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This problem was written by James from St Peter's College, Adelaide, Australia.
Draw a pentagon and draw in all the diagonals (lines joining the vertices not including the edges of the pentagon), how many diagonals is this?
This is called a pentagram. How many diagonals are there in a hexagram, heptagram, octagram, nonagram, decagram etc. up to a 20 sided shape.
Does any pattern occur when looking at the number of diagonals?
Why is this so?
Can you find a formula?