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Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Bendy Quad

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Arclets

Age 14 to 16
Challenge Level

Arclets printable sheet


Each of the following arclets is made from arcs of a circle of radius r.

          

What is the perimeter of an arclet with 3, 4, 5, and n "nodes"?

What happens when n is very large?

Explain the relationship between your answers and the perimeter of the original circle.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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