median
don steward
mathematics teaching 10 ~ 16

## Monday, 30 July 2012

### eutrigon and co-eutrigon

in some novel and interesting work dwelling on the relationships between parts to wholes, Wayne A Roberts (Canberra, see his 'principles of nature' work) has established Pythagoras-like relationships for triangles that have one 60 degree angle (he has named these 'eutrigons') and triangles with one 120 degrees angle (which he refers to as 'co-eutrigons')

he utilises unit triangles on an isometric grid
see the section on isometric areas on this blog

the relationships are straightforwardly derived from the cosine rule, substituting 60 degrees and 120 degrees but, importantly as far as appreciation is concerned, he presents justifications based on diagrams:

a 'eutrigon' is a triangle with one 60 degree angle

the eutrigon has equilateral triangles drawn on each of the sides

what is the relationship between their areas?

these diagrams might help:

the triangles that look as if they are equilateral are equilateral

a dynamic version, created by Wayne Roberts:

for the co-eutrigon, this diagram is offered by Wayne Roberts: