Pick's Theorem (From Euler's Planar Graph Formula)

In this video we'll discuss Pick's Theorem: probably the most famous theorem in lattice geometry. We'll use Euler's results from graph theory (namely, his planar graph formula) to prove this theorem.

References and Notes:

Also see Ref. 1 for proof that any primitive lattice polygon can be divided into primitive lattice triangles

FAQ : How do you make these animations?
Animations are mostly made in Apple Keynote which has lots of functionality for animating shapes, lines, curves and text (as well as really good LaTeX). For some of the more complex animations, I use the Manim library. Editing and voiceover work in DaVinci Resolve.

Supporting the Channel.
If you would like to support me in making free mathematics tutorials then you can make a small donation over at
Thank you so much, I hope you find the content useful.

[ed.puckett]

Your videos are such jewels, thank you!

[johnericksarenas]

Amazing. You earned another subscriber.

[erosravera]

Not precise:
There may exist an even number of odd vertices.