- #1

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## Main Question or Discussion Point

http://www.teacherschoice.com.au/maths_library/area and sa/area_2.htm

"NOTE: The value of p can never be known exactly, so surface areas of spheres cannot be calculated exactly."

p = pi here.

It always irks when people say "(insert irrational constant here) doesn't have an exact value" or even "we don't know pi's exact value."

I don't understand. I can't express it completely as a decimal, so what?

I know the exact value of pi through many other ways. Series, the square root of gamma function evaluated at 1/2, and at the risk of being yelled at for circular reasoning, the ratio of a perfect circle's circumference to diameter, are all pi. I can only approximate it in decimal form, but saying that means "we don't know it's exact value" or even worse that it "has no exact value" makes no more sense than saying I don't know exactly what my dog looks like because I can't draw an exact picture of him on an etchasketch.

A simpler way to show the exact value of pi is as follows:

[itex]\pi[/itex]

I mean, I just don't understand this. It's a number, it has a place on the number line, it is clearly defined.

e is exactly 1/1! + 1/2! + 1/3! ..... so yes, I do know it's exact value. It is a clearly defined number!

"NOTE: The value of p can never be known exactly, so surface areas of spheres cannot be calculated exactly."

p = pi here.

It always irks when people say "(insert irrational constant here) doesn't have an exact value" or even "we don't know pi's exact value."

I don't understand. I can't express it completely as a decimal, so what?

I know the exact value of pi through many other ways. Series, the square root of gamma function evaluated at 1/2, and at the risk of being yelled at for circular reasoning, the ratio of a perfect circle's circumference to diameter, are all pi. I can only approximate it in decimal form, but saying that means "we don't know it's exact value" or even worse that it "has no exact value" makes no more sense than saying I don't know exactly what my dog looks like because I can't draw an exact picture of him on an etchasketch.

A simpler way to show the exact value of pi is as follows:

[itex]\pi[/itex]

I mean, I just don't understand this. It's a number, it has a place on the number line, it is clearly defined.

e is exactly 1/1! + 1/2! + 1/3! ..... so yes, I do know it's exact value. It is a clearly defined number!