Epistemology m a t h 4 w i s d o m - g m a i l +370 607 27 665 My work is in the Public Domain for all to share freely. 读物 书 影片 维基百科 Introduction E9F5FC Questions FFFFC0 Software Formulate a complete exposition of triangle geometry as an example of a complete mathematical theory. Give a unified algebraic explanation for the centroid, circumcenter, orthocenter, incenter. Centroid (paths) Midpoints of sides connected to vertices. Pass through centroid. Ratio is 1:2 for each segment through the centroid. Center of mass. Circumcenter (distance) Triangle in circle. Center is equidistant to all three vertices. Obtuse angle: circumcenter is outside of the triangle. Orthocenter (angles) Three altitudes intersect at the orthocenter. In the critical case we have a right angle. Obtuse anlge - orthocenter is outside of the triangle. Centroid, circumcenter, orthocenter lie on Euclid's line. Incenter Three angle bisectors meet at the incenter. The center of the circle inside the triangle. Off of Euclid's line unless the triangle is isosceles.
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