1. 1. GOLDEN RATIO
2. 2. MATH IS A GAME
3. 3. AGENDA: OTHER NAMES: CONSTRUCTION OF THE GOLDEN SECTION GOLDEN RATIO IN ARTS AND ARCHITECTURE GOLDEN RATIO IN HUMAN AND NATURE REFERENCES INTRO:
4. 4. In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is a mathematical constant approximately 1.6180339887. The golden ratio is also known as the most aesthetic ratio between the two sides of a rectangle. The golden ratio is often denoted by the Greek letter (phi). .
5. 5. OTHER NAMES: Extreme and mean ratio, Medial section, Divine proportion, Divine section, Golden proportion, Golden cut, Mean of Phidias
6. 6. CONSTRUCTION OF THE GOLDEN SECTION: Firstly, divide a square such that it makes two precisely equal rectangles.
7. 7. Take the diagonal of the rectangle as the radius to contsruct a circle to touch the next side of the square. Then, extend the base of the square so that it touches the circle.
8. 8. When we complete the shape to a rectangle, we will realize that the rectangle fits the optimum ratio of golden. The base lenght of the rectangle (C) divided by the base lenght of the square (A) equals the golden ratio. C / A =A / B = 1.6180339 = The Golden Ratio
9. 9. GOLDEN RATIO IN ARTS AND ARCHITECTURE: LEONARDO DA VINCI THE PARTHENON THE VITRUVIAN MAN
10. 10. Many artists who lived after Phidias have used this proportion. Leonardo Da Vinci called it the "divine proportion" and featured it in many of his paintings, for example in the famous "Mona Lisa". Try drawing a rectangle around her face. You will realize that the measurements are in a golden proportion.. LEONARDO DA VINCI
11. 11. THE VITRUVIAN MAN Leonardo did an entire exploration of the human body and the ratios of the lengths of various body parts. Vitruvian Man illustrates that the human body is proportioned according to the Golden Ratio.
12. 12. THE PARTHENON Phi was named for the Greek sculptor Phidias. The exterior dimensions of the Parthenon in Athens, built in about 440BC, form a perfect golden rectangle.
13. 13. The baselenght of Egyptian pyramids divided by the height of them gives the golden ratio..
14. 14. GOLDEN RATIO INHUMAN AND NATURE GOLDEN RATIO IN HUMAN HAND AND ARM GOLDEN RATIO IN THE HUMAN FACE GOLDEN RATIO IN THE SEA SHELLS GOLDEN RATIO IN THE SNOWFLAKES GOLDEN SPRIAL
15. 15. GOLDEN RATIO IN HUMAN HAND AND ARM Look at your own hand: You have ... 2 hands each of which has ... 5 fingers, each of which has ... 3 parts separated by ... 2 knuckles The length of different parts in your arm also fits the golden ratio.
16. 16. GOLDEN RATIO IN THE HUMAN FACE The dividence of every long line to the short line equals the golden ratio. Lenght of the face / Wideness of the face Lenght between the lips and eyebrows / Lenght of the nose,Lenght of the face / Lenght between the jaw and eyebrows Lenght of the mouth / Wideness of the nose, Wideness of the nose / Distance between the holes of the nose,Length between the pupils / Length between teh eyebrows. All contain the golden ratio.
17. 17. GOLDEN RATIO IN THE SEA SHELLS The shape of the inner and outer surfaces of the sea shells, and their curves fit the golden ratio..
18. 18. GOLDEN RATIO IN THE SNOWFLAKES The ratio of the braches of a snowflake results in the golden ratio.
19. 19. GOLDEN SPRIAL The Golden Spiral can be seen in the arrangement of seeds on flower heads.
20. 20. REFERANCES http://tr.wikipedia.org/wiki/Alt%C4% B1n_oran http://www.geom.uiuc.edu/~demo533 7/s97b/art.htm http://www.mcs.surrey.ac.uk/Personal /R.Knott/Fibonacci/fibnat.html http://www.matematikce.net/maltinor an.html