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Star Gazing

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

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LOGO Challenge - Following On

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

Pentagonal

Stage: 4 Challenge Level: Challenge Level:1

If you have decided that the result holds for a regular hexagon, what is it exactly about the hexagon that lets it work?
What does a regular hexagon also have that isn't needed for this result?

For the regular pentagon, put a point somewhere inside, perhaps not at the centre.
Join that point to each of the vertices of the pentagon and think about the five triangles.

Finally, what does a regular pentagon also have that isn't needed for this result?