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## History of Pi

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Title: History of Pi

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History of pi
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• The number pi (symbol p)  is a mathematical
constant that is the ratio of a circle's circumfer
ence to its diameter, and is approximately equal
to 3.14159.
• It has been represented by the Greek letter "p"
since the mid-18th century, though it is also
sometimes written as pi.
• p is an irrational number, which means that it
cannot be expressed exactly as a ratio of
two integers (such as 22/7) consequently,
its decimal representation never ends and
never settle into a permanent repeating pattern.

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EXPLAINATION OF PI
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DEFINITION
• p is commonly defined as the ratio of
a circle's circumference C to its diameter d.
• The ratio C/d is constant, regardless of the
circle's size. For example, if a circle has twice
the diameter of another circle it will also have
twice the circumference, preserving the
ratio C/d. This definition of p implicitly makes
use of flat (Euclidean) geometry although the
notion of a circle can be extended to any

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• curved (non-Euclidean) geometry, these new
circles will no longer satisfy the
formula p  C/d. There are also other definitions
of p which do not mention circles at all, for
example p is twice the smallest positive x for
which cos(x) equals 0.

The circumference of a circle is slightly more
than three times as long as its diameter. The
exact ratio is called p.
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Role Of Leonhard Euler In Pi
• After Jones introduced the Greek letter in 1706,
it was not adopted by other mathematicians
until Euler started using it, beginning with his
1736 work Mechanica. Before then, mathematicians
sometimes used letters as c or p instead.
Because Euler corresponded heavily with other
mathematicians in Europe, the use of the Greek

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In 1748, Euler used p in his widely read
work Introductio in analysin infinitorum (he
wrote "for the sake of brevity we will write
this number as p thus p is equal to half the
circumference of a circle of radius 1") and the
practice was universally adopted thereafter in
the Western world.
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Leonhard Euler popularized the use of the Greek
letter p in works he published in 1736 and 1748.
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USES OF PI
• Because p is closely related to the circle, it is
found in many formulae from the fields of
geometry and trigonometry, particularly those
concerning circles, spheres, or ellipses.
• Formulae from other branches of science also
include p in some of their important formulae,
including sciences such as statistics, fractals,
thermodynamics, mechanics, cosmology, number
theory, and electromagnetism.

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USES OF PI
• Geometry and Trigonometry
• Probability and Statistics
• Engineering and Geology

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Geometry and Trigonometry
• p appears in formulae for areas and volumes of
geometrical shapes based on circles, such
as ellipses, spheres, cones, and torus. Some of
the more common formulae that involve p
• The circumference of a circle with radius r is
2pr.
• The area of a circle with radius r is
• The volume of a sphere with radius r is  4/3pr3
• The surface area of a sphere with

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The area of the circle equals p times the shaded
area.
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• The trigonometric functions rely on angles, and
mathematicians generally use radians as units of
measurement. p plays an important role in angles
measured in radians, which are defined so that a
complete circle spans an angle of 2p radians. The
angle measure of 180 is equal to p radians, and
• Common trigonometric functions have periods that
are multiples of p for example, sine and cosine
have period 2p.

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Sine and cosine functions repeat with period 2p.
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Probability and Statistics
• The fields of probability and statistics frequentl
y use the normal distribution as a simple model
for complex phenomena for example, scientists
generally assume that the observational error in
most experiments follows a normal
distribution. p is found in the Gaussian
function (which is the probability density
function of the normal distribution)
with mean µ and standard deviation s.

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A graph of the Gaussian function ƒ(x)  e-x2. The
colored region between the function and
the x-axis has area  .
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Engineering and Geology
• p is present in some structural engineering
formulae, such as the buckling formula derived by
Euler, which gives the maximum axial load F that
a long, slender column of length L, modulus of
elasticity E, and area moment of inertia I can
carry without buckling.

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The constant p is represented in this
mosaic outside the mathematics building at
the Technische Universität Berlin.
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In Popular Culture
• Perhaps because of the simplicity of its
definition and its ubiquitous presence in
formulae, p has been represented in popular
culture more than other mathematical constructs.

Importance Given To Pi
Palais de la Découverte
Pi Day
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Palais de la Découverte
• In the Palais de la Découverte (a science museum
in Paris) there is a circular room known as the
"pi room". On its wall are inscribed 707 digits
of p. The digits are large wooden characters
attached to the dome-like ceiling. The digits
were based on an 1853 calculation by English
mathematician William Shanks, which included an
error beginning at the 528th digit. The error was
detected in 1946 and corrected in 1949.

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Pi Room
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Pi Day
• Pi Day is an annual celebration commemorating
the mathematical constant p (pi). Pi Day is
observed on March 14, since 3, 1, and 4 are the
three most significant digits of p in the decimal
form. In 2009, the United States House of
Representatives supported the designation of Pi
Day. The earliest known official or large-scale
celebration of Pi Day was organized by Larry Shaw
in 1988 at the San Francisco Exploratorium.

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Larry Shaw, the organizer of the first Pi Day
celebration at the Exploratorium in San Francisco.
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