Finding the area of a circle

In order to find the area of a circle we need to use the equation area equals pi r squared. We can either estimate the area of a circle by putting a numeric value to pi or use pi as an infinite value that will find the area of a circle. Either way we are not finding an exact numeric value to the area of a circle.. if the area of a circle is finite. There is an exact area within a circle. But we yet to have an equation that can give you an exact numeric value to the area of a circle.

Am I correct in my analysis?

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ArishMell · 70-79, M

You are correct in strictly mathematical terms, because pi is irrational.

However, if we take pi to enough decimal places for the task in hand, the error becomes insignificant.

It cannot be taken as an infinite value for real purposes, of course, beyond that implied in the simple algebra describing the relationship between Radius and the Circumference and Area, of any Circle or circle-based figure, including Solids of Revolution found by [Pi times the integrated area].

Pi is also used in Harmonics (e.g. acoustics and electricity), but again taken to a finite limit for practical work - albeit that such value may be the physical limit of the processor in a calculator or computer.

JoyfulSilence · 51-55, M

In some cases, yes, since pi is irrational, hence cannot be represented as a terminating (or even infinite-repeating) decimal.

If r is rational, then the area A is irrational, because if A were rational then pi = A/r^2 would also be rational.

If r is irrational, most likely A will be irrational, too.

However, it is possible for r to be irrational, yet A is rational. For example, let r = sqrt(1/pi). Then A = 1. This value of r is irrational since if it were rational, then pi = 1/r^2 would also be rational.

lpthehermit · 56-60, M

my prediction was right back in junior high school...i would NEVER have a use for pi or algebra. six long wasted years

ArishMell · 70-79, M

@lpthehermit Oh the irony of your post! Oh the blissful ignorance that your "prediction was right" clause shows a self-fulfilling prophecy or wish whose result you failed to predict, perhaps because you made it far too early in your education.

It is just as well plenty of people do use pi and a great deal of mathematics generally, for which algebra is the language in the way numbers are for arithmetic.

For without them, you would not be able to denigrate it like that here, hence the irony:

- No electricity for a start.

- None of what else we take for granted nowadays in our well-off parts of the world: proper water and sewerage services, decent homes, telecommunications by wire and wireless, mechanised transport by land, sea and air, high-grade medicine and medical services, etc.

- No natural sciences aiming to understand both our own planet and life on it, and the Cosmos.

- No luxuries like modern entertainments and possessions.

Without Mathematics our standard of life would be stuck back at perhaps 15C level, if that.

Mathematics has given you the ability to tell the world you have no idea what Maths is for, only you think it useless.

I have no natural ability for Mathematics so it was one of my weakest subjects at school - the other was learning French. Consequently I lost my early dream of a career in either Science or Engineering, as both are highly mathematical. I could manage only semi-skilled "shop-floor" and laboratory-assistant work, in both areas.

However, I find pi calculations, and very basic Algebra, reasonably easy; along with basic Geometry, Trigonometry and some other topics, all in the normal school Maths syllabus. I have used these many times over my life since, both at work and in my hobbies. About the only area I have not used after leaving school, was Calculus - which did baffle me but which I know is very important in Science and Engineering.

As for French... I have never needed it professionally, but at least had the courtesy to try my fractured attempts at the language during a dozen or so subsequent holidays in France!

You though... Those six years (hang on, that's counting - numbers - arithmetic - isn't that useless too?) ... Those six years were "wasted" only by you, and only to your own loss.

You did not predict anything. Instead you failed to predict your self-imposed limits.

idontcareok · 70-79, M

there is this thing called google, I;m very sure you can get an answer there

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