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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Using GeoGebra
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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Fantastic Fractals
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Favourite
Polygon Rings
Age
11 to 14
Challenge level
Join pentagons together edge to edge. Will they form a ring?
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Favourite
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?
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Favourite
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?
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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?
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Favourite
Quad in Quad
Age
14 to 18
Challenge level
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
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Pentagon Construction
Age
16 to 18
Challenge level
Follow the instructions to create a regular pentagon. Can you prove it is indeed regular?
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Interactivities to Make You Inquisitive
These activities all have interactive elements to arouse your curiosity!