Channel: Think Twice

Category: Education

Tags: visualizationthink twicemathematicsmathsvisual matheuclidean geometryvideoexplainedcalculusgirards theoremspacesurface area3dbeautifulproblemsphereintegralphysicstutorialproofareaapplied matheducationaleducation portalvisual mathematicsinterestinglessonanimationeuler2dtheoremspherical triangleeducational videospuzzlenon euclidean geometrygradehariotts theorempigeometrymathpure mathematicsdimention

Description: For more fun and challenging 3D geometry problems head to: brilliant.org/ThinkTwice ----------------------------------------------------------------------------------------------------------- Please consider supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: twitter.com/thinktwice2580 (@thinktwice2580) ► Instagram: instagram.com/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: ► thinktwiceask@gmail.com ----------------------------------------------------------------------------------------------------------- 🎵 Music: chill. by sakura Hz soundcloud.com/sakurahertz Creative Commons — Attribution 3.0 Unported — CC BY 3.0 Free Download / Stream: bit.ly/chill-sakuraHz Music promoted by Audio Library youtu.be/pF2tXC1pXNo