How Did Pythagorean Impact The World

How Did Pythagorean Impact The World
So what this was about was how Pythagorean impacted the world around him. Whether it was about how he revolutionised math or how he made a
whole group that followed him and his beliefs. So this man thought that knowledge was being able to figure out math and do it and to follow their
rules that made up to fall in line with what they believe in. People took this knowledge and advanced it further even to today, this idea that Pythagoras
made himself and figured out. So what this was about was how Pythagorean revolutionised math and how he came up with new equations such as a
squared + b squared = C squared or
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Pythagorean Theorem In America
"How will the Pythagorean Theorem help us in the real world?" a common utterance of disinterested students sitting in their intro Geometry class. The
teacher would constantly have a plethora of real world uses of the Theorem but, to me, it never mattered whether it had any practical use later in life.
Math stimulated and interested me, the fact that it was necessary to our everyday lives was just a bonus. In the fifth grade math my teacher pulled me
aside and requested I sit in on a few Math Counts practices with the middle schoolers. At the time I was shocked, my interest in math class had peaked
during the time because my teacher made the math engaging, incorporating jokes and pop culture into the math, not because I could possibly

Pythagoras Research Paper
Pythagoras was a known as many things, a Greek philosopher, mathematician, a man of science, and the Pythagorean theorem. Pythagoras proved the
Pythagorean theorem, but did not discover it, Babylonians and Indians discovered it before Pythagoras. It took five centuries after his death before
the Pythagoras Theorem associated his name, this was because Plato's followers said it was a myth two centuries after the death of Pythagoras
making people not believe it was a possible theory. It was first published in the writings of Cicero and Plutarch (two well–respected writers of their
time). Pythagoras was learning poetry, to play the lyre, and recite Homer all when he was a child. Pythagoras has had three philosophers who
influenced him when he

Pythagoras Essay
Pythagoras
My name is Pythagoras of Samos. I believe I should win the fabulous two–week cruise on the incomparable Argo because I dedicated my life to
educating and caring for the future generations. I risked my life to share my knowledge with anyone who wanted to learn. I was born on the island
of Samos, but lived most of my life in Crotona, Italy. When I was a young man, I traveled to many different places to observe the different lifestyles
and cultures. Some of the countries I visited were India, Egypt, and Persia (Bulfinch). After viewing many different aspects of life I developed my
philosophies and beliefs. My most important philosophy is that almost everything in life can be associated in some way with numbers ....show more
content...
I am most famous for discovering the Pythagorean Theorem, which solves the length of the hypotenuse of a right triangle. Use the equation aВІ + bВІ =
cВІ, where "a" and "b" are the two sides forming the right angle to solve "c" which is the hypotenuse (Bruce E. Meserve 46). If I could meet a
Greek god or goddess I would undoubtedly choose Apollo. Apollo has many great characteristics and I think we could be good friends if we talked
with each other. One reason why I want to meet him is because I am interested in seeing what he looks like. In books they say he is the most
beautiful god represented by the color gold. He also has a golden chariot with golden horses which I want to ride. Another reason is that he is the
god of things that I'm interested in like music, mathematics, and medicine (Bernard Evslin 37). He is also a very thoughtful and kindhearted god.
The main reason I want to meet him is that he owns an oracle that can tell the future and even though I have clairvoyant powers at this moment, I
want to ask him if he will let me borrow his oracle just in case if I lose my powers (Ellen Switzer 26). I asked the Oracle of Mother Earth to tell me
how modern Greece was dealing with its current political problems. She said that Greece's prime minister was trying to resolve the Kosovo problem
by talking with both political forces. The prime minister felt that fighting and war was not the acceptable solution . He wants the

