Relationship Behind The Pythagorean Theorem

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 made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were

Overall, this group project went very well and was completed on time due to the fact there everyone including myself assigned ourselves with a task role, relational role and from the start had individual roles present such as leader, compromiser, and gatekeepers in the group that made it

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

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.

Speaking of triangle’s Pythagoras’ most famous contribution to the world of mathematics, The Pythagorean Theorem was proved during this time period. Pythagoras did not create the Theorem, the creation is credited to the Babylonians and Indians, however Pythagoras was the first man to successfully prove the Theorem. The iconic equation looks like

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.

Geometry first originated as a way to solve problems in architecture and navigation. A famous figure in geometry is Euclid. Around 300 BC, he published a book, The Elements, which contained definitions, axioms, and postulates that would be regarded as a standard of mathematical reasoning for the next two thousand years (Mueller, 1969). Euclid basically gave the foundation of what is now called Euclidean geometry. However,

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

Pythagoras developed the formula a2+b2=c2which is called the Pythagorean Theorem. They formula helps find the measure of the sides of a right triangle and is still used on a day to day basis in order for society to function. Overall, mathematics developed by the Greeks have been very useful to modern

     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

Books 7, 8, and 9 introduce the reader to arithmetic and the theory of rational numbers. Book 10 is the difficult subject of irrational numbers. The remaining three books are about elementary solid geometry. It should be noted that the elements discuss several problems, which then turns into algebra. But Euclid treats algebra in geometric terms. Euclid showed development of a new proof for the Pythagorean Theorem, the theory that only one parallel to a line can be drawn through any point. Modern mathematicians have maintained that no proof is possible; Euclid may be excused for not providing one. Spherical geometry is represented by the Phainomena, which is astronomical text based in part on a work of Autolycus of Pitane, a slightly older contemporary. Euclid wrote on music, there is no other ancient work of science; it needs a little revision to make it current. Other Hellenistic mathematicians such as, Hero, Pappus, Simplicius, and most important Proclus helped out on the Elements just like Euclid.

The Pythagorean theorem is a theorem that states that the sum of the squares of two legs of a right triangle, a and b, is equal to the square of the hypotenuse, c. This can be written and shown as the equation, a2+b2=c2.

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.