A sacred geometry of the equilateral triangle

Abstract

In this article, we investigate the construction of spirals on an equilateral triangle and prove that these spirals are geometric. In further analysing these spirals we show that both the male (straight line segments) and female (curves) forms of the spiral exhibit exactly the same growth ratios and that these growth ratios are constant independent of the iteration of the spiral. In particular, we show that ratio of any two successive radius vectors from the ‘centre’ of the spiral as we move inwards towards that ‘centre’ is always 1/2. This same elegant result is also shown to be true for successive chords. All our results are demonstrated using mostly coordinate and transformational geometry. Finally we look at two methods for constructing these spirals with ruler and compass to maximum accuracy.

Keywords:

• geometric spirals
• equilateral triangle
• sacred geometry
• coordinate geometry
• ruler and compass drawing

Notes

¹Previous affiliation.

Additional information

Notes on contributors

E.P. Doolan

1Previous affiliation.