Download Golden treasure we share

Golden treasure
we share
In the world of mathematics
Definition: What is Phi?
If the ratio of the sum of the quantities
to the larger quantity is equal to the
ratio of the larger quantity to the
smaller one.
φ = (a+b)/a = a/b
You can see it included in
everything around you, but it isn’t
obvious.
Calculating Phi
 1
   1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5 1


2
1
1
1
1....
Φ=1,61803…
Golden section in
the history of
mathematics
Ancient times
It was discovered by Egyptians and
Greeks and was used in architecture
and art-like pyramids
The ancient Greeks used it too, they
based the design of the Parthenon on
Phi
Middle Ages
Leonardo Fibonacci:
In his book "Liber abaci", he
introduced the so called
rabbits problem and the
Fibonacci-series
Leonardo Da Vinci presented
the Golden Ratio through his
famous painting Marcus
Vitruvius.
He used the golden ratio to
define all the fundamental
proportions.
Curiosities
How can be calculated the stocks
How does colors pass to each other
How appears the Phi in population growth, and
how it can be used, to predict urban
populations.
How does Phi’s mysteriousness appear in solar
system…
Construction of
geometrical forms
Special geometrical forms can be
created by using the golden ratio:
GOLDEN TRIANGLE
GOLDEN PENTAGON
AND DECAGON
Coverings
A tessellation or tiling
of the plane is a
collection of plane
figures that fills the
plane with no
overlaps and no gaps.
A non-periodic tiling can only fill the plane by
turning and mirroring the pieces, not just pushing
them.
We made it:
Golden section in
the computer
working
Text edition
The golden s. is often
used in book printing
This book was designed after
the plan above.
Picture edition
The golden section can be found in
photography, advertising and
generally in media
Isn’t it fantastic?
Fractals
A fractal is "a rough or fragmented geometric shape that can be split
into parts, each of which is (at least approximately) a reduced-size copy
of the whole," a property called self-similarity. Some fractals follow the
Fibonacci-series (Mandelbrot) or Fibonacci-spiral
THANKS FOR YOUR
PARTICIPATION!
SEE YOU IN APRIL!