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## 'Holly' printed from http://nrich.maths.org/

The ten arcs forming the edges of this "holly leaf" are all arcs
of circles of radius 1 cm. At all the spiky points the circles
touch each other tangentially. All the straight lines join the
centres of the circles they pass through and the four triangles at
the corners have angles of 45, 45 and 90 degrees.

Find the length of the perimeter of the holly leaf and the area
of its surface.

This is a 10-spike holly leaf. What is the perimeter of a
16-spike holly leaf of the same sort?

Examine some real holly leaves and you will find that they don't
lie flat. This shape is different from a real holly leaf in so far
as it does lie flat on a flat surface (or plane). See '
Giant Holly Leaf' for an extension of this problem to a more
realistic holly leaf which has negative curvature.