Channel: Think Twice

Category: Education

Tags: edge vertex facethink twicepolyhedronmathematicsgraph theorymathsmath videoeuler3dv-e+f=2polygoneulers formulageometryconvex polyhedronmathproofdimension

Description: Explore the world of 3-dimensional geometry by signing up for free at: brilliant.org/ThinkTwice ----------------------------------------------------------------------------------------------------------- Proofs for two theorems used in this video: ► Polygon triangulation: youtube.com/watch?v=2x4ioToqe_c ► Area of a spherical triangle: 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. ----------------------------------------------------------------------------------------------------------- Help me create more content by supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: twitter.com/thinktwice2580 (@thinktwice2580) ► Instagram: instagram.com/thinktwice_ltu (@thinktwice_ltu) ----------------------------------------------------------------------------------------------------------- Contact me: ► thinktwiceask@gmail.com ----------------------------------------------------------------------------------------------------------- 🎵 Music by : Jonkyoto - fiverr.com/jonkyoto ----------------------------------------------------------------------------------------------------------- #mathematics #geometry #Euler