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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 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 to the study of mathematics.
The group, as led by Pythagoras, 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 of not writing down any of there discoveries. It was
also said that Pythagoras himself sacrificed a hecatomb, or an ancient Greek
ritual of 100 oxen, when he discovered the Pythagorean Theorem. The group was
also said to have vowed to secrecy. One day the Pythagoreans discovered
irrational numbers.
They referred to these numbers as “algon” or unutterable. They were so
shocked by these numbers they killed a member of the group that mentioned them
in public. The group believed in many things had to do with numbers. They said
“all things are numbers,” and also “numbers rule the universe,” Pythagoreans
believed that numbers were divine.
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