Eudoxus Major Accomplishments

The creations of Pythagoras were very powerful during the era in which he lived in. He created a community of followers (known as the Pythagoreans) who believed that mathematics was fundamental and ‘at the heart of reality’ (source 1). The people in the society were all proficient mathematicians took mathematics very seriously, to the extent that it was similar to a religion (source 1).

Pythagoras also contributed to the music world. He expressed the musical harmony in formulas. He created a scale layout with gongs in different sizes and he proved that in the resonance of the gongs he hit, 1 octave interval is equal to 2:1 proportion, the perfect fifth is equal to 3:2 proportion, perfect four is equal to 4:3 proportion and whole notes are equal to 9:8. This, later started to be known as “Pythagorean Tuning.”

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.

For Pythagorean shapes and numbers was so important. He believed that the most perfect shape of the nature is circle. Therefore he put the earth in the center of a spherical world. According to Plato the movement of planets is in perfect circles. However now its known that the planetary orbits are ellipses and not

The mathematic that not only facilitated in the renaissance but provide the key a new science of nature from Galileo.

The author of Journey through Genius, William Dunham, begins this chapter by depicting how mathematics was spurred and developed in early civilizations. Dunham focuses primarily on the works’ and achievements’ of early Egypt, Mesopotamia, and Greece in this section. These ancient societies, as they developed, produced mathematicians such as; Thales, Pythagoras, and Hippocrates, who turned a basic human intuition for space and quantity into applicable everyday mathematics. The primary influences driving the development of early mathematics were the issues of growing civilizations, most notably counting commodities, taxation, and the division of land equally, rather than a pure desire for understanding that is seen in mathematics today. These influences culminated in the development of early arithmetic and geometry.

Greeks such as Aristotle, Pythagoras, and Hippocrates have left concepts still used in modern science and mathematics. Their ideas laid a basis for future European thoughts and studies in the fields. Their contributions such as the creating the Pythagorean theory, the writing a comprehensive classification of species and the systematizing of medical knowledge would influence the way Europeans thought and studied the world. Hippocrates’ Oath is still sworn by all medical practitioners. The contributions of the Ancient Greeks in science and math built a foundation upon which future Europeans would build and lead to the development of modern

Hipparchus of Nicaea changed the world of Math and Science for years after his final breath. Hipparchus is considered to be the father of Trigonometry, a branch of math, and to have study the orbit of the Moon and Sun determining their size and distance from Earth. Hipparchus of Nicaea is said to be one of the greatest scientist of all times. Despite his brilliancy barely anything is known about Hipparchus or his works. The information that we have on Hipparchus is second hand accounts from him many students, the work his students produced especially Almagest by Ptolemy, and the only surviving work that is still left today, Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις (Commentary on the Phaenomena of Eudoxus and Aratus).

Abstract: - The many concepts we currently have in the field of mathematics are thanks to great mathematicians from different cultures throughout time. An important era when great mathematical discoveries were made was during Medieval Times, or the Middle Ages. In this paper we discuss important discoveries and contributions that were made by three famous mathematicians of this time period including French Nicole Oresme, German Jordanus Nemorarius and Italian Leonardo Pisano, better known for his nickname of Fibonacci.

Studying the history behind Calculus can seem, for the untrained eye, an impractical use of time. One might think that since as Calculus students, we are using the most advanced and contemporary functions of calculus, it's useless to look back and see what people did before us. However, there are several reasons why looking at the historical background of Calculus is important. As the lecture stated, the main reasons why the history of Calculus is important is that it opens our, being the students, eyes. It opens our eyes to the motivation behind historical Calculus scholars. It opens our eyes to how we can organize Calculus' results. It opens our eyes to the human and personal aspects of the people who developed calculus. Finally, it opens our eyes to the link between faith and mathematics. In this historical discussion of the definite integral, we will look at several of the "founding fathers" of this concept.

In Famous scientist’s (2015) article Pythagoras it states that five 3D solids were brought into existence by Pythagoras and the Pythagoreans, these items are identical on all of the sides and today they are called dice. The ranged from four sides all the way up to twenty and later Plato believed they belonged to the five Greek elements including aether (n.pag). They said “Pythagoras believed that, like everything else, music was based on whole number ratios. He also believed in its healing properties.”(n.pag) He later would learn that music was controlled by rations, like if a sting is shortened by half it raises an octave or if it’s shortened two-thirds then it moved the pit up one-fifth discovering that octaves are split into fifths not halves (n.pag). Those are the biggest discoveries of Pythagoras and the Pythagoreans, but they still has many more different discoveries. He has been accredited with a lot for being an enigma, and having written no books in his life. Even so the thoughts from learning of this brilliant mathematician tickles the mind and creates great and wonderful thoughts and ideas for many people. Learning about all of this should inspire anyone to travel and learn the ways of other countries and customs and even grasp their mathematical

My example of irrational numbers is the Golden ratio from the Fibonacci sequence. The Fibonacci sequence starts as 0, 1, 1, 2, 3, 5,... The numbers are added together to get the next sequence number. was made famous during the 13th century by Leonardo Pisano. The Golden ratio is when you take the sequence numbers and divide each by the previous number. The Golden ratio is the final set of numbers in, "the following set of numbers: 1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.666..., 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.61538..." (Knott, 2013). The Greek letter Phi is the represented symbol for the Golden ratio (1.61538...) This number is the reason for, " the spirals in the seedheads and the arrangements of leaves in many plants."(Knott, 2013). The

Euclid’s assumptions about his postulates have set the groundwork for geometry today. He provided society with definitions of a circle, a point, and line, etc and for 2000 was considered “the father of geometry.” His postulates proved to be a framework from which mathematics was able to grow and evolve, from two thousand years ago, till Newton and even to all our classrooms today.

Mathematics has contributed to the alteration of technology over many years. The most noticeable mathematical technology is the evolution of the abacus to the many variations of the calculator. Some people argue that the changes in technology have been for the better while others argue they have been for the worse. While this paper does not address specifically technology, this paper rather addresses influential persons in philosophy to the field of mathematics. In order to understand the impact of mathematics, this paper will delve into the three philosophers of the past who have contributed to this academic. In this paper, I will cover the views of three philosophers of mathematics encompassing their