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
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Each interior angle of an equilateral triangle is 60°, therefore we could fit together three, four, or five of them at a vertex, and these correspond to the tetrahedron, the octahedron, and the icosahedron. Each interior angle of a square is 90°, so we can fit only three of them together at each vertex, giving us a cube. The interior angles of the regular pentagon are 108°, so again we can fit only three together at a vertex, giving us the dodecahedron.
That makes five regular polyhedra. However, what would happen if we had a six-sided figure? Well, its interior angles are 120°, so if we fit three of them together at a vertex the angles add up to 360°, and therefore they lie flat. For this reason we cannot use hexagons to make a Platonic solid. In addition, obviously, no polygon with more than six sides can be used either, because the interior angles just keep getting larger.
The Greeks, who had to find religious truth in mathematics, found the idea of exactly five Platonic solids very compelling. The philosopher Plato concluded that they must be the fundamental building blocks of nature, and assigned to them what he believed to be the essential elements of the universe. He followed the earlier philosopher Empedocles in assigning fire to the tetrahedron, earth to the cube, air to the octahedron, and water to the icosahedron. To the dodecahedron, Plato assigned the
Johannes Kepler (1571-1630) was a German astronomer who believed in the heliocentric theory. Kepler is a clear example of the narrow line that separated science and religion. Nonetheless, his ideas would show that things could be solved through reason alone. He believed that the harmony of the human soul could be found through numerical relationships that existed between planets. He found that the planets: Mercury, Venus, Earth, Mars, Uranus, Jupiter, and Saturn all revolved at different times. For example, the earth revolved around the sun in a year while Saturn revolved around the sun in fifty years. From this, Kepler found a mathematical ratio, nine to the two-thirds power, to explain this phenomenon. This was revolutionary to humanity’s place in the universe. People were shocked that the universe could be explained by math alone rather than religion. This went strongly
Among these people were Copernicus who believed the sun was at the center of the world and the earth, stars and planets revolved around it. Danish astronomer Brahe helped contribute to this idea by contributing a large mass of data about the universe that he was able to discover. His student Kepler kept his ideas going, as he formulated many laws of planetary motion. He said the orbits around the sun were elliptical, planets don’t move in a uniform speed and the time a planet completes its orbit is related to its distance from the sun. Meanwhile, Florentine Galileo decided to use experiments to find out what happened and not what should happen, and discovered that a uniform force makes a uniform acceleration as well as inertia laws, that an object will be in motion forever unless stopped by another force.
the heliocentric solar system. Johannes Kepler further modified the heliocentric system, by mathematically showing that the planets’ orbits are elliptical. With his invention of the telescope, Galileo made new observations about the solar system and found mathematical laws that described the movement of the planets. Later, Isaac Newton established a universal law of gravity. With the new scientific discoveries, the gap between religion and science increased. Science revolutionized the human though and its understanding of the universe.
Plato's views on Forms, Ideas, and Knowledge are all expressed beautifully in the allegory of
All his writings consisted of numerous references to God. He saw his work as a fulfilment of his Christian duty to understand the works of God. Kepler believed that God had made the Universe according to a mathematical plan. Although, Kepler did thank God for granting him insights, but the insights were still presented as rational. While studying theology at the university at Tubingen, he fell under the influence of Michael Mastlin. He then abandoned theology and became a teacher of astronomy and mathematics in Austria. Johannes Kepler’s work illustrated the narrow line that would separate magic and science in the early Scientific Revolution. Kepler compared numerical relationships between planets in harmony of the human soul. He described it as discovering the "music of the spheres." Overtime, Johannes Kepler devised the three laws of planetary motion. He confirmed Copernicus' heliocentric theory, and eliminated the scientific possibility of crystalline spheres moving in perfectly circular orbits. Eventually, Johannes Kepler’s three laws affected the eliminated idea of uniform circular motion. By the end of Kepler’s life, the Ptolemaic system rapidly lost its ground to the new ideas. Many questions do remain unanswered. However, it was an Italian scientist who achieved an important break through to a new cosmology by answering the first question and striding through the
After that, we made the front portion which consists of a rectangular prism that sits flush against the cylindrical part of the pantheon, a triangular prism, and columns. This part of the building process was far easier and relied more on accurate measurements. The rectangular base that is attached to
Mathematics and art have always been closely related: Golden ratio, symmetry, proportion and geometry are elements in the art; not surprisingly, many great artists of history have been great mathematicians; they have been supported in mathematics to express reality with an artistic language. By definition geometry comes from the Greek: Ge = earth and Metron = measure. That is, it is the branch of mathematics that studies the measurement of the Earth that is concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. (Geometry. (2015).
