Andrius Kulikauskas

  • m a t h 4 w i s d o m - g m a i l
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  • 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


Geometry, Geometry theorems

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.


  • 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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This page was last changed on February 23, 2020, at 10:30 PM