On a Geometry Problem in Plato’s Meno

In this paper, we determine necessary and sufficient algebraic conditions for the solution of the triangle inscription problem in Plato's Meno, in the form of an isosceles triangle, to be constructed with straightedge and compass. We apply these conditions to find infinitely many solutions, in...

Full description

Saved in:
Bibliographic Details
Published in:The American mathematical monthly 2024-03, Vol.131 (3), p.213-224
Main Authors: Ratcliffe, John G., Tschantz, Steven T.
Format: Article
Language:English
Subjects:
Algebra
Geometry
Mathematical problems
Mathematics
Triangles
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we determine necessary and sufficient algebraic conditions for the solution of the triangle inscription problem in Plato's Meno, in the form of an isosceles triangle, to be constructed with straightedge and compass. We apply these conditions to find infinitely many solutions, in the form of an isosceles triangle, that cannot be constructed with straightedge and compass. We prove that only countably many solutions in the form of an isosceles triangle can be constructed with straightedge and compass.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2023.2284634