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:

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