# odd

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## Phi

Phi (uppercase Φ, lowercase φ, or math symbol ϕ ), pronounced / f aɪ / FY or sometimes / f iː / FEE in English, [ 1 ] and [ˈfi] in modern Greek , is the 21st letter of the Greek alphabet . In modern Greek, it represents [f] , a voiceless labiodental fricative . In Ancient Greek it represented [pʰ] , an aspirated voiceless bilabial plosive (from which English ultimately inherits the spelling " ph " in words derived from Greek).
"We know very little about Leonardo’s apprenticeship in Verroccio’s workshop, but the short account provided by Vasari confirms that it included architectural and technological design, according to a concept that was being revived on the model of Vitruvius, as reproposed by Alberti" (Pedretti 14). Having had access to Alberti’s and Vitruvius’ treatises, it is no surprise that Leonardo produced his own version of the Vitruvian man in his notebooks. This rendering of the Vitruvian Man, completed in 1490, is fundamentally different than others in two ways: The circle and square image overlaid on top of each other to form one image. A key adjustment was made that others had not done and thus were forced to make disproportionate appendages:

## The Vitruvian Man

A logarithmic spiral , equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli , who called it Spira mirabilis , "the marvelous spiral". [ edit ] Definition In polar coordinates the logarithmic curve can be written as [ 1 ] or

## Logarithmic spiral

In the ancient world certain numbers had symbolic meaning, aside from their ordinary use for counting or calculating ... plane figures, the polygons, triangles, squares, hexagons, and so forth, were related to the numbers (three and the triangle, for example), were thought of in a similar way, and in fact, carried even more emotional value than the numbers themselves, because they were visual. [ edit ] As worldview and cosmology The belief that God created the universe according to a geometric plan has ancient origins.

## Sacred geometry

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