appear towards the bottom of this page. The Animations There are 99 animations listed below. Other Languages and Links These animations have been translated into Catalan, Spanish and Basque: En aquest enllaç podeu trobar la versió al català de les animacions Flash de Física. Many animations have been translated into Greek by Vangelis Koltsakis. Most animations have been translated into Hungarian by Sandor Nagy, Eötvös Loránd University.

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