Outline
100 Great Problems
... of Elementary Mathematics.
Materials to accompany the book by Heinrich Dörrie.
The theorems used in these proofs can be found in the Supplement:
http://www.geogebratube.org/material/show/id/74794
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(This is a personal study project. Let me know how I can make my materials more useful to you.)
Table of Contents
Planimetric Problems
- 17. Gregory's Arc Tangent Series
- 27. The Euler Line
- 28. The Feuerbach Circle (Nine-point circle)
- 29. Castillon's Problem
- 29b. Castillon's Problem
- 30. Malfatti's Problem
- 30b. Malfatti's Problem, Solution
- 31. Monge's Problem
- 31b. Monge's Problem: Vector Solution
- 32. Tangency Problem of Apollonius
- 32b. Appolonius: Differentials, v2
- 33. The Solo Compass - 1. Add two segments
- Archimedes' Formula for π (pi)
- 40a. Triangulation from 3 known points
- 40b. Position of a Ship at Sea from Two Known Points
- Involution: Point pairs on a line
- Involution: Double points
Conic Sections & Cycloids
- 47. Trammel! Van Schooten's Locus Problem
- Trammel of Archimedes
- 48. Cardan's Spur Wheel
- 52. Astroid, Rolling Circle
- Cycloids and the Rolling Circle
- 56. Area of a Parabola - Archimedes
- 58. Arc Length of a Parabola
- 59. Desargues' Theorem (Homology)
- 60. Double Elements 1 - Points on a Circle
- 60. Double Elements 2 - Rays from a Point
- 60. Double Elements 3 - Line
- Brianchon's Hexagram Theorem
Stereometric Problems