Dynamic Mathematics Explorations for Students
(Last Update: 23 Jan 2018)
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
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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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
Chair Concurrency & Locus Hard
British Mathematics Olympiad Concurrency Problems Medium
Bug Escape Problem Easy
Circle Circumference Result Easy-Medium
Quadrilateral Result and Cyclic Circum
Quadrilateral Result Medium
Exploring, Constructing & Defining Quadrilaterals Easy-Medium
Clough's Conjecture Medium-Hard
Collinear Conjecture Easy-Medium
Conic by Half-turn
Construct a Parallel-Hexagon with GEONexT Medium
Crossed Quadrilateral Properties Medium
Cyclic Crossed Pentagon Problem Easy
Cyclic Quadrilateral Arcs Theorem Hard
Cyclic Quadrilateral Rectangle Result Medium
Desargues' Theorem Easy-Medium
Geometric Solving of Some Quadratics Easy-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.
Hippocrates' Theorem Easy
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
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
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
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
Quadrilateral 1 Medium
Quadrilateral 2 Easy
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
SA Mathematics Olympiad Problem 2016, Round 2, Question 20 Medium - Hard (Updated with solution!)
Side trisection triangle concurrency Easy - Medium
Square Trigonometry Easy
Thabit's Generalization of Pythagoras. Easy
Theorem of two intersecting circles or two adjacent isosceles triangles
Medium - Hard
Theorem of Arsalan Wares
Three Circle Geometry Theorem Proofs by Transformations
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
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, 23 Jan 2018.
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