Architect of Ideas - Welcome to Organised Chaos

October 17, 2024

She has over fifty times as many subscribers as I do, so she must be doing something right!

See Architect of Ideas - Some Thoughts About Calculus and Infinity.

Oh wow, she beat me. I was just planning to do a video and started browsing through Chapter 10 of Eugenia Cheng's The Joy of Abstraction.

Here's a Google play video reading "Measurement". It goes on talk about measuring without using units at all.

A year ago, she was reading Lockhart's A Mathematician's Lament:

She only posted this today, but it was recorded on November 11, 2023.

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Here's Paul Lockhart with A Great Idea

Subscribe to Harvard University Press.

Daniel Tubbenhauer on The Wallpaper Groups. He says that only 14 of the 17 are found in the Alhambra.

Subscribe to Visual Math.

But they all can be found on walls around Lisbon in Portugal:

Subscribe to Wolfgang Gross.

Now I can watch Janet's video from yesterday!

My comment:

There's a story about this spiral way of writing the whole numbers. I think it's called "the Ulam spiral" after a guy called Stanislaw Ulam who was sitting a math lecture one day, and it was a bit boring, so he wasn't really listening. He just started with your first spiral of the numbers 1,2,3,4,5,... going around the central point and spiraling outwards. Then he shaded in the prime numbers and he noticed something, which is that there were several diagonal lines on a kind of diamond-shaped grid pattern, which had far more primes on them than all the others. So he wrote down a recursive formula for those lines and they allowed him to find a lot of prime numbers very quickly, because the prime numbers were more dense on those lines than they are on the number line. Check "Ulam spiral" on Wikipedia to see some computer drawings. There's also a version with a triangular spiral with vertical lines of primes that was discovered earlier. And there are hexagonal ones too.