Question

The Case Of the Impossible Triangles: Elliptic Curves and the Congruent Number Problem

Answer 1

It's kind of hard to read on mobile since the illustrations cover most of the screen space and can't be scrolled away.

Answer 2

What in the world are those left/right arrows though?

Answer 3

I think there is a typo on a slide with criteria in a Tunnell's theorem. In case of odd N it talks about number of integer solutions for an equation x\^2+4y\^2+8z\^2 = N/2, which seems weird since N/2 is not an integer if N is odd.

Answer 4

I'm definitely a math amateur, but I think I'm in your target audience. This has been really good! A topic I hear about occasionally, but never really understood. I can follow along really well. However, on one slide that says "From this triangle, we can compute the areas of the three squares we saw in the previous chapter, r^2, s^2, and t^2." I don't actually see how to find 1/4, 25/4, and 49/4." I could go way back to find that rectangle again, but perhaps you can refresh my memory, or call out more clearly on the rectangle slide the equations we'll use later to go from (3, 4, 5) to (1/4, 25/4, 49/4).

Answer 5

Great presentation, very approachable introduction to the topic, and the little touch of interactivity was a nice addition.

The slide navigation is rather annoying; going back to a previous chapter takes you to its first slide, different slides in the same chapter have the same url so you can't link someone a specific slide of interest, and there is no index of all slides to jump around with. (And having an artificial delay on slide transitions is always a bit of a nuisance.)

> Technical note: if x isn't a square number, we need to use a different formula than s^2 = x. The other formula works for all xx, but it's uglier and doesn't have a nice geometric interpretation, so I won't show it here

Care to elaborate?

Answer 6

It's good but you don't quite explain explicitly why 16 does not work.

Answer 7

Thanks for sharing

Answer 8

This is awesome.  I wish all mathematics was taught like this.  Insights before proofs, and using computers to help convey concepts!  I love the chaLlenge to drag the triangle to find such if 24 is a congruent number.  I feel like I can show this to my 13 year old son and he would appreciate it.

Answer 9

I'm on the successive squares bit... and it wasn't obvious to me why the length of the hypotenuse through the rectangle was 2s.  Presentation made it look as though I should be able to immediately see it. They just drew the line cutting the rectangle in halve (and so it's obvious that the area is N); and then said that this proves that N is a congruent number. But I couldn't see that. I had to do use Pythagoras' theorem and a bit of algebra to convince myself that the diagonal was 2s.

Am I missing something more obvious? A lot of the steps in the presentation have been pretty slow; so that jump feels like I've missed something.


In any case, it's a pretty good demo so far.

Answer 10

Hello, in some parts, new text appears each time both above and below the illustration, which divides attention and confuses the reader. Also, in one place, a rectangle gets smaller and then bigger again when it rotates, ironically in a part where you're manipulating areas.