This wiki was created to give students a deeper look into the Pythagorean theorem.
To begin lets look at the man who created it all. Pythagoras of Samos.
Pathagoras of Samos
Born: about 569 BC in Samos, Ionia Died: about 475 BC
Pythagoras Biography
Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, we have nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure. We do have details of Pythagoras's life from early biographies which use important original sources yet are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure.
The Pythagorean Theorem by Stephanie J. Morris The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. 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. Area Square A=a2 Area Square B=b2 Area Square C=c2
Thus, the Pythagorean Theorem stated algebraically is: a2+b2=c2
for a right triangle with sides of lengths a, b, and c, where c is the length of the hypotenuse.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. If the methods of Book II of Euclid's Elements were used, it is likely that it was a dissection type of proof similar to the following:"A large square of side a+b is divided into two smaller squares of sides a and b respectively, and two equal rectangles with sides a and b; each of these two rectangles can be split into two equal right triangles by drawing the diagonal c. The four triangles can be arranged within another square of side a+b as shown in the figures.
The area of the square can be shown in two different ways: 1. As the sum of the area of the two rectangles and the squares:
(a+b)2 = a2 + b2 +2ab
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.
This wiki was created to give students a deeper look into the Pythagorean theorem.
To begin lets look at the man who created it all. Pythagoras of Samos.
Born: about 569 BC in Samos, Ionia
Died: about 475 BC
Pythagoras Biography
Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, we have nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure. We do have details of Pythagoras's life from early biographies which use important original sources yet are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure.
For more on the biography of Pytagoras use the links below.
Pythagoras Biography 1
Pythagoras Biography 2
Pythagoras Biography 3
The Pythagorean Theorem
The Pythagorean Theorem by Stephanie J. Morris
The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. 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.
Area Square A=a2
Area Square B=b2
Area Square C=c2
Thus, the Pythagorean Theorem stated algebraically is:
a2+b2=c2
for a right triangle with sides of lengths a, b, and c, where c is the length of the hypotenuse.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. If the methods of Book II of Euclid's Elements were used, it is likely that it was a dissection type of proof similar to the following:"A large square of side a+b is divided into two smaller squares of sides a and b respectively, and two equal rectangles with sides a and b; each of these two rectangles can be split into two equal right triangles by drawing the diagonal c. The four triangles can be arranged within another square of side a+b as shown in the figures.
The area of the square can be shown in two different ways:
1. As the sum of the area of the two rectangles and the squares:
- (a+b)2 = a2 + b2 +2ab
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.For more information on the Pythagorean Theorem use the links below.
Pythagorean Theorem
Pythagorean Theorem 2
Pythagorean Theorem
Pythagorean Theorem
Videos on the Pythagorean Theorem. These videos can be use for further learning on the pythagorean theorem.