Pythagoras is considered, not only as one of the greatest mathematicians in history, but also for his works concerning music, philosophy, astrology, and many others for all the discoveries made by him. One of the greatest discoveries attributed to Pythagoras is the discovery of the musical scale used nowadays. This scale was based on the principle in which all Pythagoreans base their thought: the existence of numbers in every single aspect in existence. A philosophical belief of universal creation based upon the perfect harmony between numbers and nature. From this argument, he built a whole theory about the harmonies (referring to musical harmonies) which exists in our solar system, which was later developed by several philosophers, physicists, musicians, and so on. He stated that the distances between the different planets had a direct relation with those discovered by him in the musical scale, and that each planet would make a special sound that combined with those of the other planets would create a perfect this harmony that is known as the “Music of the Spheres” (also called “Harmony of the Spheres” or “Universal Harmony”). Based upon his geocentric theory of the solar system, his theory about the celestial harmony created by the spheres, stated that those bodies, with smaller distances to the center of the solar system, or those bodies that orbit closer to the Earth, would make a lower notes that would stay constant and would produce and sound without an end.
Through history, as said before, many philosophers have supported and developed what Pythagoras first exposed to the world. One of the most important philosophers to support Pythagoras’s ideas was Plato. In some of his writings he discusses the creation of the unive...
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The ratio between the distances of the last planet of Kepler’s system, Saturn, is 107 in its aphelion and 134 in its perihelion making it very close to a relation 5:4. In the case of Jupiter, the ratio is almost 6:5; for Mars it is a 3:2 ratio; for the Earth it is 16:15; for Venus, which has the smallest gap is 25:24; and for Mercury it is of 12:5. The harmonic intervals, as we saw before, can be represented as ratios just as the proportions of the arcs traveled by the planets. Kepler established a direct relation between these two to show what the “melody” of each planet through its orbit was. In this cases, 5/4 (Saturn) corresponds to a mayor third or a difference of four semitones between two notes. Jupiter’s ratio, 6/5, is the same as a minor third or a difference of three semitones.
Works Cited
Harmonices Mundi, Book 5, Chapter VII
In the field of philosophy there can be numerous answers to a general question, depending on a particular philosopher's views on the subject. Often times an answer is left undetermined. In the broad sense of the word and also stated in the dictionary philosophy can be described as the pursuit of human knowledge and human values. There are many different people with many different theories of knowledge. Two of these people, also philosophers, in which this paper will go into depth about are Descartes and Plato. Descartes' Meditations on First Philosophy and Plato's The Republic are the topics that are going to be discussed in this paper.
Music derived from astrology is surprisingly rare. The ancient Greek philosophers, whatever their intellectual attitudes towards astrology may have been, were certainly not ignorant of astrological teachings and ideas. It was they, after all who put forward the idea of the "Music of the Spheres", the idea that these vast objects twirling around and whirling through space, must have hummed a tone as they went along their courses, much as a ball spun on a string will whistle. They knew of seven planets: Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn. Not surprisingly, western music evolved with seven-tone scales. Music and astrology come together again in this suite devoted to the seven planets, though Uranus and Neptune have displaced the Sun and Moon. Gustav Holst (1874-1934) was apparently fascinated by various esoteric pursuits, such as astrology and Hindu philosophy, suggesting in particular a yearning to get to grips with matters of a spiritual nature. How far he got in this pursuit is unclear, but what is quite beyond doubt is the fact that The Planets is a deeply spiritual work, reaching a level of spirit expression that is rarely experienced in other works. Even without this added strength, the whole work is a sonic spectacle and has so many wonderfully exotic harmonies. Coloration, dramatic contrast and inventiveness make this the work of a genius. It was first performed in the autumn of 1918.
The influence of Aristotle can be seen in almost every era of history that followed his death over 2300 years ago. In the Middle Ages thinkers used Aristotle’s work as a sort of “final authority on all sorts of issues” (Patterns, 141). In the 16th and 17th centuries philosophers had to first tackle...
