Pythagorean Theorm Essays - Triangles, Triangle Geometry

Pythagorean Theorm Essays - Triangles, Triangle Geometry Pythagorean Theorm The Pythagorean Theorem is a geometrical expression used often in math and physics. It used to 2 2 2 find the unknown side of a right triangle. The exponential form of this theorem a + b = c . That is the equation you use when you are looking for the unknown side of a right triangle, and it is what Ill demonstrate on the attached exhibit. The upside down capital L in the bottom of the left hand corner indicates that sides A & B are the legs of the triangle. Since we know side A = 5 inches and B = 3 inches we may fill that in to 2 2 2 or equation for step one. (1) 5 + 3 = c What the theorem will help us find is the c side of this triangle. 2. 25 + 9 = c All we do is distribute 5 to the second power and 3 to the second power as seen is step two. Next, we add these two numbers together to get 34, 25+9=34, in step three. 3. 25+9=34 Then, in step four we find the square root of 34. 4. 34 In step five we see that 5.83 is the unknown side of the right triangle. 5. c= 5.83 We found this answer by using the Pythagorean Theorem as taught in geometrical form. This theorem may also be summed up by saying that the area of the square on the hypotenuse, or opposite side of the right angle, of a right triangle is equal to sum of the areas of the squared on the legs. The Pythagorean Theorem was a studied by many people and groups. One of those people being Euclid. Sometimes the Pythagorean Theorem is also referred to as the 47th Problem of Euclid. It is called this because it is included by Euclid in a book of numbered geometric problems. In the problem Euclid studied he would always use 3, 4, and 5 as the sides of the right triangle. He did this because 5 x 5 = 3 x 3 + 4 x 4. The angle opposite the side of the legs was the right angle, it had a length of 5. The 3:4:5 in the right triangle was known as a Pythagorean triple or a three digits that could be put in a right triangle successfully. These three numbers were also whole numbers and were used in the Egyptian string trick, which I will talk about later. This Pythagorean triple, 3:4:5, are the smallest integer series to have been formed, and the only consecutive numbers in that group that is important. These numbers can be, and often were, studied from a philosophical stand point. The symbolic meanings of the 3:4:5 triple told by modern writers such as Manly P. Hall say 3 stands for spirit, 4 stands for matter, and 5 stands for man. Using Halls study the symbolism of this arrangement is as follows: Matter (4) lays upon the plane of Earth and Spirit (3) reaches up to the Heaven and they are connected by Man (5) who takes in both qualities. A process similar to that of Euclid's 47th Problem was the Egyptian string trick. Egyptians were said to have invented the word geometry (geo = earth, metry = measuring.) The Egyptians used the 3:4:5 right triangle to create right triangles when measuring there fields after the Nile floods washed out there old boundary markers. The Egyptians used the same theory of Euclid, 5 x 5 = 3 x 3 + 4 x 4, to get there boundaries marked correctly. Although Euclid and the Ancient Egyptians studied the theorem, the true inventor of it ( or the person most people believed invented it first ) was Pythagoras of Samos and his group the Pythagoreans. Pythagoras was a man born in 580 B.C. on the island of Samos, in the Aegean Sea. It is said Pythagoras was a man that spent his life traveling the world in search of wisdom. This search for wisdom led him to settle in Corona, a Greek colony in southern Italy, in about 530 B.C. Here Pythagoras gained famous status for his group known as the Brotherhood of Pythagoreans. This group devoted there lives