# Phi, the Golden Number

Numerus Aureus
 The mineral world is governed by the irrational numbers, like the square root of 2 or 3; and the world of the living, by the numbers of the recurrence sequences such as Fibonacci, Lucas or Pell numbers which are related to the Golden Number or Phi (F). There is no magic, the Golden Ratio is an economical way to orchestrate harmoniously living volumes, with less effort and maximum efficiency. The Golden Rectangle The Golden Spiral
 Calculating Phi Interesting relations 1 / F = F / (F + 1) = F - 1 F2 = F / (F - 1) = F + 1
 Pentagram and Golden Triangle forming an Equiangular Spiral AB / BC = BC / AC = BC / DE = EF / DE= = DE / DF = AC / AD = 1 / F = 0.618...
We find Phi in...
(see below)
 Nature Phyllotaxy The functional arrangement of the leaves of some plants
 Geometric shapes regulated by Phi Polygons (angles 36, 72 degrees) isosceles triangles, kite, parallelogram, pentagon, decagon. Solids (having a network of pentagons or equilateral triangles) dodecahedron, icosahedron, small and large star dodecahedron.

Engineering

Le Corbusier
Construction from the Modulor.

Fibonacci Numbers
 There are a lot of interesting recurrence sequences, but the most popular one is the Fibonacci sequence. Every number or term of this sequence is the sum of the two direct preceding terms: Fn + Fn+1 = Fn+2 and lim. n to infinite: Fn / Fn-1 = 1.618... or Phi.
...-1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...
 Art Piet Mondrian Composition (1927).
Paradoxical games
 Our Quadrix Puzzles are based on the Fibonacci or Lucas numbers and on the golden ratio. When several pieces of these puzzles are permuted, a small square hole appears... It is an old mathematical trick which deceives our visual perception. With 4 terms of the Fibonacci and Lucas sequences, such as 3, 4, 5, and 7, we can build the base of a paradoxical puzzle Example Before... ...and after

The Quadrix, Geometrex and Tangramagic incredible puzzles can be purchased at:
http://www.rexgames.com , or http://www.tessellations.com

 Poster PHI, the Golden Number Price: \$15.99 Size: 16.0" x 20.0" In Stock, will ship in 2-3 business days This neat poster shows you all the secrets of the Fibonacci Numbers. Product Information: Perfect for dressing up any wall. Our high-quality poster is printed on heavyweight 7 mil semi-gloss paper using superior dye inks. More info Interesting Links: Fibonacci Number Calculator Fibonacci Numbers
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