A sacred geometry of the equilateral triangle

Author: Doolan, E. P.¹

Source: International Journal of Mathematical Education in Science and Technology, Volume 39, Number 5, July 2008 , pp. 601-629(29)

Publisher: Taylor and Francis Ltd

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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

Document Type: Research article

DOI: 10.1080/00207390701830164

Affiliations: 1: Trinity College, Dublin, Republic of Ireland