The Angle Sum of a Triangle is NOT 180 Degrees?

The angle sum of a triangle is not always 180 degrees. In fact, it depends on whether you're on a flat or a curved space. In this video, we show that the angle sum of a triangle on a sphere is strictly larger than 180 degrees and, in fact, depends on the surface area of the triangle. We can even determine whether a space is positively or negatively curved by the angle sum of all triangles on its surface. Weird math is the best math!

Media used in this video:

Oranges blood vs regular
Author: Shadiac
Source: Wikimedia Commons

Longitude (PSF)
Author: Pearson Scott Foresman
Source: Wikimedia Commons

Texas Outline
Author: World Population Review
Source: worldpopulationreview.com/states/texas/outline

Hyperbolic Paraboloid 3D Printout
Printed by Dr. Skyler Simmons


Music:

Controlled Distress
Author: Biz Baz Studio
Source: YouTube Audio Library