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

Tanya Khovanova’s Math Blog » Blog Archive » Divisibility by 7 is a Walk on a Graph, by David Wilson My guest blogger is David Wilson, a fellow fan of sequences. It is a nice exercise to understand how this graph works. When you do, you will discover that you can use this graph to calculate the remainders of numbers modulo 7. Back to David Wilson: I have attached a picture of a graph. Write down a number n. For example, if n = 325, follow 3 black arrows, then 1 white arrow, then 2 black arrows, then 1 white arrow, and finally 5 black arrows. If you end up back at the white node, n is divisible by 7. Nothing earth-shattering, but I was pleased that the graph was planar.

Microparticles allow you to live without breathing Although it may seem like science fiction, a Boston research group has developed a type of microparticles which can be injected directly into the bloodstream to oxygenate your body quickly … even if we could not breathe. An extraordinary advancement in medicine that could help to save millions of lives in a year. According to the doctors, this development would allow medical teams to keep patients alive 15 to 30 minutes even though they may have severe respiratory failure. A time for medical teams in which they could act without risk for a heart attack or permanent brain injury. The first tests in animals are completed with a success. And from what these particles are composed? Particles of oxygen acids of two to four microns in size. According to John Kheir, principal investigator who solved the problem using deformable particles: We have engineered around this problem by packaging the gas into small, deformable particles. Via: ScienceDaily

Math doesn't suck, you do. Every time I hear someone say "I suck at math," I immediately think he or she is a moron. If you suck at math, what you really suck at is following instructions. This shirt is birth control. Sucking at math is like sucking at cooking. Math is exactly like cooking: just follow the recipe. Math isn't some voodoo that only smart people understand. Theoretical math is cool as shit. Ever heard of Pascal's triangle? No, because you're too busy saying the same tired excuse every other dickhead spews out about math: "when will I ever use this in life?" First of all, if you're leading your life in such a way that you never have to do math, congratulations, you are a donkey. Why is math the only discipline that has to put up with this bullshit? But when it comes to math, everyone turns into a big pussy and starts PMSing all over the place. People didn't invent this stuff because they were bored. Don't like it?

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. 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".

Metamath Home Page 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. It can be shown that the function is continuous everywhere, yet is differentiable at no values of x. 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.

Animated Bézier Curves Play with the control points to modify the curves! These animations illustrate how a parametric Bézier curve is constructed. The parameter t ranges from 0 to 1. In the simplest case, a first-order Bézier curve, the curve is a straight line between the control points. For a second-order or quadratic Bézier curve, first we find two intermediate points that are t along the lines between the three control points. Then we perform the same interpolation step again and find another point that is t along the line between those two intermediate points. Written using the D3 visualisation library. Requires a SVG-capable browser e.g. © Jason Davies | Privacy Policy.