Category Archives: arithmetic

Animated Sieve of Eratosthenes

Posted on April 11, 2013 by

Here’s something I made yesterday! (Note, I strongly suggest watching it fullscreen, in HD if you have the bandwidth for it.) Can you figure out what’s going on? The source code for the animation is here; I was inspired by … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, video | Tagged , , , , | 11 Comments

Factorization diagram cards: help?

Posted on February 5, 2013 by

The other day I got a lovely email from Malke Rosenfeld thanking me for creating factorization diagrams and linking me to her blog post about “factor dominoes”: she printed out some factorization diagrams, glued them to cardstock, and used the … Continue reading →

Posted in arithmetic, pictures, primes | Tagged , , , | 2 Comments

Mersenne primes and the Lucas-Lehmer test

Posted on January 17, 2013 by

Mersenne numbers, named after Marin Mersenne, are numbers of the form . The first few Mersenne numbers are therefore , , , , , and so on. Mersenne numbers come up all the time in computer science (for example, is … Continue reading →

Posted in arithmetic, computation, famous numbers, iteration, modular arithmetic, number theory, primes | Tagged , , , , | 3 Comments

More factorization diagrams

Posted on November 5, 2012 by

My post on factorization diagrams from a month ago turned out to be (unexpectedly) quite popular! I got ten times as many hits as usual the day it was published, and since then quite a few other people have created … Continue reading →

Posted in arithmetic, links, pictures, primes, programming, recursion | Tagged , , | 15 Comments

Factorization diagrams

Posted on October 5, 2012 by

In an idle moment a while ago I wrote a program to generate "factorization diagrams". Here’s 700: It’s easy to see (I hope), just by looking at the arrangement of dots, that there are in total. Here’s how I did … Continue reading →

Posted in arithmetic, pictures, primes, programming, recursion | Tagged , , | 72 Comments

Fibonacci multiples

Posted on May 15, 2012 by

I haven’t written anything here in a while, but hope to write more regularly now that the semester is over—I have a series on combinatorial proofs to finish up, some books to review, and a few other things planned. But … Continue reading →

Posted in arithmetic, challenges, fibonacci, number theory, pattern | Tagged , | 12 Comments

Differences of powers of consecutive integers, part II

Posted on February 16, 2012 by

If you spent some time playing around with the procedure from Differences of powers of consecutive integers (namely, raise consecutive integers to the th power, and repeatedly take pairwise differences until reaching a single number) you probably noticed the curious … Continue reading →

Posted in arithmetic, iteration, pascal's triangle | Tagged , , , , | 3 Comments

Computing with decadic numbers

Posted on January 30, 2012 by

[This is the ninth, and, I think, final in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does "close to" mean?, The decadic metric, Infinite decadic numbers, More … Continue reading →

Posted in arithmetic, programming | Tagged , , | 2 Comments

Differences of powers of consecutive integers

Posted on January 29, 2012 by

Patrick Vennebush of Math Jokes 4 Mathy Folks recently wrote about the following procedure that yields surprising results. Choose some positive integer . Now, starting with consecutive integers, raise each integer to the th power. Then take pairwise differences by … Continue reading →

Posted in arithmetic, pattern | Tagged , , , , | 16 Comments

A self-square number

Posted on January 4, 2012 by

[This is the seventh in a series of posts on the decadic numbers (previous posts: A curiosity, An invitation to a funny number system, What does "close to" mean?, The decadic metric, Infinite decadic numbers, More fun with infinite decadic … Continue reading →

Posted in arithmetic, infinity, iteration, modular arithmetic, proof | Tagged , , , | 12 Comments