Two circles over the same wall: a genealogy of an unnamed circle
Year: 2026
Type: preprint
Abstract: Each external common tangent of two disjoint circles, centres O1 and O2, meets each internal one in a point, and these four points lie on one circle — the circle on O1O2 as diameter, a circle the classical literature states but never names. Its named twin, the circle of similitude, is orthogonal to it. This essay walks the pair through a single draggable figure: from Thales' right angle, through Newton's mean-proportional relation and its inversive twin, to the parabola that Menaechmus first drew for the sake of two mean proportionals. The asymmetry of names — one circle with a title and a literature, one with a descriptive clause — is measured along the way, and turns out to be a fact about transmission, not about geometry.
Author: Higashida, Manabu
Institution: The University of Osaka
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204888380
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