Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

Finding the area of the average triangle.

Audience:

Tags: geometrytriangles

If you keep drawing triangles in a 1x1 grid, what is the average area. This seemingly easy problem is impossible to solve with standard calculus techniques.

I used a method that combines geometry probability and calculus to find a new simple solution to this problem.



Analytics

3.65 Overall score*
114 Rank
6 Votes
5 Comments

Comments

4.5

The journey carries it: the AI fails, the classic route is out of reach, and the video builds its own way and lands the answer. The look works against the journey: cursors, selection boxes, and labels still reading “text” pull the eye off the idea. Clean frames, and the idea stands alone.

2.5

Very cool that you attacked a quirky problem that historically had only very opaque solutions (and even AI gets it wrong!). And I think you probably took a very clever approach but I really can’t understand what you did here.

Somehow you argued that the red and yellow dots will “on average” end up in two particular spots. I didn’t follow your argument (and I did re-watch it) and you’re obviously aware that you have to be very careful with “averaging” arguments when it comes to problems like this. So you lost me on that step. I half-followed the rest of the argument but I still can’t understand why you’re allowed to assume the 3rd dot will end up inside the square formed by the first two.

I think there’s probably something really cool (and original!) in here, and you should consider making a second video that very carefully goes through your solution.

5.4

I like the enthusiasm and curiosity. The story in the beginning about the numberphile video made this feel relatable. For middle/high school this may be a little advanced or difficult to understand. Pacing was good!

2.7

Not sure of the motivation. Square ratio and jittery audio. Not if jumping from Wolfram page or was a joke early break. But this is symptomatic of the video in general - interesting, but hard to follow.

3.9

That’s certainly interesting, but I’m unconvinced of it as a proof. I don’t really see how this MUST be the correct answer, only that you’ve shown that it CAN be. How do we know that it has to be a third of the way, for example? It feels like some steps are skipped.