Dynamic Explorations

Dynamic Explorations

Mathematicians often use tools to help them to make discoveries. The problems in this feature encourage you to use dynamic geometry and other interactive tools to explore, pose questions, make conjectures and prove ideas.

Polygon Rings 

Age 11 to 14 Challenge Level:
Join pentagons together edge to edge. Will they form a ring?

Shifting Times Tables 

Age 11 to 14 Challenge Level:
Can you find a way to identify times tables after they have been shifted up or down?

Semi-regular Tessellations 

Age 11 to 16 Challenge Level:
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Using Geogebra 

Age 11 to 18
Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.

Quad in Quad 

Age 14 to 16 Challenge Level:
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

Surprising Equalities 

Age 14 to 18 Challenge Level:
Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?

Pentagon Construction 

Age 16 to 18 Challenge Level:
Follow the instructions to create a regular pentagon. Can you prove it is indeed regular?

Fantastic Fractals 

Age 11 to 18
In this article from Plus, read about how computers help mathematicians to make discoveries in fractal dimensions!