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Maths and art in spirals ii
- 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):
- 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)