By your harmonizing of various voices, and through your ears, she has whispered of herself, as she i... ... middle of paper ... ... Again he positioned these two as “G” and positioned the rest according to the relation between the numbers (Kepler: Book V). Looking at all that has been mentioned, Kepler found that in fact Pythagoras had a certain approach to what the music scale, in relation to the planets, was. He managed to built melodies of the numbers that he discovered by observing the planets that brought together would create what he believed was the one true Harmony of the World.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
The first record of the movement of the planets was produced by Nicolaus Copernicus. He proposed that the earth was the center of everything, which the term is called geocentric. Kepler challenged the theory that the sun was the center of the earth and proposed that the sun was the center of everything; this term is referred to as heliocentric. Kepler’s heliocentric theory was accepted by most people and is accepted in today’s society. One of Kepler’s friends was a famous person named Galileo. Galileo is known for improving the design and the magnification of the telescope. With improvement of the telescope Galileo could describe the craters of the moon and the moons of Jupiter. Galileo also created the number for acceleration of all free falling objects as 9.8 meters per second. Galileo’s and Kepler’s theories were not approved by all people. Their theories contradicted verses in the bible, so the protestant church was extremely skeptical of both Galileo and Kepler’s
This paper is an overview of the Kepler spacecraft and its mission in space. According to the National Aeronautics and Space Association (NASA), Kepler, named after Renaissance astronomer Johannes Kepler, “is a space observatory launched…to discover Earth-like planets orbiting other stars.” Kepler does this by searching for planets within our galaxy that have a similar size to Earth within a habitable zone. A habitable zone is a distance between the planet and its star where water can exist on the planet’s surface. Additionally, Kepler is aimed at searching for planets with similar one-year orbits like that of Earth. As technology advances on Earth, increased standards of living and life expectancies have taken a toll on Earth’s fleeting, finite resources. Kepler potentially provides scientists with information regarding planets that can serve as a future home when resources have diminished and information that can foreshadow inevitabilities about Earth through older, Earth-like planets.
The ideas of early philosophers are interconnected and overlapped, resulting in difficulties defining where the beginning of philosophical thought truly lies. The first accounts given of the origins of the world were from the myth-makers, Hesiod and Homer. Their ideas depicting nature as the divine led to the Milesians, who tried to pinpoint the single unity among the multiplicity that is existence. Next came the sophists, teachers of wisdom as persuasion. Finally came Socrates, a character so influential that all the thinkers previously mentioned have been deemed “Pre-Socratics.”
and Plato. The main focus of the paper will be to deal with both sides of the
Astronomy is a very important field in science. Ancient Greece, China, and India all contributed to our everyday ideas and uses of astronomy. Ancient Greece was the most influential because the Indian’s based most of their astronomy off of Greece. The Greeks created calendars that were based off of the eclipse cycle, which they called by two different names, Hellenic Calendars and Lunisolar Calendars. Because of Ancient Greece, we now have calendars to keep us on track every day. The Greeks observed a celestial object passing through the eastern and western morning sky. After a long time of observations, they came to a realization that it was a planet and now that is the planet is well known as Venus. (Sarton, 75) Plato and Aristotle’s theories were incredible contributions on us today. Both of their theories were all about the behavior and life of the planets, such as their theory that the earth is spherical. (Sarton, 421). Ancient Greece als...
...st important scientists in history. It is said that they both shaped the sciences and mathematics that we use and study today. Euclid’s postulates and Archimedes’ calculus are both important fundamentals and tools in mathematics, while discoveries, such Archimedes’ method of using water to measure the volume of an irregularly shaped object, helped shaped all of today’s physics and scientific principles. It is for these reasons that they are remembered for their contributions to the world of mathematics and sciences today, and will continue to be remembered for years to come.
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
Both Plato and Aristotle are among the most influential philosophers in the history. Socrates was another famous philosopher who greatly influenced Plato. Plato was the pupil of Socrates and later Plato became the teacher of Aristotle. Although Aristotle followed his teachings for a long time, he found many questionable facts in his teachings and later on became a great critic of Plato’s teachings. Since Aristotle found faults in Plato, hence their work is easily comparable as it is based on the common aspects of philosophy. In this paper I will first explain some similarities and then I shall explain the differences between the theories of Plato and Aristotle.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.