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
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. It is also an example of a fourier series, a very important and fun type of series. 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.
- 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. Nerd Paradise : Calculating Base 10 Logarithms in Your Head Calculating base 10 logarithms in your head on the fly is a lot easier than you may think. It is simply a matter of memorization and a little estimation... First memorize all the single digit base 10 logs. Don't worry, it's not as painful as it sounds. Remember this rule from high school? And what about this one, you remember it too? Good. Example #1: base 10 log of 400 That's the same thing as log(4*100) which equals log 4 + log 100. log of 4 you know from the table above. Now you may ask, what if it isn't just a number with a bunch of 0's after it? Example #2: base 10 log of 35 Suppose you wanted to find the logarithm of 35. Our guess: 1.545 Calculator says: 1.544068... Now you can convince all your friends and teachers that you are autistic. Example #3: base 10 log of 290438572: This is fairly close to log(2.9 * 100000000) = log 2.9 + log 108 2.9 is close to 3. Our Guess: 8 + .45 = 8.45 Calculated Answer: 8.46305... Now run off and scare some people with your new powers. User Comments: 14 Fixed.
- StumbleUpon New Mayan calendar discovered: world won't end in 2012 Earth has a new reason to celebrate. It's looking like we will make it past Dec. 21, 2012. According to LiveScience, researchers have unearthed the oldest-known version of the ancient Maya calendar in the Guatemalan rainforest. Archaeologist David Stuart of the University of Texas, who worked to decipher the glyphs, told LiveScience the calendar does not mark the end of the world. According to SFGate the calendar, which is said to be exquisitely preserved, was found in a 1,000-year-old house in Guatemala. More from GlobalPost: Mexico uses Mayan doomsday prediction to lure tourists The newly discovered astronomical tables are at least 500 years older than those preserved in the Maya codices, said Science magazine. The ninth-century structure was first found in 2010, according to SFGate, by Max Chamberlain, a student of Saturno. Saturno was extremely excited about their find. More from GlobalPost: 1 in 10 of your friends may be counting down to the end of the world
Poker -- from Wolfram MathWorld Poker is a card game played with a normal deck of 52 cards. Sometimes, additional cards called "jokers" are also used. In straight or draw poker, each player is normally dealt a hand of five cards. Depending on the variant, players then discard and redraw cards, trying to improve their hands. Bets are placed at each discard step. The number of possible distinct five-card hands is equal to the number of possible ways of picking five cards out of a deck of 52, namely where is a binomial coefficient. There are special names for specific types of hands. The probabilities of being dealt five-card poker hands of a given type (before discarding and with no jokers) on the initial deal are given below (Packel 1981). denotes a binomial coefficient. are Gadbois (1996) gives probabilities for hands if two jokers are included, and points out that it is impossible to rank hands in any single way which is consistent with the relative frequency of the hands.
Mathematical Atlas: A gateway to Mathematics Welcome! This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions. The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages"). To reach the best page for your interests, use whichever of these navigation tools ("purple pages") you prefer: For resources useful in all areas of mathematics try 00: General Mathematics. There is a backlog of articles awaiting editing before they are referenced in the blue pages, but you are welcome to snoop around VIRUS WARNING: The Mathematical Atlas receives but does not send mail using the math-atlas.org domain name. Please bookmark any pages at this site with the URL This URL forces frames; for a frame-free version use
Methods for Studying Coincidences One of my favorite mathematics papers of all time is called “Methods for Studying Coincidences.” By Persi Diaconis and Frederick Mosteller, it aims to provide a rigorous mathematical framework for the study of coincidences. Using probabilistic analysis, the paper explores everything from why we see newly learned words almost immediately after first learning them, to why double lottery winners exist, to even the frequency of meeting people with the same birthday. For example, when it comes to newly learned words, we are often astonished that as soon as we learn a new word, we begin to see it quite frequently, or at least soon after we learn it. Their analyses hinge on something that we often forget: while something might seem astonishing and a remarkable coincidence, if enough people are involved, chances are very good that one of them will have something “coincidental” happen to them. With a large enough sample, any outrageous thing is likely to happen.
Prime Time - Mathematicians have tried in vain to this day to discoversome oreder inthe sequence of prime numbers... An Overview of Cryptography As an aside, the AES selection process managed by NIST was very public. A similar project, the New European Schemes for Signatures, Integrity and Encryption (NESSIE), was designed as an independent project meant to augment the work of NIST by putting out an open call for new cryptographic primitives. NESSIE ran from about 2000-2003. While several new algorithms were found during the NESSIE process, no new stream cipher survived cryptanalysis. As a result, the ECRYPT Stream Cipher Project (eSTREAM) was created, which has approved a number of new stream ciphers for both software and hardware implementation. CAST-128/256: CAST-128, described in Request for Comments (RFC) 2144, is a DES-like substitution-permutation crypto algorithm, employing a 128-bit key operating on a 64-bit block. A digression: Who invented PKC? 3.3. Let me reiterate that hashes are one-way encryption. A digression on hash collisions.
- StumbleUpon Perpetual Futility A short history of the search for perpetual motion. by Donald E. Simanek Popular histories too often present perpetual motion machines as "freaks and curiosities" of engineering without telling us just how they were understood at the time. Sometimes a particular device comes to us with a label, such as "Bishop Wilkins' magnetic perpetual motion machine." Bhaskara's Wheels. Villard de Honnecourt was born in the late 12th century and probably lived and worked in the north of France from 1225 to 1250. The most celebrated of his machine designs was for a perpetual motion wheel. Many a time have skilful workmen tried to contrive a wheel that should turn of itself; here is a way to make such a one, by means of an uneven number of mallets, or by quicksilver (mercury). The reference to quicksilver (mercury) indicates that Villard was familiar with the Bhaskara device, whose design had reached Europe. Mariano di Iacopo, called Taccola (Siena, 1382-1458?) 56. That's it.
A new formula for avoiding supermarket queues Supermarket queues are dreaded by many. In the TV series ‘Supernatural’, people standing in an endless queue are used as an example of what hell really looks like. (Photo: Colourbox) In researcher Kebin Zeng’s office hangs a big whiteboard filled with mathematical formulas and functions. Complicated as it looks, it’s all about solving everyday problems such as supermarket queues. ”You could say that I convert everyday life into mathematical models. His research, which is supported by MT-LAB, aims to improve on the existing mathematical models that calculate the probability of queues in places such as supermarkets or post offices. “It will for instance be possible to use our models to create an iPhone app that tells you the ideal time to go shopping if you want to avoid long queues,” he says. For an example of how to calculate supermarket queues, see the box below this article. Sorting out phone queues Kebin Zeng A handy scheduling tool It’s all about probability Software free for all