Description
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Proofs for two theorems used in this video:
► Polygon triangulation: https://www.youtube.com/watch?v=2x4ioToqe_c
► Area of a spherical triangle: https://www.youtube.com/watch?v=Y8VgvoEx7HY
Euler's polyhedron formula is one of the simplest and beautiful theorems in topology. In this video we first derive the formula for the area of a spherical polygon using two theorems proven in the previous two videos which are linked above. This result is then used to prove the fact that V-E+F = 2 is true for all convex polyhedra by projecting the polyhedron on the surface of the sphere and doing some algebraic manipulation.
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🎵 Music by : Jonkyoto - https://www.fiverr.com/jonkyoto
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#mathematics #geometry #Euler