However, the relationship was not widely publicized until Pythagoras stated it explicitly. Pythagoras lived during the 6th century B. He also lived in Egypt, Babylon and southern Italy. Pythagoras was a teacher and a philosopher. In other words, the green square's area with area c 2 equals the sum of two others.
This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. He is credited with many contributions to mathematics although some of them may have actually been the work of his students. The Pythagorean Theorem is Pythagoras' most famous mathematical contribution.
According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that the square root of 2 is irrational and therefore, cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers. They were devout in their belief that any two lengths were integral multiples of some unit length.
Many attempts were made to suppress the knowledge that the square root of 2 is irrational. It is even said that the man who divulged the secret was drowned at sea. The Pythagorean Theorem is a statement about triangles containing a right angle.
The Pythagorean Theorem states that: "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides. Figure 1. According to the Pythagorean Theorem, the sum of the areas of the two red squares, squares A and B, is equal to the area of the blue square, square C. Although Pythagoras is credited with the famous theorem, it is likely that the Babylonians knew the result for certain specific triangles at least a millennium earlier than Pythagoras.
It is not known how the Greeks originally demonstrated the proof of the Pythagorean Theorem. Therefore, the square on c is equal to the sum of the squares on a and b. Burton There are many other proofs of the Pythagorean Theorem.
One came from the contemporary Chinese civilization found in the oldest extant Chinese text containing formal mathematical theories, the Arithmetic Classic of the Gnoman and the Circular Paths of Heaven. The proof of the Pythagorean Theorem that was inspired by a figure in this book was included in the book Vijaganita, Root Calculations , by the Hindu mathematician Bhaskara. Bhaskara's only explanation of his proof was, simply, "Behold". These proofs and the geometrical discovery surrounding the Pythagorean Theorem led to one of the earliest problems in the theory of numbers known as the Pythgorean problem.
Find all right triangles whose sides are of integral length, thus finding all solutions in the positive integers of the Pythagorean equation:. The formula that will generate all Pythagorean triples first appeared in Book X of Euclid's Elements :.
In his book Arithmetica , Diophantus confirmed that he could get right triangles using this formula although he arrived at it under a different line of reasoning. The Pythagorean Theorem can be introduced to students during the middle school years. This theorem becomes increasingly important during the high school years.
It is not enough to merely state the algebraic formula for the Pythagorean Theorem. Students need to see the geometric connections as well. The teaching and learning of the Pythagorean Theorem can be enriched and enhanced through the use of dot paper, geoboards, paper folding, and computer technology, as well as many other instructional materials. Through the use of manipulatives and other educational resources, the Pythagorean Theorem can mean much more to students than just.
The following is a variety of proofs of the Pythagorean Theorem including one by Euclid. These proofs, along with manipulatives and technology, can greatly improve students' understanding of the Pythagorean Theorem. The following is a summation of the proof by Euclid, one of the most famous mathematicians.
This proof can be found in Book I of Euclid's Elements. Proposition: In right-angled triangles the square on the hypotenuse is equal to the sum of the squares on the legs. Figure 2. But when this theorem was discovered and proved the Pythagorean sacrifice huge number of bulls to their number gods.
Indian mathematicians in the ancient times knew the Pythagorean theorem, they also used something called the Sulbasutras that discuss the theorem in the context of strict requirements for the orientation, shape, and area of altars for religious purposes. The Pythagorean theorem was first originated in ancient Babylon and Egypt beginning about B.
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