The importance of mathematics to nature has been a topic of debate within the Western scientific tradition. From ancient times through the middle ages, an outbreak of mathematical creativeness was often followed by centuries of inactivity. As we all know, mathematics has always been the vital importance in astronomy, and many ancient astronomers were also mathematicians. This means that the growth of mathematics was applied and motivated by astronomical calculations. Though, not everyone studying ancient astronomy was capable to use applications of mathematics. The first developments of mathematical astronomy came during the Mesopotamian and Babylonian eras, when the techniques were developed to predict eclipses and positioning of the celestial …show more content…
Among the techniques developed and improved by them included geometry of triangulation and three dimensional applications. Greek astronomy took a crucial turn in the 4th c. with Plato (427-348) and his newer contemporary Eudoxus of Cnidus (390 – 337 B.C.). The famous Greek philosopher, Plato, was one of the most important figures of Greek mathematics who helped revolutionize geometry. His representations of various three-dimensional shapes represented a hypothetical model where the entire universe was connected through constellations and stars. He played a significant role in encouraging and inspiring Greek intellectuals to study mathematics as well as philosophy. As he was known for having math ideas that were influenced by Pythagoras and Egyptians algebraic arithmetic, he argued that the four elements (earth, water, air and fire) can be reduced to regular geometrical solids, which are reducible in turn to triangles. Therefore, for him, the fundamental building blocks of the world were geometrical. He was certain that geometry was the key to unlock the secrets of the universe (Lindberg …show more content…
The two-sphere model is a geocentric model which divides the cosmos into two regions: a spherical Earth, central and motionless (the sublunary sphere) and a spherical heavenly realm centered on the Earth, which may contain multiple rotating spheres made of aether. In one of his books, Plato described the two-sphere model and said there were eight circles or spheres carrying the seven planets and the fixed stars. He put the celestial objects in an order: Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn and Fixed stars, and proposed a question for the Greek mathematicians of his day: “By the assumption of what uniform and orderly motions can be apparent motions of the planets be accounted for?” (Lloyd 1970, p84). Eudoxus took Plato’s challenge and assigning each planet a concentric sphere. He tilted the axes of the spheres and by assigning each a different period of revolution, he was able to approximate the celestial “appearances”. Therefore, he was the first to attempt a mathematical description of the motions of the planets (Heliocentrism
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.
In 1543 Nicholas Copernicus, a Polish Canon, published “On the Revolution of the Celestial Orbs”. The popular view is that Copernicus discovered that the earth revolves around the sun. The notion is as old as the ancient Greeks however. This work was entrusted by Copernicus to Osiander, a staunch Protestant who though the book would most likely be condemned and, as a result, the book would be condemned. Osiander therefore wrote a preface to the book, in which heliocentrism was presented only as a theory which would account for the movements of the planets more simply than geocentrism did, one that was not meant to be a definitive description of the heavens--something Copernicus did not intend. The preface was unsigned, and everyone took it to be the author’s. That Copernicus believed the helioocentric theory to be a true description of reality went largely unnoticed. In addition to the preface, this was partly because he still made reassuring use of Ptolemy's cycles and epicycles; he also borrowed from Aristotle the notion that the planets must move in circles because that is the only perfect form of motion.
The Aztecs also used mathematics for astronomy. Kind of amazing right? Although most of their information in math astronomy was lost there is a pretty good synthesis of the remaining information in the book “Skywatchers” by Anthony Aveni. For example the Aztecs calculated that the cycle of Venus was 584 days. The aztecs even did the math to workout out the eclipse season although they didn’t know the shape of the earth or the size. Even though they figured out when
Aristarchus lived from about the year 310 B.C. to about 230 B.C. Aristarchus was the first Greek philosopher and mathematician to make sense of the solar system. Others before him thought that the Earth is a sphere and that it moves, but he was the first to understand the heliocentric theory, which states that the sun is in the middle. In 288 or 287 B.C. he followed Theophrastus as the head of the Peripatetic School established by Aristotle.
Ancient Greece, China, and India all had major contributions in the fields of science and math. All three of those ancient civilizations made such great contributions that they are still used today by many people. We use these contributions in school, work, and in our general every day lives. Although we don’t use the exact inventions that they created, we now use alterations of them every day. Greece’s discoveries have more of an influence on us today than those of India and China because we use these discoveries more often in the field of astronomy, theoretical sciences, important technology, and everyday mathematics.
