Pythagorean theorm Essay

This essay has a total of 1177 words and 6 pages.

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 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
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