
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
F^{2}
= 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:
F_{n} + F_{n+1} = F_{n+2}
and lim. n to infinite: F_{n} / F_{n1}
= 1.618... or Phi. 


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 23 business days
This
neat poster
shows you all the secrets of the Fibonacci Numbers.
Product
Information:
Perfect for dressing up any wall. Our highquality poster is printed
on heavyweight 7 mil semigloss paper using superior dye inks.
More
info 
Interesting
Links:
Fibonacci Number
Calculator
Fibonacci Numbers 



Read
here
before
copying and using
any of our images
or texts. Thanks 

Share
ideas and
discoveries with
other puzzle fans
contact
us 
About
Us  Sponsorship
 Pressclippings
 Cont@ct
 ©opyrights
 Tellafriend
 Link2us
 Sitemap
© Archimedes'
Lab  Privacy
& Terms  The
web's best resource for puzzling and mental activities 