What Contributions did Plato make to Geometry?

Question

I am aware of a previous post on this topic, but it was unhelpful (http://answers.yahoo.com/question/index;... If possible, could sources be included because this is for a project. Thank You.

I am aware of a previous post on this topic, but it was unhelpful (http://answers.yahoo.com/question/index;... If possible, could sources be included because this is for a project. Thank You

Also, was he involved in the creation of any theorems or postulates?

Answer 1

Plato concentrated on the idea of "proof" and insisted on accurate definitions and clear hypotheses. This laid the foundations for Euclid's systematic approach to mathematics. All of the most important mathematical work of the fourth century was done by friends or pupils of Plato, including Eudoxus, Aristotle, and Archytas.

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 being represented by the cube, tetrahedron, octahedron, and icosahedron repectively. The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.

Influence on Plato
Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. According to R. M. Hare, his influence consists of three points: a) the platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. b) there is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in science and morals". c) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both have been influenced by Orphism.[1]

Plato's harmonics were clearly influenced by the work of Archytas, a genuine Pythagorean of the third generation, who made important contributions to geometry, reflected in Book VIII of Euclid's Elements.

I could not reference your link. I hope this helps.

Answer 2

Plato (427-347 BC), the logician maximum esteemed through the Greeks, had inscribed above the front to his in call for college, "enable none blind to geometry enter right here." regardless of the indisputable fact that he replaced into no longer a mathematician himself, his perspectives on arithmetic had great effect. Mathematicians to that end generally happening his perception that geometry would desire to apply no kit yet compass and straightedge – in no way measuring contraptions which includes a marked ruler or a protractor, because of the fact those have been a workman’s kit, no longer worth of a pupil. This dictum brought about a deep learn of conceivable compass and straightedge structures, and 3 classic shape issues: a thank you to apply those kit to trisect an attitude, to construct a cube two times the quantity of a given cube, and to construct a sq. equivalent in section to a given circle. The proofs of the impossibility of those structures, finally performed in the nineteenth century, brought about significant concepts relating to the deep shape of the real quantity gadget. Aristotle (384-322 BC), Plato’s perfect pupil, wrote a treatise on strategies of reasoning utilized in deductive proofs (see good judgment) which replaced into no longer significantly superior upon till the nineteenth century