A Sacred Geometry of the Equilateral Triangle

Autor/in	Doolan, E. P.
Titel	A Sacred Geometry of the Equilateral Triangle
Quelle	In: International Journal of Mathematical Education in Science and Technology, 39 (2008) 5, S.601-629 (29 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Transformations (Mathematics); Geometric Concepts; Geometry; Mathematics Instruction; Mathematical Logic; Validity; Equations (Mathematics); Mathematical Formulas + Suchen Sie Ihr Suchwort? Transformationstheorie; Elementare Geometrie; Geometrie; Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Gültigkeit; Equations; Mathematics; Gleichungslehre; Mathematische Formel
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. (Contains 18 figures and 10 tables.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10