golden rectangles 1

Phi, the Golden Number

Numerus Aureus
golden rectangles 2
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
golden rectangle
The Golden Spiral
golden spiral

Calculating Phi
golden formula
Interesting relations
1 / F = F / (F + 1) = F - 1
F2 = F / (F - 1) = F + 1

golden triangle 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)

The functional arrangement of the leaves of some plants

Geometric shapes regulated by Phi

(angles 36, 72 degrees)
isosceles triangles, kite, parallelogram, pentagon, decagon.

golden shapes
(having a network of pentagons or equilateral triangles) dodecahedron, icosahedron, small and large star dodecahedron.


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...
mondrian 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
sarcone's paradoxes
quadrix A
...and after
quadrix B

The Quadrix, Geometrex and Tangramagic incredible puzzles can be purchased at: , or


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
Fibonacci Numbers

spot the pattern 1 spot the pattern 2
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