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(Last Update: 30 January 2017)

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"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!"

Math of Voting PDF...Rethinking Proof cover...Adventure Geometry...Boolean Algebra...Elementary Logic

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Alternate Angles Sum Cyclic Hexagon and Alternate Sides Sum Circumscribed Hexagon Medium


Anele Moli's Method: Constructing an equilateral triangle Easy


Area Ratios of Inscribed Polygons Medium-Hard


Bicentric Quadrilateral Property Medium


Bottema's Theorem Easy-Medium


Bride's Chair Concurrency & Locus Hard


British Mathematics Olympiad Concurrency Problems Medium


Circle Circumference Result Easy-Medium


Circum Cyclic Quadrilateral Result and Cyclic Circum Quadrilateral Result Medium


Classifying, Exploring, Constructing & Defining Quadrilaterals Easy-Medium


Clough's Conjecture Medium-Hard


Collinear Conjecture Easy-Medium


Conic by Half-turn Medium


Construct a Parallel-Hexagon with GEONexT Medium


Crossed Quadrilateral Properties Medium


Cosine-Sine Angle Rule Medium


Cyclic Crossed Pentagon Problem Easy


Cyclic Quadrilateral Arcs Theorem Hard


Cyclic Quadrilateral Rectangle Result 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


Finding the Median and Centroid of a Triangle by Experimentation: A gravity simulation Use to explore.


Finding the centroid of a triangle with different weights at the vertices: A gravity simulation Use to explore.


Generalizing perpendicular bisectors, angle bisectors, medians and altitudes to 3D Medium to hard.


A generalization of a Parallelogram Theorem to Parallelo-hexagons, and Douglas' Theorem Medium to hard.


Generalizing Viviani's theorem to 3D Easy to Medium.


GEONexT - online dynamic mathematics with full construction facility Use to explore.


Gielis Super Shape Formula Medium.


Haag Hexagon and its generalization to a Haag Polygon Medium.


Hexagon Explorations Easy


Hippocrates' Theorem Easy


Hypercube-Cross Polytope Duality Easy


IMO 2014 Problem 4 (Geometry) Medium-Hard


Interior Angle Sum of Polygons: a General Formula Easy-Medium


Interesting property of the number e Medium


Investigating circumcentres of iterated median triangles Medium
Investigating incentres of some iterated triangles Medium-Hard


Japanese Circumscribed Quadrilateral Theorem Hard (Updated with a solution!)


Kinky Lines Easy


Jannie's Father's Farm Problem Easy - Medium


Matric Geometry Exam Question - 1949 Easy - Medium


Maximum area of quadrilateral problem Easy


Midpoint Trapezium (Trapezoid) Theorem Generalized Easy-Medium


Miscellaneous Transformations (of geometric figures & graphs) Easy - Medium


Napoleon Variation Problem Medium


Over and over: two geometric iterations with triangles Medium - Hard


Parabola Locus Theorem and Parabola Circumcircle Theorem Easy


Parallelogram Trio Medium


Paul Yiu's problem and a generalization Medium


Perimeter of Hexagon inscribed in Triangle Easy


Pi in other geometries Medium


Platonic Solids plus Truncated Platonic Solids Easy


Pythagorean Quadrilateral 1 Medium


Pythagorean Quadrilateral 2 Easy


Pythagorean Quadrilateral 3 Easy


Quadrilateral Inequality involving Perimeter & Diagonals Medium


The quasi-circumcentre and quasi-incentre of a quadrilateral Medium


Reauleaux Triangle (a curve of constant width) - a generalization Medium


Rectangle Angle Trisection and Rhombus Angle Trisection Easy


SA Mathematics Olympiad Problem 2016, Round 1, Question 20 Medium - Hard


Side trisection triangle concurrency Easy - Medium


Similar Triangles Easy


Square Trigonometry Easy


Tangents Easy


Theorem of two intersecting circles or two adjacent isosceles triangles Medium - Hard


Theorem of Arsalan Wares Easy-Medium


Three Circle Geometry Theorem Proofs by Transformations Easy


Trapezoid Explorations Medium


Triangle Circumcircle-Incentre Result Medium


Triangle Incentre-Circumcentre Collinearity Easy-Medium


Two circles result Easy


Two different centroids (balancing points) of a quadrilateral Easy-Hard


What function? Modeling the height of water against time in a tilted container Medium


What number comes next? Easy


External Links

South African Mathematics Olympiad: Question Papers & Solutions - Junior & Senior (from 1997)

Alex Bogomolny's Cut the Knot site: Geometry Problems, Applets & much more (incl other topics)

E-Classroom Free educational worksheets for teachers & parents

Gerrit Stols' School Math(s) site: Interactive Math, Books, Math Tools, Resources, Links & more

Mathematical Digest: The mathematical magazine for South African mathematics learners and teachers

Math Forum Electronic Newsletter

Logic, Strategy & Geometry Games

Last modified by Michael de Villiers, 30 January 2017.

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