Relationship Behind The Pythagorean Theorem
Pythagorean Theorem
Introduction
The Pythagorean Theorem is a relation in Euclidean geometry among the three sides of an right angle. Pythagoras, a greek philosopher is credited for
the discovery, but it is unsure who and therefore theorem is named after him. The formula is a2 + b2 = c2.
History of the Mathematician behind the Pythagoras Theorem and the Pythagorean relationship.
People are unsure whether the relationship was made either by Pythagoras or the Pythagoreans first proof, Pythagoras is Greek from the Samos island
(570–495 B.C.). The Founder of the Brotherhood of Pythagoreans is Pythagoras. Pythagoreans have their own religion where, "Number rules the
universe".They are devoted to geometric proofs and keeping them secret. The...show more content...
Conclusion
The Pythagorean Theorem is a2 + b2 = c2. We learnt the history of the pythagorean relationship, like who made it and how it is made.We also found
proofs of the relationship and learned to understand why this relationship is true. We also learned that there are some rare relationships that exists
between Pythagorean numbers. We are very familiar with the pythagorean theorem and now we can solve complex questions involving the pythagorean
theorem now.
Reflection
Our group has had many fights but in the end we managed to complete our work very well. It was difficult to cope with having a new member join
our group and one of our members was put into another group, but we still managed to do very well in the end and had a lot of fun doing the project.
Bibliography http://www.mathsisfun.com/pythagoras.html http://www.geom.uiuc.edu/~demo5337/Group3/hist.html http://ualr.edu/lasmoller
/pythag.html http://www.ck12.org/book/CK–12–Middle–School–Math–Grade–7/section/9.3/

Pythagoras was one of many math Mathematicians and a Greek Philosopher . He was born 570 BCE Samos, Ionia and died 500–490 BCE
Metapontum, Lucanium. He also was the first philosopher ever. Pythagoras came up with the Pythagorean Theorem. The Pythagorean Theorem is a
among all 3 sides of the triangle. There's also a formula that goes along with Pythagorean Theorem, the formula is (a2 + b2 = c2). We still use
Pythagorean Theorem til this day. That formula only applies to right triangles. The Pythagorean theorem has shocked people for nearly 4,000 years.
There are now almost 367 different ways to do it. Pythagoras left Samos and went to Italy to continue with the Theorem. One of Pythagoras famous
quotes was "As soon as laws are necessary for

PythagorasвЂ™ Impact in Geometry
The most common thing people associate the mathematician Pythagoras with is the Pythagorean Theorem that describes the relationship of the
the sides of a right triangle, which is a^2 + b^2 = c^2. Some know him as the first pure mathematician. (Mastin, 2010) His teachings come before
other famous philosophers and thinkers, such as Plato and Aristotle. Who is Pythagoras and how did he impact the mathematical world of
geometry? In order to answer the previous question, there must be an understanding of who he was, what his teachings were, and how his
teachings are applied today. Pythagoras was born in Samos, Greece in 569 B.C. His marital status is unknown. He was well educated and could
recite Homer. He was not only interested in mathematics, but also philosophy, Astronomy, and music. He was taken prisoner and sent to Babylon,
where Magoi priests taught him arithmetic, music, and mathematical sciences. When he was set free, he created a school called the Semicircle. He
left the school because the leaders of Samos wanted him to be a politician. He then made a school where his followers, the Pythagoreans, were
taught, had lived, and had worked. The followers were men and women also known as mathematikoi. The theories and ideas in mathematics that his
followers made were accredited to him. They were also a very secretive group, so not much is known how they came up with their ideas and
philosophies. (Douglas, 2005) He died in approximately 500 B.C. and his followers, "continued

Pythagoras: A New Religion
This text mainly addresses the question: How did humans attempt to develop knowledge?For pythagoras, that was by creating what may as well
have been a new religion. He gave numbers gender, married a student, and had followers that altered their whole lifestyle centered around him and
numbers. He even went as far to label a triangle as an oath, as stated in the quote: "Do you see? What you take to be 4 is 10, a perfect triangle and
our oath" He also labeled odd numbers as masculine and divine, whereas even numbers were feminine and earthy. It sounds strange to a modern mind,
But back then this was perfectly legitimate, After all he did invent the pythagorean theorem, A theorem mind you, we still use and hold dear today, We
wouldn't have any

