PI

[cabernet]

Why is PI approximately 3.14 and not 3 or 4 or any whole number. Most of the universe is made up of objects based on spheres with PI=3.14. If PI was say 3 that would surely take geometry into another dimension ??.

[mollykins]

because pi is always equal to the circumference of a circle divided by its diameter which always turns out as 3.14 . . .

[mollykins]

It's been calculated to thousands, possibly millions of decimal places, it's an irrational number, one which keeps on going and going, but can often be easily expressed as a fraction.

[mollykins]

such as 22/7 (I think)

[The Builder]

Cabers ................. I guess it's simply because we figure it in base 10 (decimal) ...... in a different system it might well be whole ..................

[cabernet]

I understand what Pi is, it just seems weird that nature has adopted such an irrational number and not a whole number for such a simple divine shape. I am thinking on almost a spiritual level.

[Prudie]

Pi is not a man made number though. The circumference of every circle, whatever its size, divided by its diameter is always the same namely about 3.141.......ad infinitum. We have adopted Pi to represent this figure (which is in itself an infinite number) using our number system based on 10. In other words Pi is a naturally occurring ratio, bit like the golden section.

[woofgang]

Is it the same as fractals?

[gingejbee]

Pi isn't a number as such - it's a ratio of two variables (circumference and diameter of the same circle) which always computes to 3.14159 etc.

[The Builder]

I understand what you're saying about a spiritual level Cabers ................. perhaps it's just that, as humans, we regard Spritiuality in a rather sentimental way ......... numbers have no sentiment. 3.14 etc is just as valid as anything else in The Land of Numbers :o)

[Woody23]

Is the golden section near the g spot - just off the M6?

[Prudie]

Well good evening woody, I await more of your wisdom with bated breath....

[bibblebub]

don't forget e

[Woody23]

But surely - pi is just a concept ?

[factor-fiction]

Although л cannot be expressed as an exact number you can still have an item of length л and you can draw a line of that length. For example a circle of diameter 1 cm will have a circumference of л cm.

Similarly a number such a the square root of 2 cannot be expressed as fraction - it is 1.41421356237309504880 to 20 decimal places but the digits go on for ever. But you can construct a line that is that length- you need an isosceles right angled triangle with two sides of 1cm length. The longer side, the hypotenuse, will have a length equal to square root of 2.

Or divide a line exactly 1 metre long into 7 equal parts. Each part will be 1/7 of a metre long, or 14.2857142857142857142857.....cm.

There are other numbers that crop up in maths that seem unusual such as e (approx 2.718), the base of natural logarithms, but they are important.

These numbers seem unusual because in life we usually deal in whole numbers or at least rounded ones. How tall are you, I ask. You say 188 cm. Well using a more precise measuring device I might say your height is 188.2346cm to 4 decimal places, although your exact height may have an infinite number of decimal places.


These numbers only seem unusual because of the number system we use. If we had chosen to use Pi as representing unity then it is our numbers 1,2,3,4 etc that would seem odd.

Finally: mollykins- you make some good points, although I'd like to point out that 22/7 is only an approximation of л (Pi). Pi cannot be expressed as a fraction.

[Hopkirk]

Why would nature arrange things to keep numbers simple, on a man made numbering system?

[mibn2cweus]

So why is the hypotenuse of sides 3 & 4 eggsactly 5?

[wildwood]

or why is 10 : 3 = 3.3333333333333333333333333333333333333333333
333333333333333333333333333333333333333333333
333333333333333333333333333333333333333333333
333333333333333333333333333333333333333333333
333333333333333333333333333333333333333333333
333333333333333333333333333333333333333333333
333333333333333333333333333333333333333333333
33333333333333333333333333333333333etc.

[beso]

So why is the hypotenuse of sides 3 & 4 eggsactly 5?

x^2 + y^2 = z^2
Pythagoras's Theorem. No circles involved.

[chakka35]

mibs, I'm not sure which cheek you have your tongue in when you ask that. You're up to some mischief, methinks.

[naomi24]

^^Ha ha! So what's new? ;o)