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Someone posted a gif of this effect on birdsite and I wanted to understand it so I've built it as a space-warping raymarcher.

Its some lovely maths that I think I *mostly* understand now:

A problem shared is equal to the sum of the problems on the other two sides.

@11011110 @andrewt fun fact. there's an exact formula for how many x,y satisfy xΒ²+yΒ²=n. it's 4 times (the number of factors of n of the form 4k+1 - the number of factors of n of the form 4k+3). another fun fact: this ties into the average being Ο€ through the Taylor expansion of arctan(1)=Ο€/4

My latest bloggy thing:

As always, comments, thoughts, criticisms, and feedback, all welcome.

Have to say that this "one blog post per week" is a brutal schedule.

Also, here's a maths puzzle for Ο€-day:

Adding the brackets from this Alex Bellos column to the numbers 1, 2, 3, 4 β€”

[1, 2] β†’ 12
⟨1, 2⟩ β†’ 21
⟨[⟨1, 2⟩, 3], 4⟩ β†’ ⟨[21, 3], 4⟩ β†’ ⟨213, 4βŸ©β†’ 4213

…we can make any number except 2413, and which other?

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This is a nice little trick but a bafflingly poor article. How can anyone write an entire article about a single tweet without having understood the tweet?

This would make a strong contender in the MathsJam bake off.

Also v good doggo in VR, which is a plus

Further evidence the tiny L-P is a mathematician, at bathtime last night:

* holding a bottle full of water *
"Can you put some water in the jug, please?"
* stands bottle upright in jug, spilling none *

Must learn to speak more precisely __to my 1 year old__

Here’s a video on simulating a non-euclidean space in virtual reality with ray marching. This project is joint work with Michael Woodard and Roice Nelson.

Made a snowdecahedron. Not as nice as some people on the web, but still, I deserve a beer.

This embroidered computer is lovely. I think it works by the gold coils over the large beads being magnetically drawn to one side or the other of the base β€” and therefore making different connections β€” depending on whether or not a current is flowing through them.

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