[HN Gopher] The Geometry Junkyard
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       The Geometry Junkyard
        
       Author : Corun
       Score  : 74 points
       Date   : 2022-10-17 16:30 UTC (6 hours ago)
        
 (HTM) web link (www.ics.uci.edu)
 (TXT) w3m dump (www.ics.uci.edu)
        
       | jhfdbkofdchk wrote:
       | 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?
        
       | mysterydip wrote:
       | 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.
        
         | Someone wrote:
         | 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.
        
       | behnamoh wrote:
       | 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.
        
         | Frummy wrote:
         | Maybe you would love linear algebra?
        
           | behnamoh wrote:
           | Why? I do like linear algebra but the way it's taught in
           | universities is often unintuitive.
        
             | Frummy wrote:
             | 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.
        
         | voldacar wrote:
         | 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.
        
         | mathgenius wrote:
         | 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.
        
       | bitslayer wrote:
       | So many dead links! Sad, I would love to poke around a resource
       | like this.
        
         | ansible wrote:
         | And some others that are effectively dead, such as the page
         | with the Java applet for Euclid's geometry.
        
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       (page generated 2022-10-17 23:00 UTC)