The Life of Johannes Kepler
HIS LIFE
Johannes Kepler was a German astronomer and mathematician ho discovered that planetary motion is elliptical. Early in his life, Kepler wanted to prove that the universe obeyed Platonistic mathematical relationships, such as the planetary orbits were circular and at distances from the sun proportional to the Platonic solids (see paragraph below). However, when his friend the astronomer Tycho Brahe died, he gave Kepler his immense collection of astronomical observations. After years of studying these observations, Kepler realized that his previous thought about planetary motion were wrong, and he came up with his three laws of planetary motion. Unfortunately, he did not have a unifying theory for these laws. This had to until Newton formulated his laws of gravity and motion.
PLATONIC SOLIDS
A platonic solid is a solid having similar, regular polygonal faces. There are five Platonic solids: the icosahedron, tetrahedron, octahedron, dodecahedron, and cube. They are characterized by the fact that each face is a straight-sided figure with equal sides and equal angles:
Tetrahedron: 4 triangular faces, 4 vertices, 6 edges
Cube: 6 square faces, 8 vertices, 12 edges
Octahedron: 8 triangular faces, 6 vertices, 12 edges
Dodecahedron: 12 pentagonal faces, 20 vertices, 30 edges
Icosahedron: 20 triangular faces, 12 vertices, 30 edges
Many people wonder why there should be exactly five Platonic solids, and whether there is one that has not been found yet. However, it is easy show that there must be five and that there cannot be more than five.
At each vertex, at least three faces must come together, because if only two came together they would collapse against o...
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...ere derived strictly from careful observation and had no theoretical basis. However, about 30 years after Kepler died, the English mathematician/physicist Sir Isaac Newton derived his inverse square law of gravity, which says that the force acting on two gravitating bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Kepler's laws may be derived from this theoretical principle using calculus.
Bibliography:
1) Calculus: A First Course
James Stewart, Thomas Davison, Bryan Ferroni
McGraw-Hill Ryerson Limited
Copyright 1989
2) Applied Physics Third Edition
Arthur Beiser
McGraw-Hill Limited
Copyright 1995
3) http://www.mathacademy.com
4) http://www.encyclopedia.com/articles/06915.html
5) http://www.letsfindout.com/subjects/space/kepler.html
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Plato assumes that there exists two kinds of things in nature more commonly referred to as “the cyclical argument”: forms and opposites (Phaedo 102 a – 103 b). Plato’s forms are related universally, they do not change where ever you go for example: there are a lot of things that are
Plato seems to be saying that it is not enough to know the forms of tables or
Plato: When we discuss Forms we are not talking about something that is truly real but something that we would see or grasp intellectually. The idea of it is that what you are looking at may not be the true form of which you are looking at it. When you draw a circ...
Plato postulates that difference and sameness can’t exist in a singular entity, therefore the tripartite division of the soul describes how Plato believes that the soul is made up of multiple pieces/ has five different forms in correspondence with the five different constitutions. Aristocratic, Timocratical, Oligarchical, Democratic, and the
According to Plato, his Theory of Forms states perfection only lives in the realm of thought. There only exists one of every ideal and the rest is just a copy. This one creation is called a form, the most flawless representation of an idea. In the physical world everything is a copy of these forms and all copies are imperfect. Plato believed in two worlds; the intelligible world and the illusionistic world. The intelligible world is where everything is unchanging and eternal. We can only grasp the intelligible world with our mind. It is the world of ideas and not senses. A place where there are perfect forms of the things we know on Earth. According to Plato everything in the world we live in is an illusion. All objects are only shadows of their true forms. His theory further states every group of objects that have the same defying properties must have an ideal form. For example, in the class of wine glasses there must be one in particular that is the ideal wine glass. All others would fall under this ideal form.
Plato believed that form is true reality. It is supreme which means it doesn’t exist in space but it exists in different ways, that is why it is unchanging. No one can change the form. It is real and intelligible. The form is pure.
Plato’s concept was that a certain object could be better understood as an expression of a particular Idea. The Idea was considered an Archetype while the object expressing this archetype was a form. For example you may see a dog but it is not actually a dog but instead it is the form of the Archetype dogness which is the true perfect form. An example that Tarnas gives us of this concept is someone who is beautiful is only taking on the attribute of the absolute Form of
Plato also argues for the reality of ideas as the only way to be sure of ethical standards and of objective scientific knowledge. In the Republic and the Phaedo Plato suggests his theory of forms. Ideas or forms are the established archetypes of all phenomenon, and these ideas are the only thing completely real and true; the physical world holds only relative reality for the time being. The forms are simply ...