A ratio is the quotient of two quantities.

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Phi is a proportion or ratio - approximately
1 : 1.618

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(First defined by Euclid around 300 B.C.)

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Some systems of proportions were based on:

3. The Golden Ratio

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The Golden Ratio is also called extreme and mean ratio. According to Euclid,

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.

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“Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into mean and extreme ratios, that is , the Golden Mean. The first way may be compared to a measure of gold, the second to a precious jewel.”
- Johannes Kepler (1571-1630)

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Matemática é poesia.

Yellow Spiral Galaxies by Nasa.

Hurricane Golden Spiral by Charlie Case.

Yellow Spiral Rose by Nogwater.

Rams Horn by Istockphoto

Counting Spirals (the golden mean) by Statistics of Nature

Newgrange Entrance Stone by Laurie Young.

Yellow spiral glass by Marek Fisar.

Gentle Nautilus by Eletronic Fear of Everything.

DNA Spiral by Infinitoy.

Celtic Triskel by Lytha Studios.

Spiral Dream Catcher by Rainbow and Gifts.

the downward spiral by Trent Reznor, 1994.

Nautilus

Nautilus Shell

Swimming Nautilus

Chambered Nautilus (Nautilus pompilus, Linnaeus, 1758) by Man and Mollusk.

LiveMath graph of a Nautilus shell by The Department of Natural Science and Mathematics.

The Golden Mean (phi), golden spiral, Fibonacci spiral e a Pirâmide de Gizé.

… e por que só o tempo e apenas o tempo, não seria espiral?

Música: The Downward Spiral, Nine Inch Nails aka Trent Reznor