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Plato presents a justly famous example of geometrical discovery in the Meno (82b-85c). He shows how one might arrive at knowledge of the theorem that the area of the square on a diagonal of a square is twice as big. This way of arriving at a geometrical truth does not involve measurement.
In mapping it out as a convenient approximation to the celestial sphere, we discover that it offers a geometric framework for the Paths of Anu, Enlil and Ea of Mesopotamian astronomy, while explaining the enigma of why the constellations of the zodiac are not equally distributed along the ecliptic.
1 Ιουν 2010 · Geometric shapes exhibit symmetry as mirror reflections of each other. Symmetry in nature has been a model of beauty since the beginning of civilization.
19 Οκτ 2019 · The present paper aspires to explain fully both the supreme importance of Geometry for Plato, and also the nature of the serious criticism that Plato directs against the geometers, the cause of their faulty practice, and the means he proposes to correct it and ascend to the intelligible Geometry.
Examining each individual account leaves unresolved issues, but I show that Plato’s repetition of the geometrical examples allows him to continue discussions aimed at philosophers across several dialogues, rectifying omissions and demonstrating the value of writing as a reminder.
Platonic Solids Quick facts • The Platonic solids are named after the philosopher Plato and have been known for thousands of years. • A Platonic solid is an example of a polyhedron (plural: polyhedra). A polyhedron is a three-dimensional shape with flat faces, where each face is a polygon. For example a cuboid is a polyhedron, its faces are ...
In this paper, we analyze the two geometrical passages in Plato’s Meno, (81c – 85c) and (86e4 – 87b2), from the points of view of a geometer in Plato’s time and today. We give, in our opinion, a complete explanation of the difficult second geometrical passage.
