A generalisation of the Spieker circle and Nagel line

Michael De Villiers

doi:10.4102/pythagoras.v0i63.106

Abstract

Many a famous mathematician and scientist have described how their first encounter with Euclidean geometry was the defining moment in their future careers. Some of the most well known are probably Isac Newton and Albert Einstein. Often these encounters in early adolescence have been poetically described as passionate love affairs.

Highlights

Many a famous mathematician and scientist have described how their first encounter with Euclidean geometry was the defining moment in their future careers
Nagel point Many mathematics teachers are not aware that there are many famous special centres associated with the triangle, and the four, i.e. the centroid, orthocentre, circumcentre and incentre, normally mentioned in textbooks
Concluding comments It is hoped that this article has to some extent expelled the myth that the ancient Greeks already discovered and proved everything there is to find and prove in geometry

Summary

Introduction

Many a famous mathematician and scientist have described how their first encounter with Euclidean geometry was the defining moment in their future careers. It will discuss a possibly new generalisation of the Spieker circle and the associated Nagel line, which is parallel to that of the generalisation of the nine-point circle and Euler line discussed in De Villiers (2005). Nagel point Many mathematics teachers are not aware that there are many famous special centres associated with the triangle, and the four, i.e. the centroid, orthocentre, circumcentre and incentre, normally mentioned in textbooks.

Results

Conclusion