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Regular polygons can be subdivided to basic units in the shape of right-angled triangles, the number of these triangular sub-units being equal to twice the number of sides of the comprising polygon. The sides of these triangular sub-units consist of the radius of the circle circumscribing the polygon, the bisecting perpendicular line from the centre to the side of the polygon and one half of the side of the polygon.
From this we can observe that the basic triangular sub-units of all the polygons with a common circumscribing circle differ only in the proportion of their two perpendicular sides.
Hence, possibly, comes the notion that “the triangle is to geometry as one is to numbers”. It is this constant relationship of the parts to each other, which is described as ‘proportion’, which determines the shape and properties of regular geometric forms irrespective of size.