Tag Archives: tree

Post without words #23

Posted on October 29, 2018 by Brent
Posted in pattern, pictures, posts without words | Tagged , , , | 11 Comments

Now on mathstodon.xyz

Posted on May 16, 2017 by Brent

Christian Lawson-Perfect and Colin Wright have set up an instance of Mastodon—a decentralized, open-source Twitter clone—as a place for mathy folks to be social. It’s appropriately named mathstodon.xyz, and because it’s open-source they were able to easily hack in support. … Continue reading →

Posted in meta, proof | Tagged , , , , , , | 3 Comments

Computing optimal play for the greedy coins game, part 4

Posted on May 12, 2017 by Brent

Last time I explained a method for computing best play for instances of the greedy coins game, which is feasible even for large games. This general approach is known as dynamic programming and is applicable whenever we have some recursively … Continue reading →

Posted in computation, games, recursion | Tagged , , , , , , , , , , , | Comments Off on Computing optimal play for the greedy coins game, part 4

Computing optimal play for the greedy coins game, part 3

Posted on May 10, 2017 by Brent

In a previous post we saw how we can organize play sequences in the greedy coins game into a tree. Then in the last post, we saw how to work our way from the bottom of the tree upward and … Continue reading →

Posted in computation, games, recursion | Tagged , , , , , , , , , | 2 Comments

Computing optimal play for the greedy coins game, part 2

Posted on May 4, 2017 by Brent

I want to explain in more detail how we can think about computing the best possible score for Alice in the greedy coins game, assuming best play on the part of both players. I glossed over this too quickly in … Continue reading →

Posted in computation, games, recursion | Tagged , , , , , , , , , | 1 Comment

Apollonian gaskets

Posted on April 27, 2016 by Brent

In my last post I showed off this tantalizing picture: This pattern of infinitely nested circles is called an Apollonian gasket. Over the next post or two I’ll explain some cool math behind actually constructing them. Mostly I will state … Continue reading →

Posted in geometry, pattern, pictures, recursion | Tagged , , , | 4 Comments

The hyperbinary sequence and the Calkin-Wilf tree

Posted on October 18, 2009 by Brent

And now, the amazing conclusion to this series of posts on Neil Calkin and Herbert Wilf’s paper, Recounting the Rationals, and the answers to all the questions about the hyperbinary sequence. Hold on to your hats! The Calkin-Wilf Tree First, … Continue reading →

Posted in arithmetic, computation, induction, iteration, number theory, pattern, proof, recursion, sequences, solutions | Tagged , , , , , , | 6 Comments