Q1.

Pythagoras is recognized for discovering and proving the Pythagorean Theorem .

Q2.

Pythagorean Theorem is very important since it is the easiest way to evaluate the length of a hypotenuse in a right angled triangle if the other two are provided. The theorem says that the squire value of the hypotenuse in a right-angled triangle equals the sum of the squire values of the others.

Q3.

Pythagoras Theorem presents one of the bases of mathematical science. Its concepts are simple, and it is valuable when undertaking studies on mathematics. The theorem is expressed in trigonometric functions where it is referred to as the Pythagorean Trigonometric Identity. Together with the sum of angles formulae, it is used to demonstrate the relationship between the cosine and sine functions. From this relationship, all other functions can be derived. The Pythagorean Trigonometric Identity states that; sin^{2 }θ^{ }+ cos^{2 }θ = 1. When the hypotenuse in a right angled triangle has the length of one, then the legs have the lengths of cosine and sine of one the two angles touching the hypotenuse. This proves that trigonometric identities originated from the Pythagorean Theorem.

Q4.

Pythagoras Theorem simplifies computations, and that is why it has been widely used since its discovery. There are many examples of its application. Mathematicians use it frequently while evaluating problems and also when teaching students. Electricians and engineers use it in estimating lengths of wires and heights of structures. It can be used when calculating vectors in collisions that involve subatomic particles, or during investigations of motor vehicle accidents. It is used in enlarging drawings, laying foundations, and calculating square angles. Surveyors use it in estimating the heights of mountains, while astronomers apply it in calculating the distance between planets, or their circumferences. Lastly, carpenters use Pythagoras Theorem in order to keep their projects squire. In all these instances, it he helps improve accuracy.

Q5.

Pythagoras lived during a period when there were continuous conflicts at his home city of Samos. These conflicts made him migrate to a more peaceful city Croton. Initially, he experienced so many problems as he tried to set up a school. In fact, the school had to close at first because the number of students was inadequate. Later he succeeded but it was later destroyed by the Italian army who then scattered the students. Moreover, he got married as an old man. These challenges made his work very difficult.

Q6.

Pythagoras believed that numbers could rule the universe. He held a belief that realities are mathematical in nature. He wanted the Pythagoreans to keep applying the Pythagoras theorem so that its knowledge does not disappear. Some people believe that Pythagoras made a huge religious sacrifice after this theory was completed. This demonstrates that Pythagoras was committed to the work of developing this theory and he had trust in it.

Q7.

Pythagoras proved the Pythagoras Theorem at around 540 BC. He had discovered it as he was considering the special side ratio that exists with triangles. As he studied them more closely, he found that squiring the values of the two shorter sides and then adding these squire values gave a numerical value which is equal to the squire value of the longest side. He also proved that this does not apply for any other triangle, apart from a right angled one.

Q8.

The Pythagoras was at the Pythagorean School in Croton during the discovery of the Pythagoras Theorem. It is in Croton that Pythagoras established his society. Croton neighbored the city of Locri which was near another prosperous city of Sybaris.

Q9.

As Pythagoras escaped instability at home, he met a young man named Thales who advised him to go to Egypt. In Egypt, he gained so much knowledge that helped him to establish a religious and philosophical school that became famous with time, and attracted many students. His followers came to be known as the Pythagoreans and their philosophy was founded on mathematics. These are the people that worked with Pythagoras, and helped him to proof the Pythagoras Theorem.

Q10.

The work of Pythagoras, and especially his discovery and prove of the Pythagoras Theorem, has been greatly appreciated over the centuries. It is these discoveries that made his school very famous, and many people wanted to join it. Its knowledge has been applied from the time it was discovered. The Italians used it when they laid the corner foundations of buildings. They used this theory and its special triangle, especially when they did not have the carpenter’s squire within their reach. Many students appreciate learning the Pythagorean Theory, as it helps them solve several mathematical problems. Many people apply it in technological fields with much satisfaction.