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A Taste of Pi

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Belani W

on 9 December 2013

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Transcript of A Taste of Pi

A Taste of Pi
What is Pi?
Pi is an infinite number that equals to approximately 3.14. It's the number you get when you divide the circumference of any circle (the distance around a circle) by it's diameter (the length of a straight line passing through the center of a circle). This works for any circle, and will
ALWAYS
equal approximately 3.14. The value of pi is the number of times the diameter of a circle would wrap around it's circumference.
What Type of Number is Pi?
Pi is an
irrational
and
transcendental
number. It's an
irrational number
because it can't be written as a simple fraction or ratio. The closest fraction anyone has ever gotten for pi is
22/7 = 3.1415926...
(although this is close, it is not accurate). Another reason for pi not having a simple fraction, is because it's a
transcendental number
. A transcendental number is one that has an infinite amount of decimal places.
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ....
Since pi is a transcendental number, here are it's first 100 digits...
1650 B.C.
250 B.C.
European Renaissance Period
14th - 17th century
1900–1680 B.C.
2600 B.C.
Ancient Egyptians
In ancient Egypt when the Rhind Papyrus was discovered, it showed how to calculate the area of a circle using the following formula: Area = (8/9 d)^2. The Rhind Papyrus also stated that the value of pi was 3.16
Archimedes of Syracuse, Greece
The greek mathematician, inventor, astronomer and engineer was the first person to come up with a theoretical calculation of pi with the number precisely almost to the thousandth decimal. Archimedes figured out that the value of pi was between 3 10/71< π < 3 1/7 . This gave an approximate value for pi of 3.14
Mathematical formulas, discoveries and approximations related to Pi were made by many mathematicians during this time period
-
Francois Viete
-
1593
(created a formula for pi)
-
John Wallis
-
1695
(discovered that pi was a continued fraction)
-
James Gregory
-
1638
(created a new formula for approximating pi)
-
Gottfried Lebniz
-
1646
(refined Gregory's formula and approximated pi)
-
Sir Issac Newton
-
1665
(created arcsin functions related to pi)
-
John Machin
-
1706
(created a new formula, and refined the work of Lebniz)
The Egyptians
There is some indication that the architects of the pyramids of Egypt going all the way back to 2600 B.C. knew about pi. This is because there are certain dimensions of the pyramids that suggest that π or π/2 (π over 2) were used in it's construction, and instead of approximating it, they just used 3.
Ancient Babylonia
The ancient Babylonians calculated the area of a circle by taking 3(r^2) and using 3 as π. However one Babylonian tablet showed the value of π being 3.125
The History of Pi
1761 - 1794
1882
2013
1949
1873
1737
Johann Lambert
Lambert discovered that pi was an irrational number. Meaning that it has an infinite decimal that will never repeat.
Ferdinand Von Lindemann
Lindemann proved pi to be a transcendental number. Other transcendental numbers, other than pi, always have an infinite number of decimals typically repeating. Transcendental numbers are typically non-rational, meaning that no two rational numbers can fractional represent a transcendental number. In other words, it can't have a fraction that represents itself.
John Louis Von Neumann
After the invention of the computer, Neumann was the first person to approximate pi using a computer, the
ENIAC
computer to be more precise (
E
lectronic
N
umerical
I
ntegrator
A
nd
C
omputer). The ENIAC approximated
2,037 decimal places of pi
.
Present Day
Over the years the value pi has been approximated past the trillions and will continue to be approximated forever. However it has been rounded down to 3.14 for the purpose of simplifying calculations and the value of pi itself.
Leonard Euler
The symbol for pi (π) became a standard/popularized when Leonard Euler adopted it in 1773. However it was first introduced by English mathematician William Jones in 1706. The symbol 'π' for pi is a letter in the Greek language and is the first letter of the Greek word “perimeter.” It is also shown as the Latin word "pi" and in English is pronounced as "pie".
William Shanks
Shanks used the formula
π = arctan (1/2) + arctan (1/3)
that John Machin created in 1706, to approximate pi to 707 decimal places. He published his work in 1873, but it was discovered much later on that only 527 of his decimals were accurate.
(1761)
Legendre discovered that π^2 was irrational alongside π as well
(1794)
100
Interesting Pi Facts
1.
Pi is the most recognized mathematical constant in the world

2.
The world record for most digits of pi memorized and recited is held by Chao Lu of China. He went up to 67,890 decimal places and did it with 4 years of practice and within 24 hours and 4 mins

3.
There is an annual celebration of π on Pi Day on March 14 {which was chosen because it resembles 3.14 (3/14)}. The official celebration begins at 1:59 p.m., to make an appropriate 3.14159 when combined with the date. It was started by Larry Shaw in 1988 at the San Francisco Exploratorium.
4.

5.
Pi was first figured out by drawing a 97 sided polygon within a circle

6.
Some people refer to pi as a "circular constant" or "Archimedes constant"

7.
π is the 16th letter in the Greek alphabet

8.
Pi day shares a birthday with Albert Einstein, Astronomer Giovanni Schiaparelli and commander of Apollo 8, Frank Borman
A real-life example of how pi is used to calculate
circumference
Let's say there was a jeweler who needed to know the distance around a costumer's old ring to make a new copy of it. However the only measurement the jeweler had of the ring was it's diameter of 2cm. The measurement the jeweler would have to figure out is the circumference of the ring. The jeweler could do this by multiplying π by the diameter of the ring to find out the circumference. This is what the equation, formula, and answer would look like:
C=
πd
C=
3.14(2cm)
C=
6.28cm
Therefore the and circumference of the ring is 6.28cm
A real-life example of how pi is used to calculate
area
2 cm
Let's say an electrician needed to know the area of a button on a doorbell so that he could engrave a design on it. However, he only knew the diameter of the button which was 3.5 cm. How would he find out the area? The electrician could find the area of the surface on the button by first dividing the measurement of the diameter he has by 2 in order to get the radius (half the diameter) of the button. After he does this, he has to multiply π by r^2. The equation, formula, and answer to this example is shown here:
A=
πr^2
=
3.14 (3.5cm)^2
=
38.47 cm^2
Therefore the area of the surface of the button, on the doorbell, on which a design will be engraved is 38.47 cm^2
3.5 cm
Diameter
Diameter
Conclusion
Although pi will never come to an end, this presentation has. I hope it gave you more information about pi and that you've enjoyed watching it!
Thank
You
Belani .W.
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