Category Archives: pattern

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

Penrose tiles on my refrigerator!

Posted on March 8, 2013 by

I got some Penrose refrigerator magnets in the mail the other day! They look nice on my fridge, don’t you think? Here’s a close-up: (Unfortunately, since this was just a Kickstarter project there’s no way to order more at this … Continue reading →

Posted in geometry, pattern, pictures | Tagged , , , , | 6 Comments

The Steinhaus-Johnson-Trotter algorithm

Posted on January 3, 2013 by

In a previous post I posed the question: is there a way to list the permutations of in such a way that any two adjacent permutations are related by just a single swap of adjacent numbers? (Just for fun, let’s … Continue reading →

Posted in combinatorics, pattern, solutions | Tagged , , , , , | 9 Comments

Visualizing Pascal’s triangle remainders

Posted on October 20, 2012 by

In a comment on my previous post, Juan Valera mentioned something about visualizing multiples of prime numbers in Pascal’s Triangle: In college, there was a poster with different Pascal Triangles, each of them highlighting the multiples of different prime numbers. … Continue reading →

Posted in fractals, modular arithmetic, pascal's triangle, pattern, pictures | Tagged , , | 15 Comments

Visualizing nim-like games

Posted on August 16, 2012 by

Inspired by the comments on this post, I’ve had some ideas brewing for a while—I’m just only now getting around to writing them up. The topic is visualizing winning strategies for "nim-like" games. What do I mean by that? By … Continue reading →

Posted in games, pattern, pictures | Tagged , , , | 4 Comments

Searchable tiling database

Posted on August 2, 2012 by

Just a link today—check out this awesome tiling database! It’s got tons of beautiful plane tilings (with information and further reading about each one) and many ways to search through the database. It’s a great way to find examples of … Continue reading →

Posted in geometry, group theory, links, pattern, pictures | Tagged , , , , | 2 Comments

Picture this

Posted on June 13, 2012 by

Picture this! is a very cool interactive thingy, made by Jason Davies, intended to get students (or anyone, really) thinking about some interesting math. Go play around with it and see if you can answer any of the listed questions … Continue reading →

Posted in challenges, links, pattern, pictures | Tagged , , , | 6 Comments

Fibonacci multiples, solution 1

Posted on June 9, 2012 by

In a previous post, I challenged you to prove If evenly divides , then evenly divides , where denotes the th Fibonacci number (). Here’s one fairly elementary proof (though it certainly has a few twists!). Pick some arbitrary and … Continue reading →

Posted in fibonacci, modular arithmetic, number theory, pattern, pictures, proof, sequences | Tagged , , , | 5 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

17×17 4-coloring with no monochromatic rectangles

Posted on February 9, 2012 by

Quick, what’s special about the following picture? As just announced by Bill Gasarch, this is a grid which has been four-colored (that is, each point in the grid has been assigned one of four colors) in such a way that … Continue reading →

Posted in open problems, pattern, people, pictures | Tagged , , , , , | 5 Comments