Pythagoras was an Ionian Greek philosopher, mathematician, and putative founder of the Pythagoreanism movement. He was born in Samos, Greece
and died in Metapontum. His parents were Mnesarchus and Pythais. Some say that Pythagoras had three daughters and one son. Others say he never
got married and had children. He is referred to as the first pure mathematician. He was a well educated man and was interested in mathematics,
philosophy, astronomy, and music. It is said that he was influenced by Pherekydes (philosophy), Thales (mathematics and astronomy) and Anaximander
(philosophy, geometry). They don't know very much about his mathematical achievements. They don't have any of his writing's like they do other
philosophers. Pythagoras settled

Pythagoras was an Ionian Greek philosopher, mathematician, and the founder of pythagoreanism, he is also often referred to as the first pure
mathematician. The Pythagoreans advance the mathematics and showed that is needed in our everyday life. Pythagoras was well educated, and he
played the lyre throughout his lifetime, and also knew poetry. He was interested in mathematics, philosophy, astronomy and music, and was actually
greatly captivated by Pherecydes (philosophy), Thales (mathematics and astronomy) and Anaximander (philosophy, geometry).Pythagoras stayed in
Crotona, a Greek colony in southern Italy, where he found a school where most of his followers lived. He was the master of society and all his
followers were known as mathematikoi...show more content...
Pythagoras contributed to our understanding of triangles, angles, areas, proportion, polygons, and polyhedra. Pythagoras also related music to
mathematics so that's why he is also credited with the discovery that the intervals between the harmonious musical notes always have whole number
ratios. For instance, playing half a length of a guitar string gives the same note as the open string, but an octave higher; a third of a length gives a
different, but harmonious note; etc. He had long played the seven string lyre, and learned how harmonious the vibrating strings sounded when the
lengths of the strings were proportional to whole numbers, such as 3:2, 2:1, 4:3. But Pythagoras intelligence not only came from him but with the
help of his followers, so yeah it wasn't all truly all his work but he was for sure a good mathematician. Furthermore, in conclusion I feel like
Pythagoras was an amazing mathematician for sure and his followers as well because though they did not get the credit for it they also were a great

Questions On The Pythagorean Theorem Essay
Tasfia HaqueMath Research Paper
December 8, 2015Mr. Rubinstein Period 6 The Pythagorean theorem is a theorem that states that the sum of the squares of two legs of a right
triangle, a and b, is equal to the square of the hypotenuse, c. This can be written and shown as the equation, a2+b2=c2. Because a2+b2=c2, we can
solve for the sides of the legs of the right triangles, in terms of this formula of the Pythagorean theorem.
C=в€
љ(A2+B2)
A=в€
љ(C2–B2)
B=в€
љ(C2–A2)
This diagram represents the Pythagorean theorem as well. Because the squares of each side of the right triangle are used in the theorem, this can be
shown as an extension to each side of the triangle, where there are three squares and one side of each square is apart of the triangle. The sum of the
areas of the two squares attached to the legs of the triangle is equal to the area of the square attached to the hypotenuse. This is because to find the area
of the square, you square its side, which also happens to be the side of the triangle. This perfectly shows and represents the Pythagorean theorem
because the sides have to be squared and added to create the equation, a2+b2=c2. This can also be shown through other extensions and shapes that are
attached to each side of the triangle, not just with squares. For example, the sum of the area of circles or hexagons attached to the two legs of the right
triangle is equal to the area of the circle or hexagon attached to the hypotenuse. This is

