My site is entirely SAFE and FREE of viruses and spyware, but you might get an INSECURE SITE message from your browser simply because it is HTTP and not HTTPS.

Dynamic Mathematics Explorations for Students

(Last Update: 10 March 2024)

Back Home

"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 research 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 research mathematics, there is seldom a book at all - no ready-made questions and problems; even those one often has to invent oneself!" - Michael de Villiers

............

NEW! Problem solving and logical thinking games for young children Contact dynamic learn @mweb. co. za (without the spaces) to order.

*********

Alternate Angles Sum Cyclic Hexagon and Alternate Sides Sum Circumscribed Hexagon Easy - Medium (Updated!*)

(NEW*!)

Area Ratios of Inscribed Polygons Medium-Hard (Updated*!)

Bicentric Quadrilateral Construction Challenge Medium - Hard (NEW*!)

Bottema's Theorem aka Carnot's Theorem Easy-Medium (Updated!)*

(Updated!*)

(Updated!*)

Circle Circumference Result Easy-Medium

Circle Concurrencies Easy-Medium (NEW*!)

(Updated*!)

Clough's Conjecture Medium-Hard

Collinear Conjecture Easy-Medium

Concurrent Angle Bisectors of Quadrilateral Easy (NEW!*)

Conic by Half-turnMedium

Conway's Circle Theorem as special case of Side Divider Theorem Easy-Medium NEW!*

Cyclic Quadrilateral Rectangle Result Medium (Updated!)

Desargues' Theorem Easy-Medium

Dirk Laurie Tribute Problem Medium (NEW!*)

Double Angle Triangle Medium

Dynamic Art: A Parquet Deformation Tiling An art project idea (Updated!*)

Equi-inclined Lines Problem Easy (NEW!*)

The Equi-partitioning Point of a Quadrilateral Easy-medium (NEW!*)

Euclid 1-43 Parallelogram Area Theorem Easy-Medium

Euler line proof Easy (NEW!*)

(Updated!)*

(Updated!)*

Finsler-Hadwiger Theorem plus Gamow-Bottema's Invariant Point Medium-Hard (NEW!*)

Forgotten Similarity Theorem Easy (NEW!*)

A Fundamental Theorem of Similarity Easy-Medium (NEW!*)

Further properties of a particular hexagon Easy-Medium (NEW!*)

(Updated!*)

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

Geometry Loci Doodling with a Cyclic Quadrilateral. Medium - Hard. (NEW!*)

Gielis Super Shape Formula Medium. (Updated!)

Hexagon ExplorationsEasy (Updated!*)

Hippocrates' Theorem Easy (Updated!*)

IMO 2014 Problem 4 (Geometry) Medium-Hard (Updated!*)

Interior Angle Sum of Polygons: a General Formula Easy-Medium (Updated!*)

Interesting Collinearity Medium-Hard (NEW!)

(NEW!)

Jannie's Father's Farm Problem Easy - Medium

Kinky Lines Easy

Klingen's Theorem of two intersecting circles or two adjacent isosceles trianglesMedium - Hard (Updated!*)

The Lux problemMedium - Hard (NEW!*)

Matric Geometry Exam Question - 1949 Easy - Medium (Updated!*)

Minimum Area of Miquel Circles Centres Triangle Medium (NEW!*)

Parallelogram Distances Easy (NEW!*)

Parallelo-hexagon with Obtuse Angles Easy (NEW!*)

Parallelogram Trio Medium

Parallel-pentagon and the Golden Ratio Medium - Hard (NEW!*)

Paul Yiu's problem and a generalization Medium (Updated!*)

Pi in other geometries Medium

Point & Line Reflections in Concurrent Lines Easy (NEW!*)

Pompe's Hexagon Theorem Medium-Hard (NEW!*)

(Updated!*)

(Updated!*)

SA Mathematics Olympiad Problem 2022, Round 2, Question 25 Medium - Hard (NEW!*)

Side trisection triangle concurrency Easy - Medium

Similar Triangles Easy (Updated!*)

Six Point Cevian Circle Hard (NEW!*)

TangentsEasy

Tangential Quadrilateral - Pitot's Theorem. Easy (NEW!*)

Tangential Quadrilateral - Theorem of Gusic & Mladinic. Easy - Medium (NEW!*)

Tangential Hexagon Incircles Application. Medium (NEW!*)

Theorem of Arsalan Wares Easy-Medium (Updated!*)

Trapezoid Explorations Medium

Trapezoid Explorations Medium

Triangle Incentre-Circumcentre Collinearity Easy-Medium

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

Number Patterns: What number comes next? Easy (Updated!*)

***