Tuesday, 19 March 2013 08:41

Maths Corner – Pi - remember it, use it and celebrate it!

Written by  Kimberley Pounder
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Pi

This special number is essential when you are working with circles. In this quarter’s CAMI Express we look at who discovered Pi, a neat trick to remembering it to 30 decimal places, using it to find circumference and area of circles as well as the traditions of Pi Day!

 

 

 

Pi_mugπ - Where did it come from?

 

No one really knows how Pi was discovered; mathematicians have known the number for over 4000 years though! Euclid who was a Greek mathematician, born in 325 BC, was responsible for Euclidean geometry and this was the first recorded system used to show Pi as a mathematical constant.

 

William Jones first used the Greek symbol ‘π’ in 1706 when he published his book: A New Introduction to Mathematics. This notation became standard after it was adopted by Leonhard Euler in 1737.

Pi_scroll

 

An approximation of Pi is 3.14159.

 

It was Aryabhatt in the fifth century who used the approximation 22/7 as the constant in the calculation to measure the earth’s circumference.

 

Pi has now been evaluated to over a trillion decimal places by computer!

 

Check out this website to see one million digits of Pi! http://www.piday.org/million/

 

 

Remember Pi to 30 decimal places…

 

Impress everyone at your Pi Party and write Pi to 30 decimal places using this neat trick provided by our fantastic tutor manager, Mark, at the CAMI Tutor centre!

 

Memorise the following nonsense rhyme:

 

 

Sir, I sent a rhyme excelling

In sacred truth and rigid spelling

Numerical sprites elucidate

For me the lexicon’s dull weight

If nature gain not you complain

And Dr Johnson fulminate

 

 

The number of letters in each word represents a digit of Pi:

 

Sir,

I

sent

a

rhyme

excelling

3.

1

4

1

5

9

In

sacred

truth

and

rigid

spelling

2

6

5

3

5

8

Numerical

sprites

elucidate

9

7

9

For

me

the

lexicon’s

dull

weight

3

2

3

8

4

6

If

nature

gain

not

you

complain

2

6

4

3

3

8

And

Dr

Johnson

fulminate

3

2

7

9

 

3.141592653589793238462643383279 

 

To look extra impressive you can even look up further digits of Pi and make up more lines to the poem!

 

So, now you know a little about the history of Pi and a cool trick, it’s time to get serious before you learn how to party for Pi!

 

What do we use Pi for?

Pi_-_circle_diameter_radius

 

For any circle, circumference ÷ diameter = 3.141592....... (π)

You can’t work out an exact value of π (remember it has over a trillion digits and counting!), so approximations are used. These include 3.14, 3.142 and 22/7.

All scientific calculators have a π button. You can use this to make your calculations more accurate.

If no calculator is available, or an approximate answer to a calculation involving π is required, then round π to 3 (or whatever is suggested).

Circumference

Circumference is the length of the edge all the way around a circle.

We know that circumference ÷ diameter = π

Therefore, circumference = π × diameter.

This can be shown in the following formula:

C = π d

The diameter is twice the length of the radius. This formula can be written as:

C = 2 π r

So if, a circle has a diameter of 10cm. Find the length of its circumference. (Use π = 3.14)

Circle_10cm_5cm

Using C =πd
C = 3.14 × 10
C = 31.4 cm

Using C = 2 πr
C = 2 × 3.14 × 5
C = 31.4cm

Area

Area is the space inside a circle.

This is the formula for the area of a circle:

A = π

πr2 means π × r × r.

Be careful with this as only the 'r' is squared, not Pi.

Example 1

Find the area of a circle of radius 6cm

r = 6cm, so we calculate A = 3.14 × 6 × 6 = 113.04cm2

Example 2

Find the area a circle of diameter 10cm

The diameter is 10cm, so the radius is 5cm. We calculate A = 3.14 × 5 × 5 = 78.5cm2

When calculating the area of a circle, remember to use the radius, not the diameter.

 


pieA Pi Party?! balloons  When?!! popper


Pi Day is celebrated on March 14th. (3/14! à 3.14!)

einstein

 

 

This is also Albert Einstein’s birthday (1879)!



You may have missed National Pi Day this year, however you can celebrate Pi on the 22nd of July as well! 22/7!

 

Some Top Tips for Pi celebrations

  1. Eat Pi foods!

 

There are lots of ways to do this. Obviously you should start with pies! Meat pies, vegetable pies, fruit pies, lemon meringue pies, key lime pies!

 

You can also drink and eat food that has the word ‘pi’ within it: pizza, pineapple, pine nuts…

 

 

  1. Create a Pi Party atmosphere!

 

Wear a Pi T-shirt, Pi jewellery, use a Pi mug…

 

Change your computer wallpaper to something Pi related!

 

Play music that reminds you of Pi e.g. American Pie. You can also listen to Kate Bush. She performed a song called ‘π’ on her 2005 album, Aerial, in which she sings Pi to its 137th decimal place (well, excluding the 79th to the 100th decimal digits! No one knows why!)

 

Make Pi decorations – balloons with ‘π’ on them and digits from Pi!

 

 

  1. Play Pi games!

 

Get a piñata! Have a pie eating contest, answer Maths questions, design Pi posters, find the most creative way to write Pi or contests to see who can recite the most digits of Pi (see above for this cool party trick!)

 

  1. Go for a Pi mile run (or walk)!

 

You can do this with family and/or friends and even raise money for charity.

 

  1. Keep celebrating Pi every year – on March 14th and 22/7 if you are very dedicated!

Last modified on Tuesday, 19 March 2013 09:14
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