Pythagoras was a Greek mathematician known for formulating the Pythagorean Theorem. He was born in 570 BC on the islands of Samos and passed
away 495 BC at around the age of 75 in Metapontum. He was once a philosopher who taught that numbers were the essence of all things and was
described as the first pure mathematician. People describe him as an extremely important person in mathematical history and yet not many people
know much about him. There is little reliable records about his life and accomplishments. He linked numbers with virtues, colors, music and other
qualities. He also believed that the human soul is immortal and he believed that after death human soul moves into another living being. Pythagoras
created and organized a group...show more content...
He also believed that that the sun, moon, and other planets had their own movements. His beliefs led to the Copernican theory of the universe. The
principles of the Pythagorean Theorem had already been known by the Egyptians before Pythagoras formulated it. No one today is sure how
Pythagoras himself proved the Pythagorean Theorem because he never allowed anyone to record his teachings in writing. Most likely, like most
ancient proofs of the Pythagorean Theorem, it was geometrical in nature. The Pythagoreans knew that any triangle whose sides were in the ratio 3:4:5
was a right–angled triangle. But, they had a desire to find mathematical of all things led them to prove the geometric theorem. Although the Egyptians
were the first to discover the theorem, Pythagoras was the first to prove it.
Pythagoras Theorem was a demonstration that the combined areas of squares with side length of a and b. These side lengths will equal the area of a
square with sides of length c, where a, b, and c represent the lengths of the two sides and hypotenuse of a right triangle. However, the Pythagoreans did
not consider the square on the hypotenuse to be that number c multiplied by itself c^2. Instead, it was conceptualized as a geometrical square c
constructed on the side of the

What Is Pythagoras And How Do They Work?
Dear, 7th Grader Who is Pythagoras and why should you care? Pythagoras was a Greek Philosopher. He really liked math. He liked math so much
that he treated it like it was his religion. He was good at math and he eventually got a group of followers. His followers were called Pythagoreans.
They credited him with all their discoveries. Pythagoras and the Pythagoreans became very powerful, so powerful that the government got scared and
banned them from meeting. They still met, except only in secret. Pythagoras and his followers discovered the Pythagorean theorem. The Pythagorean
theorem is a formula that helps when people want to find the length of a side of a right triangle when they know the lengths of 2 of the sides known.

Pythagoras Accomplishments
Did you know that Pythagorean Theorem was actually created well before our generation's time period? Yes, it seems that is pretty basic knowledge,
but did you know it was actually created in B.C. and instead of A.D.? The brilliant mind to thank for such an achievement is the man who goes by the
name Pythagoras. However the Pythagorean Theorem isn't his only accomplishment, he was so advanced for his time, that he had many achievements.
But to the best way to examine these accomplishments is to start at the beginning. In around 569 B.C on a small island of Samos, Pythagoras was born.
His mother, named Pythais, was a native to the island Samos and his father, named Mnesarchus, was a traveling merchant. Due to his father being a
traveling merchant, Pythagoras spent his most of his childhood traveling with his father, thus causing young Pythagoras to become more intelligent and
worldly compared to other youth at the time. Along the travels he picked up reading and reciting poems created by Greek Poet, Homer. Though there
were two...show more content...
Many of the theorems we have today our proven fact, while back in Pythagoras' day math was more critical thinking rather than problem solving. One
example of Pythagoras' critical thinking comes in the form of a simple triangle which he called Tetractys. A tetractys, or also known as tetrad, a
triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of
the fourth triangular number. This later became the mystic symbol of the Pythagoreans. Speaking of triangle's Pythagoras' most famous contribution to
the world of mathematics, The Pythagorean Theorem was proved during this time period. Pythagoras did not create the Theorem, the creation is
credited to the Babylonians and Indians, however Pythagoras was the first man to successfully prove the Theorem. The iconic equation looks like

