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    Pythagorean Theorem Essay (1019 words)

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    The Pythagorean Theorem is a geometrical expression used often in math andphysics. It used to 2 2 2 find the unknown side of a right triangle. Theexponential form of this theorem a + b = c .

    That is the equation you use whenyou are looking for the unknown side of a right triangle, and it is what Illdemonstrate on the attached exhibit. The upside down capital L in the bottom ofthe left hand corner indicates that sides A & B are the legs of thetriangle. Since we know side A = 5 inches and B = 3 inches we may fill that into 2 2 2 or equation for step one. (1) 5 + 3 = c What the theorem will help usfind is the c side of this triangle.

    2. 25 + 9 = c All we do is distribute 5 tothe second power and 3 to the second power as seen is step two. Next, we addthese 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. 83is the unknown side of the right triangle. 5.

    c= 5. 83 We found this answer byusing the Pythagorean Theorem as taught in geometrical form. This theorem mayalso be summed up by saying that the area of the square on the hypotenuse, oropposite side of the right angle, of a right triangle is equal to sum of theareas of the squared on the legs. The Pythagorean Theorem was a studied by manypeople and groups. One of those people being Euclid. Sometimes the PythagoreanTheorem is also referred to as the 47th Problem of Euclid.

    It is called thisbecause it is included by Euclid in a book of numbered geometric problems. Inthe problem Euclid studied he would always use 3, 4, and 5 as the sides of theright triangle. He did this because 5 x 5 = 3 x 3 + 4 x 4. The angle oppositethe side of the legs was the right angle, it had a length of 5. The 3:4:5 in theright triangle was known as a Pythagorean triple or a three digits that could beput in a right triangle successfully. These three numbers were also wholenumbers and were used in the Egyptian string trick, which I will talk aboutlater.

    This Pythagorean triple, 3:4:5, are the smallest integer series to havebeen 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 ManlyP. 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 tothe 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 stringtrick.

    Egyptians were said to have invented the word geometry (geo = earth,metry = measuring. ) The Egyptians used the 3:4:5 right triangle to create righttriangles when measuring there fields after the Nile floods washed out there oldboundary 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 AncientEgyptians studied the theorem, the true inventor of it ( or the person mostpeople believed invented it first ) was Pythagoras of Samos and his group thePythagoreans. Pythagoras was a man born in 580 B.

    C. on the island of Samos, inthe Aegean Sea. It is said Pythagoras was a man that spent his life travelingthe world in search of wisdom. This search for wisdom led him to settle inCorona, a Greek colony in southern Italy, in about 530 B.

    C. Here Pythagorasgained famous status for his group known as the Brotherhood of Pythagoreans. This group devoted there lives to the study of mathematics. The group, as led byPythagoras, could be described as almost cult-like because that it had symbols,rituals, and prayers. The group was also cult-like because of there odd ways ofnot writing down any of there discoveries. It was also said that Pythagorashimself sacrificed a hecatomb, or an ancient Greek ritual of 100 oxen, when hediscovered the Pythagorean Theorem.

    The group was also said to have vowed tosecrecy. One day the Pythagoreans discovered irrational numbers. They referredto these numbers as algon or unutterable. They were so shocked by thesenumbers they killed a member of the group that mentioned them in public. Thegroup believed in many things had to do with numbers.

    They said all thingsare numbers, and also numbers rule the universe, Pythagoreans believedthat numbers were divine. He also thought numbers one through ten, those of adecade, were especially sacred. Pythagoreans also thought that numbers hadcharacteristics: 2 was female, 3 was male, odd numbers were good, and evennumbers were evil. This belief by the Pythagoreans led to many discoveriesincluding the Pythagorean Theorem. The Pythagoreans first discovered numberscould be associated with shapes. Numbers six, ten, and fifteen were alltriangular numbers because they can be arranged in equilateral triangles.

    Thisstudy of numbers and shapes eventually led to the discovery of many differentand important theory having to do with geometry. Although, nobody is reallypositive who invented the theorem, Pythagoras or the Pythagoreans? This isunknown because of there vow so secrecy and there neglect of writing therediscoveries down. So now nobody is even sure if Pythagoras had anything to dowith the discovery. The puzzle of who invented the Pythagorean Theorem,Pythagoras or his followers, is so confusing because the group studied such awide variety of different topics. Studies of the group includes many geometricproofs, astronomy, and music.

    The Pythagoreans believed that all these thingshad to do with numbers. If you would ask my opinion on the theorem, I would haveto say the original inventors were the Egyptians. They used the theorem, but thePythagoreans were the first ones to write about and describe it more thoroughly. I think that the theorem was an important discovery for the future .

    I say thisbecause the theorem was studied by so many great thinkers. The theorem iscomplex but simple because it is easy to use with right angles after you learnit, but it also has many philosophical meanings and parts to it. In all I thinkthe Pythagorean Theorem is a confusing, but an important part to the past,present, and future of geometry.Mathematics

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