Pythagorean Theorm
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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
I’ll 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 Hall’s study the symbolism of this arrangement is as f...
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