Essay on pythagoras and his theorem - Pythagorean theorem essay - Essay Writing Service Deserving Your Attention

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 and plugging numbers into the formula. 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. In right-angled triangles the square on the hypotenuse is equal to the sum of the squares on the legs. Figure 2 Euclid began with the Pythagorean configuration shown above in Figure 2.

Then, he constructed a perpendicular line from C to the segment DJ on the square on the hypotenuse. The points H and G are the intersections of this perpendicular with the sides of the square on the hypotenuse.

Essay on Pythagorean Theorem - Words | Major Tests

It lies along the altitude to the right triangle ABC. He proved these equalities using the concept of similarity.

So and Since the sum of the areas of the two rectangles is the area of the square on the hypotenuse, this completes the proof. Euclid was anxious to place this result in his work as soon as possible.

However, since his work on similarity was not to be until Books V and VI, it was necessary for him to come up with another way to prove the Pythagorean Theorem. Thus, he used the result that parallelograms are double the triangles with the same base and between the same parallels.

Essay, Research Paper: Pythagorean Theorem

There was always a certain amount of friction between the two groups and eventually the sect became caught up in some fierce local fighting and ultimately dispersed.

Resentment built up against the secrecy stephen murray homework exclusiveness of the Pythagoreans and, in BCE, all their meeting places were burned and destroyed, with at least 50 members killed in Croton alone.

Odd numbers were thought of as female and even numbers as male. The Pythagorean Tetractys The holiest number of all was "tetractys" or ten, a triangular number composed of the sum of one, two, three and four.

Pythagoras

It is a great tribute to watch homework 1982 Pythagoreans' intellectual achievements that they deduced the special place of the number 10 from an abstract mathematical argument rather than from something as mundane as counting the fingers on two hands.

However, Pythagoras and his school - as well as a handful of other mathematicians of ancient Greece - was largely responsible for introducing a more rigorous mathematics than what had gone before, building from first principles using axioms and logic.

Before Pythagoras, for example, geometry had been merely a collection of rules derived by empirical measurement. Pythagoras discovered that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth.

Written as an equation: What Pythagoras and his followers did not realize is that this also works for any shape: One of the simplest proofs comes from ancient Chinaand probably dates from well before Pythagoras' birth. It was Pythagoras, though, who gave the theorem its definitive form, although it is not clear whether Pythagoras himself definitively proved it or merely light homework sheets it.

Either way, it has become one of the best-known of all mathematical theorems, and as many as different proofs now exist, some geometrical, some algebraic, some involving advanced differential equations, etc.

This discovery rather shattered the elegant mathematical world built up by Pythagoras and his followers, and the existence of a number that could not be expressed as the ratio of two of God's creations which is how they thought of the integers jeopardized the cult's entire belief system.

Poor Hippasus was apparently drowned by the secretive Pythagoreans for broadcasting this important discovery to the outside world.