The Geometry Junkyard | Hacker News Reader

The Geometry Junkyard

ics.uci.edu

103 pointsCorun14 comments

I actually like the term "web pointers" on the page over the traditional [hyper]links, as it's more accurate to what happens in reality: The reference is one-way, without feedback on if what is being referenced changes or disappears entirely.

Case in point, I wanted to check out the "escher in reality" 3D models and got a 404.

It would be fun (but also highly impractical to implement) if the web were garbage collected, with all open windows and bookmarked URLs as root pointers.

IPFS is this

So many dead links! Sad, I would love to poke around a resource like this.

You might have luck on the wayback machine. But some of the links are really, really old: [Inscribing a regular pentagon in a circle – and proving it](https://web.archive.org/web/20001205213400/http://www.cut-th...) fell off the web after 2000!

And some others that are effectively dead, such as the page with the Java applet for Euclid's geometry.

I always liked geometry, but wasn't particularly talented in it. Still, I wonder whether geometry could explain certain algebraic concepts much more intuitively, or even lead to new discoveries that would be extremely difficult to do using math symbols.

A lot of geometric results like trig identities come out most elegantly when stated using complex numbers. I always struggled remembering trig identites until I took complex analysis, and after that class they just seemed totally obvious.

I think "higher dimensional algebra" is some kind of attempt at doing this. String diagrams (for tensor networks) is one example. John Baez has written about this stuff.

Maybe you would love linear algebra?

Why? I do like linear algebra but the way it’s taught in universities is often unintuitive.

Well, if you stand on really strong foundations, you can picture everything that happens in your minds eye. It’s algebra with a geometric twist. Simplest example I can think of now is intersections of planes as solution spaces, thats the picture you could imagine from a bunch of equations. Sorry I had it 4 years ago but at the time I could have written better about it. I used contemporary linear algebra, howard anton. Another simpler example is span, the total space of points that you can get by adding and scaling specific vectors that you have. Imagine an infinite plane created by the configurations of two vectors.

One of the pages talks about a problem he got talking to mathematician on sci.math. Where do mathematicians talk about math and collaborate on problems nowadays?

Either in person, on Math Overflow (https://mathoverflow.net/), or specialist sites like (maybe) the n-category Cafe (https://golem.ph.utexas.edu/category/).

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