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The Significance of Pi
Transcript of The Significance of Pi
Approximation of pi are 3.14 and 22/7
Pi is a constant term.
Usually represented by the symbol seen on the previous slide.πππππ
Pi is irrational and cannot be expressed as a fraction or a decimal.ππππππππππππππππππππππππππ
The Significance of Pi
Why Pi is so important!
What is Pi?
Pi as a Decimal - It is Infinite!
Pi is irrational so there are an infinite number of decimals. To give you an example of how long pi is, here are the first 1000 digits.
The History of Pi
Lets talk about the history of pi first and see how many mathematicians from different places and time periods calculated this astonishing number.
The ancient Babylonians calculated pi by using the formula 3r^2 (which means pi is 3), but a Babylonian tablet (ca. 1900–1680 BC) indicates a value of 3.125 for pi, which is a close approximation.
From the Rhind Papyrus (ca.1650 BC) we know that ancient Egyptians calculated the area of a circle by using the formula:
This got them a value of 3.1605 (256/81) for pi.
A very interesting reference of pi comes from the Bible itself.
"And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about." (I Kings 7, 23; II Chronicles 4, 2.)
They made an estimate of pi which was 3.
Archimedes, a very famous Greek mathematician was also trying to calculate pi. He worked out that 223/71 is less than pi and pi is less than 22/7. This was achieved by circumscribing a circle with polygons. Starting with a hexagon, he eventually reached 96!
He first found the area of a regular polygon inscribed within the circle, then he found the area of the polygon outside of the circle. The area of the circle is found within these 2 area of these 2 polygons.
The Chinese such as Zu Chongzhi used this method and got approximately 3.1415926.
James Gregory (1638-1675) developed another formula to calculate pi, though it was very inefficient.
pi/4 = 1 - 1/3 + 1/5 - 1/7 + . . . . . . . . . . .
But using this would mean you have to add 5 million terms to work out the value of pi/4 that only goes to 6 or 7 decimal places.
In 1706, another mathematician, John Machin developed a more refined version of Gregory's formula,
This is still used today.
So now that we know all about how they calculated pi and the number of digits they found, guess what the current record of the highest number of digits found?
This was found by Shigeru Kondo in 2011 using a computer.
How Pi was Named
You might all be wondering by now, why pi is named pi and how the symbol came to be.
In 1707, Welsh mathematician William Jones was the first to use the Greek letter to represent pi.
Popularised in 1737 by the mathematician Euler and it became standard.
The π symbol was taken from the Greek word for "perimeter".
Here is the real question. Why is it so important and significant in history?
Pi had to mean something for so many people to try and work out what pi is.
One of the reasons is that pi is used to measure and calculate:
The circumference of a circle
The area of a circle
The area of ellipsis
The volume and surface area of spheres
The volume and surface area of cylinders
The volume and surface area of circular pyramids.
Why does this matter to us?
Simply because we use these formulas for things such as:
Designing- wheels, gears
Architecture- supports, circle roof
Measuring- size of earth and other spheres
Another reason is that the usage of pi has advanced the technology and knowledge of mankind. Wheels would be hard to make, structures and buildings would be unstable. This would impair the development of mankind. Instead of focusing on inventing new things, you would be too busy trying to build a solid foundation for your house because it would be trial and error without pi.
Also, pi is not only used to calculate the area and circumference of circles. It is vital in other fields or subjects which require pi in some of their formulas. Examples of this would be trigonometry, number theory and statistics among many others.
In trigonometryπ, pi is important because they use a measurement of radians, which are defined so that a complete circle spans an angle of 2 piπ radians.
Another interesting to note is that since pi is such a well known number. Many people actually use pi to test how fast and accurate their computers were. Technology is pretty amazing at calculating pi and D. F. Ferguson calculated pi to 620 digits in 1945 using just a desk calculator. Now this is impressive but nothing compared to the recent records we had:
From 2002 we had over a trillion digits calculated using a computer
In 2009 we had over 2 and a half trillion
In 2010 there were 5 trillion
Then in 2011, we found 10 trillion digits of Pi ( 10,000,000,000,050 decimal places)
Pi is a constant ratio defined by the circumference divided by the diameter and is irrational
Pi has had a long history where people from different places and time periods were trying to work out the value of pi
Pi is VERY important to mankind
I hope you have enjoyed this presentation.
By Codey Tse