1. INTRO TO π
Pi (π) is the 16th letter of
the Greek alphabet, and is
used to represent the
most widely known
mathematical constant.
Pi is the ratio of the
circumference of a circle
to its diameter. In other
words, pi equals the
circumference divided by
the diameter (π = c/d).
Conversely, the
2. 𝐶𝐼𝑅𝐶𝑈𝑀𝐹𝐸𝑅𝐸𝑁𝐶𝐸
𝐷𝐼𝐴𝑀𝐸𝑇𝐸𝑅
π =
π 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
3. WHAT TYPE OF A NUMBER π IS?
π is an irritational number,
meaning that it can not be
written as the ratio of two
integers such as 22/7 or
other fractions that are
commonly used to
approximate.
When starting off in math,
students are introduced to
pi as a value of 3.14 or
4. The notation of π
The first to use the symbol of
pi (π) with its current meaning
was William Jones in 1706.
Leonhard Euler adopted the
symbol of pi (π) in 1737 and it
soon became a standard .It is
widely believed that the great
Swiss-born mathematician
Leonhard Euler (1707-83)
introduced the symbol π into
common use.
WILLIAM JONES
LEONHARD EULER
5. How was π developed
The ancient Babylonians calculated the area of
a circle by taking 3 times the square of its radius,
which gave a value of pi = 3.14 .
The first calculation of π was done by
Archimedes of Syracuse (287–212 BC), one of
the greatest mathematicians of the ancient
world.
Around 250 BC the Greek mathematician
Archimedes created an algorithm to
approximate π with arbitrary accuracy.
6. Archimedes method to find an
approximation ofπ
Archimedes' method finds an
approximation of pi by determining
the length of the perimeter of a
polygon inscribed within a circle
and the perimeter of a polygon
circumscribed outside a circle .
By doubling the number of sides
of the hexagon to a 12-sided
polygon, then a 24-sided polygon,
and finally 48- and 96-sided
polygons, Archimedes was able to
MONTE CARLO
7. Archimedes found that if they drew circles in polygons and
calculated the inner and outer polygon’s perimeters and
calculated the value that estimates that the pi was 3.1419…
econd major advancement in understanding pi came with the develop
calculus .
8. Newton’s approximation of π
In 1665, English
mathematician and
physicist Isaac Newton
used infinite series to
compute pi to 15 digits
using calculus he and
German mathematician
Gottfried Wilhelm
discovered.
ISAAC NEWTON
GOTTFRIEDWILHEM
9. PI WAS DEVELOPED
NOT made !
In 1704 John Machin developed a
converging series that calculated up to 100
decimal places.
By the year 1949 digital computers were
invented and could calculate 100’s of
decimal places of pi in hours. In 1949 John
Von Nuemann calculated 2037 digits of pi
10. pi (π) in the professions
Agricultural professionals may use π to determine
the area covered by a pivot irrigation system or
storage facility . They would use the formula of-
𝐴𝑟𝑒𝑎 = 𝜋𝑟2
Architect and construction works would both use
the formula for the area extensively. The also use the
formula of the volume extensively to fill columns of
concrete and to know the space a building would
take up. They would use the formula of-
𝑉𝑜𝑙𝑢𝑚𝑒 = π𝑟2
h
11. Uses of pi (π)
Electrical engineers use it for
solving problems of electrical
applications .
Statisticians use it to track
population dynamics.
Clock designers use it when
designing pendulums for the clocks
.
Aircraft designers use it to calculate
areas of the skin of the aircraft .
Medicine benefits from it when
studying the structure of our eyes.
Bio chemists see it when trying to
12. π fun facts
The current Guinness world
record is held by Lu Chao of
China in 2005 who recited
67,890 digits of π in 70
hours.
July 22 is π approximation
day also known as casual pi
day ,the day is dedicated to
the mathematical constant
π.
