median
don steward
mathematics teaching 10 ~ 16

Saturday, 11 January 2020

dissecting regular polygons into rhombuses

find the angles in each of the rhombuses
this involves knowing how to find the interior angle of a regular polygon

only polygons with an even number of sides are considered (i.e. they are examples of 'zonogons')

the rhombuses will all have the same side length
pairs of opposite sides are parallel, so stripes of rhombuses are formed when you 'step' from one edge to one parallel to it - a 'zone'

a ppt is here

three types of dissection methods:
  1. spreading out from a vertex (a fan)
  2. spanning out from the centre ('rosette')
  3. adjacent edges paired, from the outside



type 1: growing from a vertex




look at a stripe of rhombuses

what happens to e.g. the top left angles?













type 2, dissecting from the centre:




with diagonals drawn in

what happens for a sequence of angles?




















type 3:
starting from pairs of edges on the regular (even-sided) polygon
sometimes this results in rhombuses at the centre and sometimes it does not
when?
why?























see Paul Stephenson's article in SYMetryplus 68 (spring 2019) here


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