Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Four rods of equal length are hinged at their endpoints to form a
rhombus. The diagonals meet at X. One edge is fixed, the opposite
edge is allowed to move in the plane. Describe the locus of the
point X and prove your assertion.
A rectangular field has two posts with a ring on top of each post.
There are two quarrelsome goats and plenty of ropes which you can
tie to their collars. How can you secure them so they can't fight
each other but can reach every corner of the field?
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
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..
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