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Mathematics and the Arts.
- Since the ancient times pursued to depict a man’s body with perfect proportions, while sculptors – to carve it from stone.
- Not only they tried to test it in practice, but also they left many manuscripts of this subject.
- For example, the sculptor Polykleitos wrote a treatise of mathematical proportions for carving an ideal man.
- The ancient Egyptians and Greeks knew about the golden ratio – an aesthetically pleasing ratio and implied it in their paintings, buildings.
- The idea of the Egyptian triangle was realized in the design of such famous buildings as the Pyramid of Cheops, the Parthenon and the Colosseum.
- A famous Renaissance painter Leonardo da Vinci also used mathematics in his works.
- Being Luca Pacioli’s student, he studied his book Summa, from which he copied tables of proportions.
- In Mona Lisa he used the idea of Golden Rectangles.
- In The Last Supper he intensively sought how to arrange characters at the table.
- So the whole painting was constructed in a ratio of 12:6:4:3.
- With the further development of Mathematics works of artists became more complicated, what we can detect in the paintings of the best-known representative of an imp-art M. C. Escher.
- He explored the concepts of infinity and symmetry and masterly used it.
- He used to tile surfaces with regular shapes such as triangles, squares and hexagons, irregular polygons.
- In the middle of 1980-s the fractal art was developed.
- A fractal is a self-congruent set.
- The considered icons of it are the Julia set and Mandelbrot set.
- Geometry was always the most beautiful branch of Mathematics and it made a great impact on the Arts, and it still makes.
- Thus, they were bounded together tightly for many decades.
- Yuradem
September 2014
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