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Drawing a truncated cube and a cuboctahedron from a cube....
As for understanding truncation: You can imagine having a cheese cube and just cutting of the vertices...
- - -- --- -----
Truncated cubes and cuboctahedra are Archimedian solids.
----- --- -- - -
I used isometric dot paper.
I bought a bag of these snacks... mainly because they are hexagonal (and also because I am hungry - and the pretty hexagonal shape makes them more appealing to me)
a tiny möbius strip I created with a simple plugging method and foil.
Crafting and assembling this tiny möbius strip with 14 pairs of "plugging cuts" and the plugging method was quite easy - But doodling an explanation of the assembly is FAR from easy!
How the fuck do I simplify my reasoning and explain that in a simple manner?
For now I give up. That is the awful unsorted ideas I scribbled down today.
I might consider splitting it in multiple steps and rethink how I name the points. In todays scribbles its just a confusing mess and is not helpful for explaining it. (I also make it more complicated than it actually is)
Splitting into multiple steps:
1st: How to create the base strip (where the cuts go.)
2nd: assembly
2.1 (the merely simple basics) of this plugging method
2.2 möbius strip versus torus - how to assembly this strip and how NOT to.
i’ve been learning about automatic differentiation but i don’t get how to implement it. you need a number e such that e ≠ 0 but e² = 0. So okay, number had. Then all numbers of form a + be are dual numbers. Alright.
Now f(a + be) = f(a) + bf’(a)e
Er... alright? I understand why this works for polynomials, presumably the reason it works for everything else is because you can break analytic functions into polynomials, eg by taylor series.
But how do you implement this? What is b? Do you need to know the derivative of cosine, sine already? Etc
Computing integrals, derivatives in haskell.
Integral is slow as fuck, since literally you add 0.00001 of something several times
Technically his original conjecture remains unproven. The famous one is actually just over rational numbers. His original conjecture is over all number fields. They just got around to proving that it holds for real quadratic fields.
That’s... even sadder. Though I think it underlines how impressive his original conjecture was that a weaker version is... major enough to have an entire course devoted to explaining it. But still. Almost.. jeez, what is it now? Almost sixty years have elapsed, and they’re still hacking away at the original problem.
:(
...I won’t say that invalidates what he did, because I know the painful way that it’s much easier to have an insight and call it than to act upon it. So his ‘loss of confidence in his future’ might well have been rational, as a judgment that he knew the sort of things that he wanted to do and... knew also that he couldn’t do it.
...that’s very sad...
No, it’s not significant, but it’s very sad. People mourn the death of celebrities. This is the local equivalent for my field. He would be turning 88 this year. His collaborator, Shimura, is still going strong at 85, so... it’s just very surprising. And sad.
...that’s very sad. I’m sorry, that’s just very sad.
And no, that feeling can’t be generalized to myself, because this is someone who came up with a revolutionary conjecture and I’m a nothing. Would I feel the same way if he wasn’t the author of the Taniyama-Shimura-Weil conjecture? ...probably not, speaking somberly. Were this before the conjecture was proved -- that is, were it still a controversial conjecture that seemed out of reach of current techniques -- it probably wouldn’t seem so tragic. Or at least it would be tragic in some dramatic, sensationalized way of ‘the conjecture left behind by that guy who committed suicide’ or some other thing. Because he was vindicated and now it’s an established, important result, it just seems... stunning. I knew nothing about the name save what he had done, and now I find out there wasn’t much more to know -- except that he had committed suicide. That’s... very sad...
