Shape - May 2006, Stage 4&5

Problems

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A Roll of Patterned Paper

Stage: 4 Challenge Level: Challenge Level:1

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

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One Reflection Implies Another

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .

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Rotations Are Not Single Round Here

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .

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Spokes

Stage: 5 Challenge Level: Challenge Level:1

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

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Footprints

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Make a footprint pattern using only reflections.

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Gold Yet Again

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."