C According to the Syrian historian Iamblichus c. In any case, it is known that Pythagoras traveled to Egypt about bce to further his study, was captured during an invasion in bce by Cambyses II of Persia and taken to Babylon, and may possibly have visited India before returning to the Mediterranean.
Get Full Essay Get access to this section to get all help you need with your essay and educational issues. By and large, most anyone who has taken high school algebra has encountered this theorem without every really understanding it.
In words, the Pythagorean Theorem states that the square on the hypotenuse of a right triangle has an area equal to the combined areas of the squares on the other two sides. This paper will explore several aspects of the Pythagorean Theorem, from its history to how it found in art, how it relates to music and how it occurs in everyday life, whether people know it or not.
The History Of the Pythagorean Theorem It is not conclusively known that Pythagoras can be solely credited with his famous theorem, but it is known that he was the first to prove why a right triangle behaves the way it does.
Born in Samos now in Turkey in about B. Various scenarios of his early life put him in Egypt, Babylonia, and Italy, where he founded his school that survived for a few hundred years. Pythagoras was not interested in solving mathematical problems; he focused on pure mathematics and geometric relationships.
The Pythagoreans were a mystical group, and Pythagoras himself identified numbers with mysticism. It is possible that Pythagoras saw the knotted triangle in Egypt and went about assigning a numerical value to the geometry of the triangle.
Nothing of his was written down, though, and pythagoras and euclid write about the theorem is attributed to him it could well have been one of his brethren or students that invented the theorem; since all in the Pythagorean school was community property, and since his name was the name of the school, we have come to know the famous theorem as it is today.
How do we know that they Pythagorean Theorem was known before Pythagoras?
So far, nothing has been shown in terms of an equation in relation to a right triangle before Pythagoras, but the right triangle was certainly known for its special properties, as can be seen in the figure below, which depicts the pattern of Oriental tiles in use at least one thousand years before Pythagoras: Looking at this pattern, it is easily determined that the proof of the theorem lies within the pattern itself; yet its proof is credited to Pythagoras.
The Pythagorean Theorem is pure mathematics. It involves no irrational numbers but is found just about everywhere we look. Yet the Pythagorean Theorem is seen in the most profound occurrences of nature, architecture and music.
One problem exists with the formula though…it only relates to integers, and therefore cannot fully translate itself into geometry as it is known today, although in plane geometry the theorem is undeniably valuable. Setting the areas equal to each other and subtracting equals yields the proof of the theorem.
This proof shows that the area of the square is the same no matter what final shape it takes: Evolution Of the Pythagorean Theorem Given that the Pythagoreans shunned anything other than whole numbers, an entire universe of geometric applications in terms of describing harmony and unity was lost to them.
While the Pythagorean Theorem was indispensable for building and measuring perfect squares and rectangles it could not stand alone in terms of the patterns of nature without revision and the introduction of irrational numbers.
By applying the Pythagorean theorem to irrational numbers, a beautiful array of patterns emerges, as was initially discovered by Euclid. Other mathematicians have even managed to take the Theorem into three dimensions. Incredibly, the Pythagorean theorem as it was originally expressed, in whole numbers only, was limited.
But using it as a platform for other geometries sparked an entire cosmology in mathematics and philosophy, demonstrating that the Theorem is fairly universal in its ability to be the springboard to other dimensions of mathematical expressions and mechanics. Here is one example of the use of irrational numbers plugged into the Pythagorean Theorem, creating a crude spiral: Continuing, we see the building blocks for the Golden Spiral: By viewing this diagram, it is easy to imagine how the Pythagorean theorem has been used for building spiral staircases, applying the Theorem in three dimensions.
But it is also important to recognize how the Pythagorean theorem is hidden within innumerable other theorems, and by deduction it can be found even when it is not obvious. Euclid greatly advanced geometry, including the Pythagorean theorem, resulting in the Golden Spiral or Golden Ratio or Golden Meanwhich uses the Pythagorean theorem as an integral part.
The Golden Ratio was explosive in the exploration of natural occurrences, harmonics, architecture and physics. There is such beauty in the Golden Ration and so much was done with it in ancient times that it lends a particular appreciation to the Pythagorean Theorem; take the Golden Ratio apart and there is the right triangle, ready to expand again into something greater.
But it was Euclidian thinking that took the Pythagorean theorem to a whole new level by applying the Theorem to irrational numbers and circular functions. Instead of stopping at the 3: Below is a diagram of the beginnings of the Golden Section, beginning with the Golden Rectangle and the geometric construction of the Golden Section, both based on the Pythagorean theorem: Math Sciences Web Page.Euclid's Proof of Pythagoras' Theorem (I) For the comparison and reference sake we'll have on this page the proof of the Pythagorean theorem as it is given in Elements I, see Sir Thomas Heath's translation..
In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle.
Alongside Pythagoras, Euclid is a very famous name in the history of Greek geometry. He gathered the work of all of the earlier mathematicians and created his landmark work, 'The Elements,' surely one of the most published books of all time. The Pythagorean Theorem calculator is a special calculator that calculates the length of a hypotenuse or an unknown leg of a right triangle.
The hypotenuse in the . What were the major accomplishments of Pythagoras and Euclid? Update Pythagoras’ scientific accomplishments include the discovery of the ‘Pythagorean theorem’ of of a square with its side (the “irrationality of square root of 2), and the beginning of Mathematics.
Yet, it is Euclid who will write the first systematic treatise of. Nov 17, · Pythagoras was a Greek mathematician and philosopher who lived in the 6th century BC and is best remembered for the Pythagorean theorem (the square.
He quotes Proclos, a commentator of Euclid's elements, 'if we listen to those who wish to recount the ancient history we may find some who refer this theorem to Pythagoras, and say that he sacrificed an ox in honor of his discovery'/5(5).