The Story of Hagge and Speckman

TL;DR

This paper explores the historical and mathematical connections between Hagge's circle and Speckman's triangle perspective and similarity, revealing underlying relationships in classical Euclidean geometry.

Contribution

It uncovers the link between Hagge's and Speckman's geometric concepts, showing their interrelation in the context of triangle and circle properties.

Findings

Hagge's circle passes through the orthocentre of a triangle.

Speckman's work involves triangles in perspective and indirect similarity.

The paper demonstrates a unifying geometric relationship between these concepts.

Abstract

This concerns theory first developed by Hagge and Speckman in the Edwardian era. Speckman investigated triangles that were simultaneously in perspective and indirectly similar. On the other hand Hagge studied circles that pass through the orthocentre of a given triangle. Superficially these subjects look unrelated, but this is not the case, as we describe.