Eudoxus' Contribution to Calculus

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 was the first person to really influence the founding of Calculus. He was an Ionian greek philosopher, mathematician, and has been credited as the founder of the movement called Pythagoreanism. Keep in mind he was born in 570 BC and died in 495 BC, so yeah, he’s kind of old. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and traveled the world, visiting Egypt and Greece, and possibly India, and in 520 BC he returned Samos. Around 530 BC, he moves to Croton, in Magna Graecia, and there he established some kind of school or guild.

Thales was the next person in the chronological history of philosophy. He was an astronomer and a

Greek mathematical and scientific ideas have also been a large contribution. Euclid, a Greek mathematician, wrote many theorems. His theorems have been very substantial because they are included in today’s mathematical problems. One of his theorems include “If two straight lines cut one another, the vertical, or opposite, angles shall be equal.” This specific theorem is used in proofs and it proves that all vertical angles are equal. Hippocrates was a Greek physician who created the Hippocratic Oath. This oath

Hipparchus was a greek astronomer, geographer, and mathematician born 190 B.C. in Nicaea and died in 120 B.C. Rhodes, Rhodes, Greece. Hipparchus is accredited as the inventor of trigonometry because of his discovery of the first table of chords and also because he's the only person with valid data of the discovery and usage of trigonometry. In order to calculate the rising and setting of zodiacal signs, Hipparchus brought to light the division of circles into 360 degrees and the calculation of chords by looking at the triangles (spherical triangles or triangles that made up a circle) differently. Hipparchus experimented putting all triangles to be within a circle and with the three points each touching the

Finally, during the European enlightenment, men like Fermat, Pascal, and Isaac Barrow further pursued the emerging new field developing the concept of the derivative. Barrow even offered the first proof of the fundamental theorem of calculus linking the concepts of differentiation and integration; however, it was one of Barrow’s young students, Isaac Newton who would make the next big splash in the creation of the art of calculus.

He discovered the laws of planetary motion, explained how gravity works, and invented calculus, a new branch of mathematics that proved invaluable to modern scientists and mathematicians.

The history of calculus falls into several distinct time periods, most notably the ancient, medieval, and modern periods. The ancient period introduced some of the ideas of integral calculus, but does not seem to have developed these ideas in a rigorous or systematic way. Calculating volumes and areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c. 1800 BC), in which an Egyptian successfully calculated the volume of a pyramidal frustum.[1][2] From the school of Greek mathematics, Eudoxus (c. 408−355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes while Archimedes (c. 287−212 BC) developed this idea

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.

Archimedes produced formulas to find the area of regular shapes by using the shapes he already knew how to calculate (The History of Archimedes). An example of this would be the circle. Archimedes would draw a polygon on the outside of the circle and then a smaller one on the inside and he would solve the area of the polygons. Although he knew this only would only get him a range and that the actual calculation might never be found (The History of Archimedes). He similarly was able to find the calculation of the volume of a sphere. He did this by cutting the sphere into a series of cylinders, (The History of Archimedes) and then adding the volumes of the cylinders. Archimedes noticed that the smaller he cut the cylinders the more accurate. His approximation eventually became an exact calculation. Despite all of Archimedes’ contributions to mathematics, the story he is probably the most well-known for would be his discovery of a method for finding the volume of an object with an irregular shape (The History of Archimedes). Hiero had asked the royal goldsmith to fashion a new royal crown for him. Hiero provided a thing of gold to make it, but once Hiero was given his newly made crown he began to believe that the goldsmith cheated him out of some of his gold a replaced it with silver. He asked Archimedes if he could determine this. So while bathing Archimedes noticed

Eratosthenes was a great Ancient Greek mathematician known for creating the Sieve of Eratosthenes. He is also known for measuring the circumference of the earth accurately. He was born in Cyrene, Greece, which is now known as Libya, North Africa, in 276 B.C. He was born to Agalus and his wife. After his birth he was at the front seat of learning, he was educated at The Plato’s Academy in which he learned under the philosophies of Plato.

     Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know

Eratosthenes was born in 276 B.C. in a Greek colony in Cyrene, a country in North Africa better known in the present day as Libya. He raised by modest parents, his mother’s name is not known, and his father’s name could be one of two that have been discovered, Aglaos or Ambrosios. Even though they were modest parents, they were somehow able to have enough money for an education for their son. They would have had to own land that was worth at least 20 minas (type of Athenian currency), and his parents would have been free citizens. He was a typical, curious baby and as he grew older, he asked hundreds of questions that no one could answer. He was extremely interested in the sky, because it was something that he could not reach up and touch. He wondered how what the distance between the sun and earth was and what the sun was made of, why there was wind, and why the stars moved. Like most young Greek boys, when Eratosthenes was about six, he began to go to school in the local gymnasium, where he learned reading, writing, mathematics, poetry, music and physical education. He was very strong in math but geography was by far his favourite subject. In his early years, he was given the nickname Beta, the second letter of the Greek alphabet, because he never came in first place (taken by Archimedes). Later in life, he got the nickname Pentathlos. This word meant an athlete that participated in 5 sporting events or to describe someone who was good at a variety of different

Bernoulli was soon exposed to Euler’s brilliance in analytical science and presently saw his true potential, and gained a new respect for him. Euler procured his degree of Master of Arts in philosophy in 1723 by comparing and contrasting the ideas of Descartes and Newton. He then attempted to gain degrees in Theology and Oriental languages on his father’s request, but did not complete the course due to disinterest in the subject, and soon, with his father’s permission, returned to the study of mathematics.

Although Euclid (or the school) may have not been first proved by him, (in fact much of his work may have been based upon earlier writings,) he did manage to insert assumptions and definitions of his own to strengthen the various postulates into the form we know today.