Isogonal conjugate and a few properties of point X(25)

A seemingly simple question – “where lies the center of the triangle?” – turns out to lack an easy answer. Many different constructions emerged during centuries of mathematical discussion. Each of these points is somehow special, and none is a better fit for “the triangle center” than the others. There is even an “Encyclopedia of Triangle Centers” containing more than 40000 of different points – and my paper increased this number by another 35. I’ve started from a notion of isogonal conjugate – something already known in geometry. On this basis I’ve introduced the hodpiece of a point – the main construction of my article. The final and the most important result of my paper is that Bloom’s point (X40139) cannot be constructed using only a compass and straightedge.

Category: MATHEMATICS Country: POLAND Year: 2021


Radosław Marek Żak