Dynamic Mathematics Explorations for Students
(Last Update: 27 April 2012)
"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!"
20% discount till 18 May 2012 Downloadable PDF papers/books on Geometry, Mathematics & Mathematics Education for sale
Alternate Angles Sum Cyclic Hexagon and Alternate Sides Sum Circumscribed Hexagon Medium
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
Collinear Conjecture Easy-Medium
Conic by Half-turn
Medium
Construct a Parallel-Hexagon with GEONexT Medium
Cosine-Sine Angle
Rule Medium
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
Euclid 1-43 Parallelogram Area Theorem Easy-Medium
Finding the Median and Centroid of a Triangle by Experimentation: A gravity simulation Easy
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.
GEONexT - online dynamic mathematics with full construction facility Use to explore.
Gielis Super Shape Formula Medium.
Hexagon Explorations
Easy
Hypercube-Cross
Polytope Duality Easy
Interior Angle Sum of Polygons: a General Formula Easy-Medium
Kinky Lines Easy
Miscellaneous Transformations (of geometric figures & graphs) Easy - Medium
Napoleon Variation Problem Medium
Parabola Locus Theorem and Parabola Circumcircle Theorem Easy
Parallelogram
Trio Medium
Paul Yiu's problem and a generalization Medium
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
Reauleaux Triangle (a curve of constant width) - a generalization Medium
Rectangle Angle Trisection and Rhombus Angle Trisection Easy
Similar
Triangles Easy
Square Trigonometry Easy
Tangents
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 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)
Gerrit Stols's School Math(s) site: Interactive Math, Books, Math Tools, Resources, Links & more
Mathematical Digest: The mathematical magazine for South African mathematics learners and teachers
Last modified by Michael de Villiers, 27 April 2012.
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