1. Golden treasure we share In the world of mathematics

3. 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.

4. Calculating Phi Φ=1,61803…

5. Golden section in the history of mathematics

6. 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

7. 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.

8. Curiosities

9. 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…

10. Construction of geometrical forms

11. Special geometrical forms can be created by using the golden ratio: GOLDEN TRIANGLE GOLDEN PENTAGON AND DECAGON

12. Coverings

13. A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps.

14. A non-periodic tiling can only fill the plane by turning and mirroring the pieces, not just pushing them.

15. We made it:

16. Golden section in the computer working

17. Text edition The golden s. is often used in book printing This book was designed after the plan above.

18. Picture edition The golden section can be found in photography, advertising and generally in media Isn’t it fantastic?

19. 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

20. THANKS FOR YOUR PARTICIPATION ! SEE YOU IN APRIL!