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Volume 32, Number 2, pages 165-168 (2021)
https://doi.org/10.26830/symmetry_2021_2_165
THE BEAUTY OF QUANTIZED FORM AND THE PLEASURES OF CONSTRUCTING WITH EQUALITY - EUCLID’S PLATONIC SOLIDS
Nina Chen*
* Snowray Design, 345 N LaSalle Drive #3008, Chicago, IL 60654, U.S.A.
E-mail: snowraydesign@gmail.com
Web: http://www.snowraydesign.com
Abstract: What is quantized form? Has it anything to do with beauty? Commensurability is at the root of musical harmony, but perhaps not so evident is that the golden ratio, long hailed to be a force of life and source of beauty in nature and art, also embodies commensurate qualities related to growth. In Book XIII, the last book of The Elements, Euclid demonstrates the various commensurable qualities inherent in the golden ratio. He also instructs how to construct, within the same sphere, the five Platonic Solids, the only objects of equal side and angle in our universe. Lastly, he compares the squares on the sides of the Platonic Solids. Doing as Euclid instructs, one discovers two primary ratio systems coming into play – one related to music, and the other to the golden ratio. Both systems are beautiful, both are quantized, and both are born out of equality.
References:
Euclid. (2010) The Elements. 2nd ed., Santa Fe: Green Lion Press, 404 pp.
Kepler, J. (1997) The Harmony of the World. The American Philosophical Society, 549 pp.
Taisbak, C.M. (1982) Coloured Quadrangles. A Guide to the Tenth Book of Euclid’s Elements. Copenhagen: Museum Tusculanum Press, 78 pp.
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