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.

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Join pentagons together edge to edge. Will they form a ring?

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Can you find a way to identify times tables after they have been shifted up or down?

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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

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Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

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Take any triangle, and construct squares on each of its sides. What do you notice about the areas of the new triangles formed?

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Follow the instructions to create a regular pentagon. Can you prove it is indeed regular?