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## 'Rolling Triangle' printed from http://nrich.maths.org/

The triangle **ABC** is equilateral. The arc
**AB** has centre **C** , the arc
**BC** has centre **A** , the arc
**CA** has centre **B** and all three
arcs have the same radius equal in length to the sides of the
triangle.

Imagine a roller that has this cross-section. Place it on the
floor and lay a plank of wood across it. Try to push the plank
horizontally on the roller. What happens and why?

Though the animation shows the rolling triangle contained in a
box, we are asking you to describe what happens when it rolls along
the floor with a plank of wood on top of it..

See also the

Coke Machine problem. This relates to the 50 pence
piece which is a seven sided rouleaux (rolling) figure, based on a
regular septagon.

CHRISTMAS DECORATIONS

If you make lots of these rolling triangles from old greetings
cards and score them along the edges of the equilateral triangles
you can make the regular solids (a tetrahedron, an octahedron and
an icosahedron) by sticking the flaps together. They look good with
the flaps projecting outwards and they are easy to make. You can
also make a dodecahedron using 12 rolling pentagons. A rolling
pentagon is made in a similar way starting with a regular
pentagon.