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Threesomes

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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Pick's Theorem

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

problem icon

Threesomes

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Pinned Squares

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Pin those squares down! A geoboard is a piece of wood with pins hammered into it. The diagram shows a 5 by 5 board with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins as shown. What is the total number of squares that can be made on a 5 by 5 board? How many squares can be made on an N by N board?

pinned board
A virtual pinboard is available here.