Triangles and Pythagorean Theorem
4.14 TRIANGLES
Triangles are three–sided shapes that lie in one plane. Triangles are a type of polygons. The sum of all the angles in any triangle is 180Вє.
Triangles can be classified according to the size of its angles. Some examples are :
Acute Triangles
An acute triangle is a triangle whose angles are all acute (i.e. less than 90В°). In the acute triangle shown below, a, b and c are all acute angles.
Sample Problem 1:
A triangle has angles 46Вє, 63Вє and 71Вє. What type of triangle is this?
Answer: Since all its angles are less than 90В°, it is an acute triangle.
Obtuse Triangles
An obtuse triangle has one obtuse angle (i.e. greater than 90Вє). The longest side is always opposite the obtuse angle. In the obtuse triangle shown
below, a...show more content...
The area of the rectangle is b Г— h, so either one of the congruent right triangles forming it has an area equal to half of that rectangle. Right triangles
can be neither equilateral, acute, nor obtuse triangles. Isosceles right triangles have two 45В° angles as well as the 90В° angle. All isosceles right
triangles are similar since corresponding angles in isosceles right triangles are equal. If another triangle can be divided into two right triangles, then the
area of the triangle may be able to be determined from the sum of the two constituent right triangles. Also the Pythagorean theorem can be used for non
right triangles. a2+b2=c2–2c
The side lengths of a right triangle form a so–called Pythagorean triple. A triangle that is not a right triangle is sometimes called an oblique triangle.
Special cases of the right triangle include the isosceles right triangle (middle figure) and 30–60–90 triangle (right figure).
4.14.2 Solutions Of Right Triangle
In geometry, the triangles are made up of three line segments. When the two segments are perpendicular to each other (angle is 90 degree) then it is
called as right triangle. The sizes of the angles and lengths of the sides are related to one another. If the triangle is a right triangle, we can be able to use

Pythagorean Theorem In America
"How will the Pythagorean Theorem help us in the real world?" a common utterance of disinterested students sitting in their intro Geometry class. The
teacher would constantly have a plethora of real world uses of the Theorem but, to me, it never mattered whether it had any practical use later in life.
Math stimulated and interested me, the fact that it was necessary to our everyday lives was just a bonus. In the fifth grade math my teacher pulled me
aside and requested I sit in on a few Math Counts practices with the middle schoolers. At the time I was shocked, my interest in math class had peaked
during the time because my teacher knew how to make the math engaging, incorporating jokes and pop culture into the math, not because

Background:
The Pythagorean Theorem was discovered and first proven by the Greek mathematician, Pythagoras. The Pythagorean Theorem states that the sum of
the squares of the two legs of a right triangle equals the square of the hypotenuse of the triangle. In simpler words, when looking at the right triangle
below, aВІ+bВІ=cВІ. This major discovery in the history of mathematics lead to the accomplishments of many other basic things we do in life. The
Pythagorean Theorem does not just stop at the famous equation of aВІ+bВІ=cВІ, but it has many other aspects. Whole numbers that can fit into this
theorem are commonly referred to as Pythagorean Triples. The Pythagorean Theorem includes numerous amounts of poofs, from the basic proof to the
...show more content...
Once the concept of the Pythagorean Triples was discovered, mathematicians were eager to validate the concept. Euclid created a widely accepted
formula in deriving a Pythagorean Triple, which can be proved with the help of the unit circle and algebra.
Euclid's Formula and its Proof
Euclid's formula for a Pythagorean triple is: a = 2mn, b = m^2 – n^2, c = m^2 + n^2
The variables: m and n: stand for positive, rational integers. It is important to remember that m has to be greater than n, otherwise the statement valuing
variable b on a Pythagorean triangle would be false because b cannot
This can be understood in terms of the rational points on the unit circle. A unit circle is a circle with the radius of 1.
We can draw a right triangle: a and b are the legs c is the hypotenuse
In the next part, we must use the trigonometric identity of sin2+cos2=1. For representational purposes, we must look towards the following diagram for
how the triangle would be represented in this proof.
The next step in formulating this next equation would require us to find the sine and cosine of triangleABC. The sine formula is opposite/hypotenuse,
which would equate to a/c. Additionally, the formula for cosine is adjacent/hypotenuse, equating to b/c. Knowing the trigonometric identity, we can
derive the new eqution:
For the next step, we will need to know the equation of a [unit] circle: x2 + y2 = 1
We know that

