median
don steward
mathematics teaching 10 ~ 16

Tuesday, 11 December 2012

convex pentagon tiles

there are a few pentagons that tesselate
it can be an interesting but demanding challenge to find some
the properties of presented tiling patterns can be explored:

the 14 (?)
from Wikipedia
(note: convex)

see the 'mathpuzzle' site for more information










some concave pentagons will also tessellate


could these be the same concave pentagon as for the tiling above?











 demonstration tilings from Wolfram

what shape 'units' can be seen?
what angle properties must these have?

what do the angle/side properties seem to be?
















the well-known 'Cairo' tiling:

 is fully explored on the Catnaps website (along with many details of Islamic design)

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