Is 22/7 an accurate value of pi?
By André Hayward

André’s project on pi won a gold medal at regional expo and National Eskom Expo for young Scientists in 2006. He has also participated at the ESI (Expo Science International) 2007 in Durban where he was also a judge. He has received International colours in expo (Kingfisher Colours from NYDT) and participated in the ISTF expo where his project was judged as superior. He has donated DVDs of his project to schools in rural areas to teach them about pi.



A short history of pi:
Pi is a value which has been among us for many years. You can even read about it in the Bible. The Egyptians and Babylonians were some of the first cultures to use Pi. William Jones, a British mathematician, first used the symbol π in 1706. 

Pi is the circumference of a circle divided by its diameter. Pi is used to calculate the circumference, area and volume of circles, cylinders, cones and spheres.

Archimedes introduced 22/7 to the world as the value of pi in 250 B.C.

A short description and conclusion of my project:
With my project I have tried to prove that 22/7 is not an accurate value of pi but only an approximation. I have done that by doing a series of calculations with circles, cylinders, spheres and cones. I have calculated their circumferences, areas and volumes.

I have also done calculations on practical examples like silos, dams and pipelines. The conclusion I was that all the answers I got with 22/7 were bigger than the answers with pi. Thus if you use 22/7 in your calculations the answers is going to exceed the capacity of the dam, silo or pipeline if you work with the volume.

My final conclusion is that 22/7 as a value of pi is not a true or accurate value of pi. 

Here are some calculations:

Dam

r = 55 dm
h = 20 dm

Volume of a cylinder = πr²h

Calculated with

π = 190 066,3555 l.

22/7 = 190 142,8571 l

π – 22/7 = -76,50160067 l.

Silo

Volume of a cylinder = πr²h

r = 75 dm
h = 340 dm

Calculated with

π = 6 008 295.9 l.

22/7 = 6 010 714. 286 l.

π – 22/7 = -2 418. 335 724 l.
 
Volume of a cone = ⅓πr²h

π = 88 357. 293 38 l.

22/7 = 88 392, 857 14 l.

π – 22/7 = -35, 563 760 64 l.

Final difference =difference of cylinders +
2(Difference of cones)

= -2 489, 463 246 l.

True values = True answers

As you can see in the practical examples, the answer using 22/7 is bigger that the answer using pi. It would cost companies money if they use the wrong value and put more into a dam, silo or pipe than it can hold. I am not worried about the engineers because they know that 22/7 is an inaccurate value. I am worried about the children in the schools that don’t know what the real value of pi is!

With my project I want to prove to the world that there is just one value for pi and not two. At the moment people are confused and don’t know what is the true value but with my project I show that there is just one value for pi.

22/7 ≠ Pi

André Hayward is currently a Matric learner in Hoёrskool Rustenburg. He was born in Welkom in the Free State and when he was 8 he moved to Hartbeespoort Dam. André likes to think and talk about every day problems like air pollution, the war in Iraq and the oil crisis.

His hobbies are solving MENSA puzzles, collecting and reading World War II books and collecting stamps. He also likes Maths and Science and learning about the newest technology. Some of the people who have inspired him are Sir Isaac Newton, Albert Einstein, Thomas Edison, Bill Gates and Mark Shuttleworth.

André wants to become a Chemical Engineer and help to make the world a better place for everyone. His dreams are to solve global warming, save the planet and also to one day win the Nobel Prize!