Around Two thousand five hundred years ago, a Greek mathematician, Pythagoras, invented the Pythagorean Theorem. The Theorem was related to the
length of each side of a right–angled triangle. In a right–angled triangle, the square on the hypotenuse, the side opposite to the right angle, equals to the
sum of the squares on the other two sides. (148, Poskitt) To know more about this famous theorem, we can look at the other forms of thePythagorean
Theorem, such as it can also be written as c^2–a^2=b^2 which is for reverse operations like finding side b with the data of a and c. Meanwhile, the
proofs of the theorem can make us understand more about the invention of the theorem and how Pythagoras figured it out. And with the invention of this
...show more content...
To solve this equation, place 3^2 to the right side, which makes it negative. The equation then become this: b^2=5^2–3^2. After subtracting the squares
of 5 and 3, you get b^2=16 . Then if you root 16 (в€
љ16), you get 4, therefore b=4. And a new form of the theorem appeared: b^2=c^2–a^2. If you do
some rearrangements, a^2=c^2–a^2 also works the same. Generally, the Pythagorean Theorem works with different form of algebraic equations by
rearranging a^2+b^2=c^2, to solve different cases.
Pythagoras made proofs to prove that is theorem is always correct and goes to all right–angled triangles. Some proofs were very old and had been used
for a long time and is very famous. As time passes by mathematicians from around the world figured out new proofs that were getting easier. After all
there were over three hundred proofs around the world. To start with, this proof was one of the proof created by Pythagoras and looks like this:
Firstly, each side of the biggest square (blue + yellow) equals to a+b. Therefore, the area of this biggest square is гЂ–(a+b)гЂ—^2. (Area of Square =
гЂ–"Length" гЂ—^2) Secondly, the area of the tilted yellow square equals to c^2, since the length of each side is c. Thirdly, the area of one small blue
triangle is 1/2 ab (Area of Triangle = "LengthГ—Height" /2), so the area of four blue triangles is 4(1/2 ab) simplified to 2ab. Therefore the area of the
four blue triangles and the yellow tilted square

How Does The Pythagorean Theorem Work?
a2+b2=c2 is the famous theorem that Pythagoras discovered and named, calling it the Pythagorean Theorem. This theorem applies to the right triangle
stating, that by adding the length of both legs squared you can then find the squared length of the hypotenuse. This theorem is set up in way that if you
know two of the variables, whether it is a leg(b or a) and the hypotenuse (c) or both legs (a and b), you will always be able to find the third
measurement. However, why does this theorem work? Why does a2+b2=c2? That is the question that is asked hundreds of times by thousands of
people. The answer to it is not a complicated one, the reasoning behind that is because there are at least 367 Pythagorean Theorem proofs out there
(Source four). They...show more content...
Step Seven: You then solve the equation. c2=(a–b)2+2ab =a2–2ab+b2+2ab = a2+b2
Proof Four
Step One: Create four copies of a right triangle
(Note: Each has an area ofab/2)
Step Two: Combine the the triangle so that it forms a square with the side of (a+b) and a hole with the side of c.
Step Three: Then calculate the area of the big square in two ways by creating the equation; (a+b)2=4ab/2 +c2. (When simplified you will get the
required identity.)
Step Four: We then use the identity created in the third proof and add it to the identity we created in step three.
Step Five: Add the two identities together. c2=(a–b)2+4ab/2 c2=(a+b)2–4ab/2
2c2=2a2+2b2
c2=a2+b2
Overall there are hundreds of ways to prove the Pythagorean Theorem. As stated before these proofs range from effortless geometric and algebraic
proofs to intricate and complex trigonometric and calculus proofs. The proofs shown above are predominantly straightforward and easy to understand
and do. Once again, these proofs are only a small portion of other proofs out there in the world. However, it will never matter what proof you choose
to prove the Pythagorean Theorem, because no matter what they will all have the same end

How Did Pythagorean Impact The World

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