Going through some Beast Academy level 1 with my 7yo this summer, looking forward to seeing how they cover category theory.

I haven't seen *nearly* enough here, and almost nothing from the !! So here are some of my most-visited pages, according to my browser history.

ncatlab.org/nlab/show/Thomason

(weak equivalences created by taking nerves)

ncatlab.org/nlab/show/multicat

(morphisms can have n-ary source for n > 1)

ncatlab.org/nlab/show/simplici

(combinatorial version of topological space)

ncatlab.org/nlab/show/Grothend

(convert a general functor into a fibration of slice categories)

Another cat picture!

This is another picture from early in the pandemic. She's back from exploring builders' progress on our back deck. This was *just* before supply chain shortages started hitting our area; back when a person could just go to the lumber store and get normal amounts of lumber at normal prices. Wild times.

Posting more cat pictures as a treat. This one is from early in the pandemic, which I now realize was two years ago. Around that time she started a new behavior: periodically screaming VERY LOUDLY!! Relatable, but we eventually realized it's because she's gone deaf! Old girl no longer has a sense of how loud she is. But she does still have a clear sense of when she wants attention and/or food :/

My mother somehow got ostrich and emu eggs for decorating a few weeks ago, and I think they turned out great! (Certainly not perfect, but enjoyable.) We had a blast.

I appreciate the posts that people are writing! But I don't like writing my own!! Anyway, I'll try.

I'm a research mathematician, interested in social media for both professional and recreational reasons. If you follow me, you'll see a mix of math and non-math.

Here are four pictures of things I've been involved in. I'll add a little more in a comment below.

Good morning all. Here's another picture of our cat enduring our attention.

As a special treat for people migrating from the bird site, here's a picture of my cat, Willow, seated at a tea party my daughter set up. Willow is very small, but is about 16 years old.

Pythagorean Theorem

0. Subdivide a right triangle into two smaller right triangles.

1. $$\alpha+\tau = 90 = \sigma+\tau$$ so $$\alpha = \sigma$$. Likewise $$\beta = \tau$$.
Hence the three triangles are similar.

2. By similarity,
$\frac{s}{a}=\frac{a}{c}, \quad \frac{t}{b} = \frac{b}{c}.$

3. By construction $$c = s + t$$.

4. Combining these, we have
$c = \frac{a^2}{c} + \frac{b^2}{c},$
therefore
$c^2 = a^2 + b^2.$

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