Bisecting horn angles
Abstract
A horn angle between a circle and its tangent is considered in Euclid's Elements, and Euclid remarks that it is smaller than any acute rectilinear angle. Already in antiquity, Proclus wondered whether it is possible to bisect horn angles. We will give a construction of a bisector which was within the means of ancient geometers since the time of Archimedes and Apollonius. We will also compare it to the conformal bisection method introduced in modern times.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.09499
- arXiv:
- arXiv:2206.09499
- Bibcode:
- 2022arXiv220609499K
- Keywords:
-
- Mathematics - Metric Geometry;
- Mathematics - History and Overview;
- 51M04 01A20 01A60 30C20 51M15
- E-Print:
- 8 pages, 6 figures