Monthly Archives: February 2016

Fibonacci numbers are golden

Recall that a “golden number” (this is not standard terminology) is a number such that one (or both) of or is a perfect square. In this post, I’ll explain Gessel’s proof that every Fibonacci number is golden. First, we need … Continue reading

Posted in arithmetic, computation, famous numbers, fibonacci, proof | Tagged , , , , , | 1 Comment

Testing Fibonacci numbers: the proofs

In my last post I stated this surprising theorem: is a Fibonacci number if and only if one of is a perfect square. If one of is a perfect square, then let’s say that is a “golden number” (a nod, … Continue reading

Posted in arithmetic, computation, famous numbers, fibonacci, proof | Tagged , , , | 1 Comment

Testing Fibonacci numbers

From a recent post on Brian Hayes’ blog, bit-player, I learned the following curious fact: is a Fibonacci number if and only if either or is a perfect square. Recall that the Fibonacci numbers begin where each number is the … Continue reading

Posted in arithmetic, computation, famous numbers, fibonacci | Tagged , , , | 8 Comments

Network reliability

Over on my other blog I’ve started writing about an interesting but apparently nontrivial problem, which some readers of this blog may find interesting as well. Suppose you have a network of computers with some one-directional wires between them. Each … Continue reading

Posted in links, probability | Tagged , , , | 2 Comments

An amazingly symmetric icosahedron edge coloring

In my last post I showed off the stellated icosahedron I made out of folded paper: I also claimed that it uses a very particular and elegant color scheme. When I set out to make it, I did some googling … Continue reading

Posted in geometry, pattern | Tagged , , , , , , , ,

Origami stellated icosahedron!

Continuing what I started in December, I finally finished making a stellated icosahedron out of 30 Sonobe units. Each Sonobe unit corresponds to an edge of the icosahedron, and interlocks with three others to give the whole thing a remarkable … Continue reading

Posted in geometry, group theory | Tagged , , , , , | 4 Comments

Post without words #5, explained

If you stared for a while at the images in my previous post, you probably noticed some patterns, and maybe you even figured out some sort of rule or algorithm behind them. Commenter Yammatak expressed it as “You split it … Continue reading

Posted in pattern, pictures, posts without words, sequences, solutions | Tagged , , , , , | 4 Comments