History of Pi - PowerPoint PPT Presentation

View by Category
About This Presentation
Title:

History of Pi

Description:

This ppt will give you a brief insight on PI – PowerPoint PPT presentation

Number of Views:868

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: History of Pi


1
History of pi
2
  • 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.

3
EXPLAINATION OF PI
CLICK HERE
4
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

5
  • 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.
6
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.

7
 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.
8
Leonhard Euler popularized the use of the Greek
letter p in works he published in 1736 and 1748.
9
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.

10
USES OF PI
  • Geometry and Trigonometry
  • Probability and Statistics
  • Engineering and Geology

11
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

12
The area of the circle equals p times the shaded
area.
13
  • 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.

14
Sine and cosine functions repeat with period 2p.
15
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.

16
A graph of the Gaussian function ƒ(x)  e-x2. The
colored region between the function and
the x-axis has area  .
17
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.

18
The constant p is represented in this
mosaic outside the mathematics building at
the Technische Universität Berlin.
19
(No Transcript)
20
(No Transcript)
21
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
22
 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.

23
Pi Room
24
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.

25
Larry Shaw, the organizer of the first Pi Day
celebration at the Exploratorium in San Francisco.
26
Google Doodle on Pie Day
Pi Pie at Delft University
and
27
EFFORTS BY ARPAN GOYAL
SUBMITTED TO - JITENDER SIR
About PowerShow.com