... section) or the Golden Section. (a line cut at "an extreme and mean ratio" - see below) Note how these simple shapes (i.e. the mollusk- shell,) appear most frequently in nature - snail shells, and even apple-seed stars that form a pentagram, have proportions to Phi. Geometric shapes of these (Golden Ratio) dimensions can also be found in magnificent works of art - and most mathematicians agree, they ... height! Theories of this sort have just started to come out, (in the 21st century!) and are being used in corrective surgery. Plato (428/427 B.C. - 348/347 B.C.) saw these geometric shap...

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... much is known about what advances in geometry were made between the times of Thales and the Pythagoreans. The Pythagoreans advanced the understanding of not only triangles, but a number of geometric shapes. They were the first to relate relative areas and use the concepts to formulate a primitive algebra. Plato did not make any famous contributions to geometry. However, he made important advances ... ...

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... "(Collins 327-328). One group of researchers searched the waters of Cuba. The crew from Advanced Digital Communications attempted to analyze the geometric shapes of stone about two thousand feet below the water (Sullivan A25). It was thought that these shapes could have been remains from Atlantis. Underwater research has had many finding in the search for Atlantis. " Researchers with a Canadian exploration company ... ...

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• Grade Level: High School

... from the material. He believed that mathematics in its ideal form could still be applied to the heavens. The heavenly bodies, as he thought to be true, were in perfect geometric form; he decided also that since the heavens were perfect, the various heavenly bodies would have to move in exact circles. Also in mathematics, Plato's name is attached to the ... Platonic solids. In the Timaeus there is a mathematical construction of the elements (earth, fire, air, and water), in which the cube, tetrahedron, octahedron, and icosahedron are given as the shapes of the atoms of earth, fire, air, ...

• Word Count: 629
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• Grade Level: High School