Triangle Centers (Euclidean and Hyperbolic Geometry)
- Author:
- Dr. Jack L. Jackson II
Triangle Centers and Related Constructions in Euclidean and Hyperbolic Geometry
Explore these constructions by manipulating the vertices and checking and unchecking the various checkboxes. Some of these produce three objects (e.g. 3 bisectors of the interior angles, 3 perpendicular bisectors of the sides, etc.). Potentially there are 6 possible intersection points produced by these three figures, but there is actually only 1. Can you prove these results and the other structures you notice above?
Taxicab Geometry: All of the constructions in Euclidean Geometry also apply to Taxicab Geometry except for the two circles. If there is a circumscribed circle, then it may not have the Euclidean circumcenter as its center, and if there is an inscribed circle, then it may not have the Euclidean incenter as its center. Circles in Taxicab are not Euclidean circles.