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
  letter spread rapidly.

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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
  radius r is 4pr2

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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
  1  p/180 radians.
• 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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Google Doodle on Pie Day
Pi Pie at Delft University
and
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EFFORTS BY ARPAN GOYAL
SUBMITTED TO - JITENDER SIR