The document discusses several ancient Greek mathematicians and their contributions including Pythagoras and his theorem relating the sides of a right triangle, Thales and his work measuring the height of pyramids, and Euklides who developed Euclidean geometry. It then covers later mathematicians like Euler who studied graph theory and bridges, and Mandelbrot who pioneered the field of fractal geometry and used it to study irregular shapes in nature. A variety of applications of mathematics are also mentioned spanning fields like biology, mechanics, and astronomy.

1. Before science ...

3. OUR 5 GROUPS
● Eukleides ● Use wikipedia or other
● Herakleitos resources to find out
informations about the
● Hypatia personnalities in order
● Pythagoras to complete the map
that follows and the
● Thales table 1

5. Who is behind the following
sentences ?
● Everything is number.
● Earth floats on water.
● Follow the common.
● He is the father of geometry

6. Pythagoras

7. Geometrical representation of numbers :
Square numbers : 1, 4, 9, ...
Triangular numbers : 1, 3, 6, ...
The tetractys

8. Commensurability

9. The proportions and means
Arithmetic : 1,8,15
Geometric : 5,10,20
Harmonic : 12,8,6

10. Thales
Measuring the pyramid

11. Eukleides
The elements
The euclidian geometry
Arithmetic

12. Many years after ...
The story of maths continues ...
each theory has a nice story and unexpected
applications

13. Euler (1707-1783)
The bridges of Konigsberg

14. The theory of graphs

15. Applications

16. ELEPHants

18. Benoit Mandelbrot (1924 - 2010)
How long is the coast of Britain ?

19. The Olbers paradox
Why is the night dark ?
Why is the space dark ?

20. Some fractals objects

21. The Pythagorian tree

22. The Koch snowflake

23. The sierpinsky triangle

24. The Mandelbrot set

25. Fractal art

26. Applications
In biology : The total area of the lung
In mechanics : Soundwalls
In astronomy : Laurent Nottale and the scale relativity