eTwinning Project 2019

1. Maths and Art in Spirals II
7 A Grade
“Jean Monnet” High School
Bucharest
Teacher Mihaela Git
-2019-

2. Mara
The Spiral of Theodorus ( square root spiral)
is a spiral composed of right triangles, placed edge-to-edge.
It was named after Theodorus of Cyrene.
https://youtu.be/_hhbRuKtikAVideo tutorial (10C):

3. Clara Brândușa

4. Tudor T Luca

5. Matei

6. Irina

7. Theo

9. Maria
The Pythagoras tree
is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher
Albert E. Bosman in 1942, it is named after the ancient
Greek mathematician Pythagoras because each triple of touching squares encloses a right
triangle, in a configuration traditionally used to depict the Pythagorean theorem.

13. Timea

14. Mara

15. Let be an equilateral triangle of side l. Each colored equilateral triangle has the side length
twice smaller than the preceding one.
Thus, the so-called "Spiral of the equilateral triangles" is formed.
Calculate
approximately the
area of the green
surface!

16. Mara
It is considered a square with side l. The first red triangle is obtained by connecting the
middles of two consecutive sides of the given square; the second red triangle is obtained by
connecting the middle of the hypotenuse of the first triangle with the middle of the side of the
second square, etc. You get a Red spiral, consisting of rectangles, isosceles triangles.
What is the area of this spiral?

17. Mara
Construct a regular hexagon with side l. Successively construct regular hexagons determined
by the middles of the sides of the preceding hexagon. Each green triangle is determined by a
hexagon tip and two means of consecutive sides.
A spiral with isosceles triangles with an angle of 120 ° is formed.
In the second figure are highlighted 3 green spirals out of the 6 that can be drawn.
To calculate the area of a green spiral.

21. Bibliography:
• https://www.facebook.com/ArtOfMathematics/
• https://en.wikipedia.org/wiki/Spiral_of_Theodorus
• https://en.wikipedia.org/wiki/Pythagoras_tree_(fractal)