License: CC0 1.0 Universal (CC0 1.0) Public Domain Dedication. creativecommons.org/publicdomain/zero/1.0
To the extent possible under law, Hugo Spinelli has waived all copyright and related or neighboring rights to this video. This work is published from: Brazil.
All code files below are released under the "MIT No Attribution" (MIT-0) license.
Code used to create the video: github.com/hugospinelli/Holditch-Manim
Interactive Holditch curve plotter: github.com/hugospinelli/Holditch-Matplotlib
Blender model for the ellipsograph: github.com/hugospinelli/Holditch-Manim/blob/master/Images/Trammel/Trammel.blend
References:
[1] Holditch, H. (1858). Geometrical theorem. The Quarterly Journal of Pure and Applied Mathematics , 2 , 38. resolver.sub.uni-goettingen.de/purl?PPN600494829_0002
[2] Wetzel, J. E. (2010). An ancient elliptic locus. The American Mathematical Monthly , 117 (2), 161-167. doi.org/10.4169/000298910X476068
[3] Monterde, J., & Rochera, D. (2017). Holditch's Ellipse Unveiled. The American Mathematical Monthly , 124 (5), 403-421. doi.org/10.4169/amer.math.monthly.124.5.403
[4] Rochera, D. (2019). On Holditch's theorem and related kinematics [Doctoral dissertation, Universitat de València]. roderic.uv.es/handle/10550/72339
00:00 Holditch's Theorem for Circles
00:50 Holditch's Theorem for Rectangles
01:11 Ellipsograph or Trammel of Archimedes
01:44 van Schooten's Locus Problem
02:01 Monterde & Rochera's Proof
05:04 Standard Proof
07:00 Non-Convex Examples
09:26 References