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
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. . . .
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. . . .
Draw three equal line segments in a unit circle to divide the
circle into four parts of equal area.
Make a footprint pattern using only reflections.
Nick Lord says "This problem encapsulates for me the best features
of the NRICH collection."
Great reasoning from Alice who knows exactly when the speed is zero even if the motion doesn't stop in the way you might expect.
Go to last month's problems to see more solutions.
Some simple ideas about graph theory with a discussion of a proof
of Euler's formula relating the numbers of vertces, edges and faces
of a graph.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
A Sudoku that uses transformations as supporting clues.