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Spherical Geometry: Deriving The Formula For The Area Of A Spherical Triangle

For more fun and challenging 3D geometry problems head to: https://brilliant.org/ThinkTwice ----------------------------------------------------------------------------------------------------------- Please consider supporting Think Twice on: ► Patreon:   / think_twice   ► Twitter:   / thinktwice2580   (@thinktwice2580) ► Instagram:   / thinktwice_ltu   (@thinktwice_ltu) ----------------------------------------------------------------------------------------------------------- Summary: ► A spherical triangle is a surface area of a sphere bounded by 3 arcs of great circles. ► Any spherical triangle has it's antipodal duplicate ► Each of these spherical triangles are intersections of 3 different spherical lunes. ► Adding up the area of all 6 lunes results in the surface area of a sphere with 4 additional spherical triangles. ►Girard's Theorem: the area (T) of a spherical triangle, with interior angles a,b and c, is given by T = r^2 (a + b + c - pi). The ----------------------------------------------------------------------------------------------------------- Contact me: ► [email protected] ----------------------------------------------------------------------------------------------------------- 🎵 Music: chill. by sakura Hz   / sakurahertz   Creative Commons — Attribution 3.0 Unported — CC BY 3.0 Free Download / Stream: http://bit.ly/chill-sakuraHz Music promoted by Audio Library    • Chill – sakura Hz (No Copyright Music)