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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### Semi-regular Tessellations

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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### Shifting Times Tables

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

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### Quad in Quad

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

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### Surprising Equalities

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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### Pentagon Construction

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!