Mathematical Number of Shapes: Explained for Intro Physics

[Medgirl314]

In the following video, the physicist says something about the mathematical number of a shape at 2:49. There's a mathematical number for shapes?? That's beyond interesting. Could someone please give a somewhat simple explanation? I'm only in introductory physics but was told this is more advanced.
http://derekowens.com/access2/physics/Chapter06/html5/6.4.3a_Conservation_of_Angular_Momentum.html

 

[WannabeNewton]

He is referring to the moment of inertia (usually about the center of mass in this context) when he talks about the number associated with the "shape" of the person. When we talk about spin angular momentum conservation about a fixed axis we can think of the moment of inertia and the angular velocity as inversely proportional values that keep the spin angular momentum constant.

 

[Medgirl314]

I think I kind of understand. He's talking about all the quantities that describe the shape at that moment of inertia, not, for example, saying a square with an area of 314 is assigned a number n?

Thank you!