Pythagoras held that an accurate description of reality could only be expressed in mathematical formulae. “Pythagoras is the great-great-grandfather of the view that the totality of reality can be expressed in terms of mathematical laws” (Palmer 25). Based off of his discovery of a correspondence between harmonious sounds and mathematical ratios, Pythagoras deduced “the music of the spheres”. The music of the spheres was his belief that there was a mathematical harmony in the universe. This was based off of his serendipitous discovery of a correspondence between harmonious sounds and mathematical ratios. Pythagoras’ philosophical speculations follow two metaphysical ideals. First, the universe has an underlying mathematical structure. Secondly the force organizing the cosmos is harmony, not chaos or coincidence (Tubbs 2). The founder of a brotherhood of spiritual seekers Pythagoras was the mo...
...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.
What I have found to be most interesting about both Deontology and Utilitarianism isn’t their approach to ethics, but rather their end goal. Deontology promotes “good will” as the ultimate good; it claims that each and every person has duties to respect others. On the other hand, Utilitarianism seeks to maximize general happiness. While these may sound rather similar at first glance (both ethical theories essentially center around treating people better), a deeper look reveals different motivations entirely. Deontology focuses on respecting the autonomy and humanity of others, basically preaching equal opportunity. Utilitarianism does not specify any means by which to obtain happiness—happiness is its only mandate. While happiness sounds like a great end goal, it is a rather impractical one and the lack of consideration of motivations and means of utility-increasing actions has some serious negative consequences. I prefer Deontology over Utilitarianism for its focus on individual’s rights, opportunity, and personal autonomy.
He also used evidence based on observation. If the earth were not spherical, lunar eclipses would not show segments with a curved outline. Furthermore, when one travels northward or southward, one does not see the same stars at night, nor do they occupy the same positions in the sky. (De Caelo, Book II, chapter 14) That the celestial bodies must also be spherical in shape, can be determined by observation. In the case of the stars, Aristotle argued that they would have to be spherical, as this shape, which is the most perfect, allows them to retain their positions. (De Caelo, Book II, chapter 11) By Aristotle's time, Empedocles' view that there are four basic elements - earth, air, fire and water - had been generally accepted. Aristotle, however, in addition to this, postulated a fifth element called aether, which he believed to be the main constituent of the celestial bodies.
Since the first Egyptian farmers discovered the annual reappearance of Sirius just before dawn a few days before the yearly rising of the Nile, ancient civilizations around the Mediterranean have sought to explain the movements of the heavens as a sort of calendar to help guide them conduct earthly activities. Counting phases of the moon or observing the annual variations of day length could, after many years' collection of observations, serve as vital indicators for planting and harvesting times, safe or stormy season for sailing, or time to bring the flocks from winter to summer pastures. With our millennia of such observation behind us, we sometimes forget that seeing and recording anything less obvious than the rough position of sun or nightly change of moon phase requires inventing both accurate observation tools (a stone circle, a gnomon used to indicate the sun's shadow, a means to measure the position of stars in the sky) and a system of recording that could be understood by others. The ancient Greeks struggled with these problems too, using both native technology and inquiry, and drawing upon the large body of observations and theories gradually gleaned from their older neighbors across the sea, Egypt and Babylonia. Gradually moving from a system of gods and divine powers ordering the world to a system of elements, mathematics, and physical laws, the Greeks slowly adapted old ideas to fit into a less supernatural, hyper-rational universe.
Nicholaus Copernicus is one of the most well known astronomers of all time. He is even labeled as the founder of modern astronomy for the proposition of his heliocentric theory (“Nicolaus Copernicus”, Scientists: Their Lives and Works). The heliocentric theory was revolutionary for Copernicus’ time. Copernicus lived during the Renaissance. “The era of the Renaissance (roughly 1400-1600) is usually known for the “rebirth” of an appreciation of ancient Greek and Roman art forms, along with other aspects of classical teachings that tended to diminish the virtually exclusive concentration on religious teachings during the preceding centuries of the “Dark Ages.” New thinking in science was also evident in this time…” This time period became known as the scientific revolution (“Copernicus: On The Revolutions Of Heavenly Bodies). In other words, old ideas were revived in the arts and other means and less emphasis was placed o...
The Scientific Revolution was sparked through Nicolaus Copernicusí unique use of mathematics. His methods developed from Greek astr...
Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
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.