(Last Update: 23 Jan 2018)
"A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery". - George Polya in How to Solve It (Princeton 1945).
"In real mathematics, the answers are not in the back of the book nor are the problems simply variations of preceding, carefully worked examples. In fact, in real mathematics, there is no book at all - no ready-made questions and problems; even those one has to invent oneself!"
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Area Ratios of Inscribed Polygons Medium-Hard
Bottema's Theorem Easy-Medium
Bug Escape Problem Easy
Circle Circumference Result Easy-Medium
Clough's Conjecture Medium-Hard
Collinear Conjecture Easy-Medium
Conic by Half-turn Medium
Desargues' Theorem Easy-Medium
Descartes' Geometric Solving of Some Quadratics Easy-Medium
Double Angle Triangle Medium
Dynamic Art: A Parquet Deformation Tiling An art project idea
Euclid 1-43 Parallelogram Area Theorem Easy-Medium
Generalizing Viviani's theorem to 3D Easy to Medium.
Gielis Super Shape Formula Medium.
Hexagon Explorations Easy
Hippocrates' Theorem Easy
IMO 2014 Problem 4 (Geometry) Medium-Hard
Japanese Circumscribed Quadrilateral Theorem Hard (Updated with more solutions and generalizations)*
(Updated with more solutions and generalizations)*
Kinky Lines Easy
Jannie's Father's Farm Problem Easy - Medium
Matric Geometry Exam Question - 1949 Easy - Medium
Napoleon Variation Problem Medium
Over and over: two geometric iterations with triangles Medium - Hard
Parallelogram Trio Medium
Pi in other geometries Medium
Pythagorean Quadrilateral 1 Medium
SA Mathematics Olympiad Problem 2016, Round 2, Question 20 Medium - Hard (Updated with solution!)
Side trisection triangle concurrency Easy - Medium
Similar Triangles Easy
Square Trigonometry Easy
Theorem of Arsalan Wares Easy-Medium
Trapezoid Explorations Medium
Triangle Incentre-Circumcentre Collinearity Easy-Medium
Two circles result Easy
Last modified by Michael de Villiers, 23 Jan 2018.
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