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The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

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Grid Points on Hyperbolas

Find a condition which determines whether the hyperbola y^2 - x^2 = k contains any points with integer coordinates.

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Parabella

This is a beautiful result involving a parabola and parallels.

Napoleon's Hat

Stage: 5 Challenge Level: Challenge Level:1
One possibility is to use coordinates. You need to use the coordinatesof the centroids of the triangles.