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
The first pillar we come across is Logos. Plato demonstrates his appeal to logic from the start with a series of metaphorical questions. During this created dialogue his questions strengthen the idea that the prisoners who have only seen the shadows will believe them to be the real objects. This is a metaphor for societies, and the common thought that people only believe what they can see. That they tend to be closed minded and slow moving when it comes to new ideas. So plato gives them a way so they can understand
Plato seems to be saying that it is not enough to know the forms of tables or
In 1687, Newton published Philosophiae Naturalis Principia Mathematica (also known as Principia). The Principia was the “climax of Newton's professional life” (“Sir Isaac Newton”, 370). This book contains not only information on gravity, but Newton’s Three Laws of Motion. The First Law states that an object in constant motion will remain in motion unless an outside force is applied. The Second Law states that an object accelerates when a force is applied to a mass and greater force is needed to accelerate an object with a larger mass. The Third Law states that for every action there is an opposite and equal reaction. These laws were fundamental in explaining the elliptical orbits of planets, moons, and comets. They were also used to calculate
Plato was born in Athens, Greece around 427 B.C. He was always interested in politics, until he witnessed his mentor and teacher, Socrates, death. After learning of the callousness of politics, Plato changed his mind and eventually opened up The Academy, which is considered if not the first, one of the first Universities. Students at the Academy studied many different fields of science, including biological and astronomical. The students also studied many other fields, such as math. Plato developed many views that were mathematical in nature. He expressed these views through his writings. According to Dr. Calkins of Andrew University, "Timaeus is probably the most renowned of Plato's thirty-five dialogues. [In it] Plato expresses that he believes that the heavenly bodies are arranged in perfect geometric form. He said that because the heavens are perfect, the various heavenly bodies move in exact circles." (Calkins 1). Of course that is a much summarized view of what Plato discusses in Timaeus, but still a solid view on Plato's beliefs about cosmology. Cosmology can be loosely defined as everything being explained and in its place or beautiful. The cosmos is beautiful because everything is perfect. Plato understood that when he defined the most perfect geometric design as the circle. In a circle one line is always equidistance from one point. In Plato's universe there are two realms, eternity and time. The factor that creates "time" out of the chaos of "eternity" is the Demiurge. Plato's Demiurge can be defined as an architect creator theological entity. The importance of the Demiurge in this paper is to compare and contrast him with Boethius's God in The Consolation of Philosophy.
Isaac Newton’s story of how an apple falling from a tree that hit his head inspired him to formulate a theory of gravitation is one that all school children grow up hearing about. Newton is arguably one of the most influential scientific minds in human history. He has published books such as Arithmetica Universalis, The Chronology of Ancient Kingdoms, Methods of Fluxions, Opticks, the Queries, and most famously, Philosophiæ Naturalis Principia MathematicaHe formulated the three laws of gravitation, discovered the generalized binomial theorem, developed infinitesimal calculus (sharing credit with Gottfried Wilhelm Von Leibniz, who developed the theory independently), and worked extensively on optics and refraction of light. Newton changed the way that people look at the world they live in and how the universe works.
Plato’s view on existence can be understood by discussing his theory of Forms. The theory of Forms or Ideas is about the existence of ideas in higher form of reality, the existence of a reality inhabited by forms of all things and concepts. Plato used example of objects such as table and rock and concepts like Beauty and Justice to illustrate the notion of Forms. Plato further describes Forms as a being possessed by concepts. For example, Virtue has different characters; but they all have a common nature which makes them virtuous.
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 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: 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...
Therefore, many of the philosophers disagreed with each other and came up with very different answers for the same concepts. Plato also did not know the answers to all of the questions that arose in the pre-Socratic era. Plato decided to look back on the pre-Socratics era in particular at the philosophers Heraclitus and Parmenides. He agreed with Heraclitus who believed our world is constantly changing and with Parmenides who believed that the real world is not the same as the world of our experience. Plato chose to look at materialism and also his theory of Forms in a two-world setting in order to attempt to answer the questions of the universe. The two worlds Plato is talking about are: a world that is in constant flux (the world we live in) and a world that is ever-changing (the real world, otherwise known as Forms). Plato’s Forms distinguishes things that are real from things in our mind that we perceive as real. Plato also made the argument that reality is different than our worldly experience. Plato believed that material objects can imitate the forms because they have order, however, Aristotle’s disagreed. However, Aristotle thought that Plato’s concept of “participation” didn’t make sense. Aristotle believed that the world we live in is our reality and he argued that Plato’s idea of forms
He argues that non-physical forms or ideas represent the most accurate reality. There exists a fundamental opposition between in the world like the object as a concrete, sensible object and the idea or concept of the objects. Forms are typically universal concepts. The world of appearance corresponds to the body. The world of truth corresponds with the soul. According to Plato, for any conceivable thing or property there is a corresponding Form, a perfect example of that or property is a tree, house, mountain, man, woman, Table and Chair, would all be examples of existing abstract perfect Ideas. Plato says that true and reliable knowledge rests only with those who can comprehend the true reality behind the world of everyday experience. In order to perceive the world of the Forms, individuals must undergo a difficult
Tarnas covered a few concepts during the first 40 pages. The first of these concepts was the idea of Archetypal Forms. Platonism revolves around this main idea that pushed the existence of archetypal ideas and forms. The question Plato wanted to answer was “What is the precise relation between the platonic Forms of Ideas and the empirical world of everyday reality?” Plato uses the words idea and eidos which mean idea and form.
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 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 ...