Euclid's Orchard, the Euclidean algorithm, and Fibonacci numbers, with pretty pictures: mathlesstraveled.com/2017/07/2 mathstodon.xyz/media/JemTCvyUm

Here's a better one with a white background instead of transparent. I wish there were a way to preview toots before posting. mathstodon.xyz/media/fePe1dPgQ

The first AlphaGo - Ke Jie match was exquisite. Definitely worth staying up until 2am my local time to watch the whole thing, though I fear doing that for all the matches is not really feasible, sleep-wise.

Super excited for the first match of Ke Jie vs AlphaGo tonight (2:30am UTC). events.google.com/alphago2017/

mathlesstraveled.com/2017/05/1 Contemplating how the existence of symmetric Venn diagrams relates to the existence of symmetric planar embeddings of hypercube graphs...

@jeffgerickson You probably hear this a lot, but thanks so much for making all your algorithms notes and assignments available. I just finished teaching my second iteration of an undergraduate algorithms course, and being able to draw on your collection of homework and exam problems made my job a lot easier!

Let $$G$$ be a graph with $$|V|=n$$. Any two of the following imply the third: 1. $$G$$ is connected; 2. $$G$$ is acyclic; 3. $$G$$ has $$n-1$$ edges.

1,2 => 3: by induction. Any walk must reach a leaf. Delete it and apply the IH.

1,3 => 2: by induction. Sum of degrees is $$2(n-1)$$, so there are at least two leaves. Delete one and apply the IH.

2,3 => 1: Let $$G$$ have $$c$$ connected components. Since 1,2 => 3 for each, the total number of edges is $$n-c$$, hence $$c=1$$.

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