Johannes Kepler was a man who made a surplus of achievements and discovery. What he is most known for is discovering that planets don’t go in a circular motion around the
Platos Forms are also called The theory of Ideas. Platos Form is the usual sense of shape, structure, and appearance. The presocratics influenced Plato by their thinking of reality such as Thales idea of reality was unified by water, while anaxiams idea of reality was that reality was boundless and nothing can oppose it. Plato was able to create the idea of forms from these pre socratics because of their ideas of reality. One of PLatos Form is Intellgible which means as transcendent realtiese they cannot be grasped by the senses but by only the intellect. These ideas come from the help of the pre socratics who were already thinking about the idea where reality was made of a specific thing. Plato was able to use all these ideas from the pre socratics and was able to create the Platonic forms. I think that the Pre socratics had started the idea of Forms for Plato and Plato elaborated the ideas of the presocratics to create it. I think Plato used Heraclitus idea of the fire in one of his forms. Platos form of Eternal was influenced by Heraclitus idea of fire. Platos Eternal states that as transcendant realities they are no subject to time and therefore not subject to motion and change. I believe Plato was also influenced by Paramenides because of his idea of self evident truth or “it is”. This idea is where the only thought can
Plato’s view on form, is described with what a form contains. Form is divided into six characteristics which are: transcendent, pure, archetypes, ultimate real, causes and systematically interconnected. Forms are transcendent in that they cease to exist in time and space, in that we see that a form never changes. Plato uses the example of roundness to explain that a ball can change but its form of being round will always stay. Forms are pure and they stay true to their identity, by this we see that an object is made of several characteristics, these characteristics work together to make an object, but the form of the characteristics is always pure. If you have a tire, it is formed of many characteristics (black, round, etc.), but the tire is round so the roundness of the tire is just pure roundness, it doesn’t share any other
When Kepler first began his work on the orbit of Mars he was under the assumption, as many scientists were, that the planetary orbits were circular, and that the Sun was at the center of the orbits. This type of system is called a heliocentric system. Also at this time only six planets were known. When Kepler obtained Brahe's data he discovered that the orbits were not perfect circles, but instead were ellipses that were only slightly flattened. The reason nobody else realized this was because the orbits were so slightly elliptical that extensive investigation and data would be needed to show this. It also turned out that the reason the orbit of Mars was very difficult to understand was because its orbit was more eccentric than the other planets that Kepler and Brahe had data about. To understand a lot of Kepler's work you must first
Johannes Kepler was a German astronomer and mathematician who lived between 1671-1630. Kepler was a Copernican and initially believed that planets should follow perfectly circular orbits (“Johan Kepler” 1). During this time period, Ptolemy’s geocentric theory of the solar system was accepted. Ptolemy’s theory stated that Earth is at the center of the universe and stationary; closest to Earth is the Moon, and beyond it, expanding towards the outside, are Mercury, Venus, and the Sun in a straight line, followed by Mars, Jupiter, Saturn, and the “fixed stars”. The Ptolemaic system explained the numerous observed motions of the planets as having small spherical orbits called epicycles (“Astronomy” 2). Kepler is best known for introducing three
“Everything which exist in this world and all things that we see around us are not as they appear to us” this is the core idea behind plato’s theory of forms.From this idea only he moves towards explaining his world of forms or ideas.
After Tycho’s death, his assistant, young mathematician Johannes Kepler used Tycho’s observations and came up with his First Law that orbits of the planets are elliptical instead of round like Copernicus believed. With his Second Law, Kepler stated that the speed of the planets depends on their distance from the sun which helped English astronomer and physicist Isaac Newton, to come up with his Law of Universal Gravitation.
Plato was interested in how we can apply a single word or concept to many words or things. For example how can the word house be used for all the individual dwellings that are houses? Plato answered that various things can be called by the same name because they have something in common. He called this common factor the thing’s form or idea. Plato insisted that the forms differ greatly from the ordinary things that we see around us. Ordinary things change but their forms do not. A particular triangle may be altered in size or shape but the form of a triangle can never change. Plato concluded that forms exist neither in space or time. They can be known not only by the intellect but also by the senses. Because of their stability and perfection, the forms have greater reality than ordinary objects observed by the senses. Thus true knowledge is knowledge of the forms.