Pythagoras' Invention of the Pythagorean Theorem Essay

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

The area of a right triangle is 2. The length of the base is the same as the length of the height. Find this length.

perimeter of big rectangles equals scale factor times perimeter of small rectangle equals scale factor times 58 & it results with 4.5.

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.

Step Three: Then calculate the area of the big square in two ways by creating the equation; (a+b)2=4ab/2 +c2. (When simplified you will get the required identity.)

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.

I labeled the length and width as 4x and 3x. I need to solve for the side lengths. So I made the equation 280= 4x + 3x + 4x +3x. I solved the equation and found that x is equal to 20. So the length is 80 units and the width is 60 units. And I have to multiply the side lengths together to find the area. The area of the rectangle is four thousand eight hundred. Now, to find the area of the circle, I have to find the radius. I saw that if I connected the corners of the building to form a diagonal line, it would form the diameter of the circle. So I made an equation using the pythagorean theorem. I found the hypotenuse was one hundred. I then added one hundred and eight because the pond extends four units on each side. So the radius is fifty-four. And to find

We use mathematics to our great advantage to explain many things. Although Pythagoras, applied A^2+B^2=C^2, he did not create the substance of the equation, this theorem is timeless, he only brought it to our attention.

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

In summer of 1609, Galileo Galilei (1564-1642) pointed his revolutionary astronomical telescope to the heavens under the starry Venetian sky; his greatly important observations unveiled the mysteries of universe and would end up changing the course of scientific thought forever. Galileo lived in an age where there was much status quo, when scientists and philosophers would accept scientific and religious doctrine that had stood for hundreds, if not thousands, of years instead of challenging the accepted knowledge in favor of intellectual progress. Galileo’s scientific methods lead to significant discoveries explaining key scientific laws, such as 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.

According to Victor Katz in “A History of Mathematics (3rd Edition)” (Pearson, 2008), trigonometry developed primarily from the needs of Greek and Indian astronomers. But today, trigonometry and geometry were used on various fields such as: architecture, physical sciences, engineering, astronomers, medical imaging (CAT scans and ultrasounds), etc.