Newpaper reports on Pi Day 3.14

[ramsey2879]

"Most people with a basic understanding of math probably knew that Thursday was 3.14 and therefore Pi Day, because that is the number of the ratio between a circle's circumference and its diameter."
"But the actual number is much longer -- in fact, the decimals go on for at least 10 trillion digits. Math geeks had to give up counting, and computers are still trying to find the figure."

Never mind that the number Pi is infinite in length, i.e. the decimal Pi is never ending; and thus, computers will never "find" the length of Pi.

Found in "Pupils acquire a taste for pi," about a group of fifth graders who measured the diameter and circumference of various circular objects and computed the ratio. The Freelance Star, Fredericksburg, Va. Could it be that the education system deems that 5th grade is too early to explain that the actual number Pi is infinite in length? Or are fifth graders more knowledgeable about math than the reporter?

 

[micromass]

But numbers like ##1## and ##1/3## are also infinite in length...

 

[Bachelier]

But numbers like ##1## and ##1/3## are also infinite in length...

Hence computers will never find the lengths of ##1## and ##1/3##.

##QED##​

 

[HallsofIvy]

But my ruler gives about 4 mm as the length of 1!:tongue:

I strongly suspect that the fifth graders knew a lot more about pi than this reporter!

 

[ramsey2879]

But numbers like ##1## and ##1/3## are also infinite in length...

Technically speaking, the length of a decimal number does not include an ending infinite string of zeros because the portion of those zeros after the decimal point can be dropped without changing the value of the number. Thus the length of 1 or 1/10 is 1 and the length of 1/80 or 1/10000 is 4. Any integer has a finite length equal to the highest power of 10 less than or equal to the number plus 1. Any fraction, reduced to its lowest form, where the denominator is a product of the numbers 2 to the ith power and 5 to the jth power [tex] i,j \in N[/tex] has the length after the decimal point equal to i if i > j-1 or j if j>i-1.

 

[micromass]

Technically speaking, the length of a decimal number does not include an ending infinite string of zeros because the portion of those zeros after the decimal point can be dropped without changing the value of the number. Thus the length of 1 or 1/10 is 1 and the length of 1/80 or 1/10000 is 4. Any integer has a finite length equal to the highest power of 10 less than or equal to the number plus 1. Any fraction, reduced to its lowest form, where the denominator is a product of the numbers 2 to the ith power and 5 to the jth power [tex] i,j \in N[/tex] has the length after the decimal point equal to i if i > j-1 or j if j>i-1.

Ah! But then the length is ill-defined! Because ##1=0.999999...##, it appears that ##1## has both finite and infinite length! :tongue2:

 

[Bacle2]

Hence computers will never find the lengths of ##1## and ##1/3##.

##QED##​

But I think there is an important difference: 1/3 can be described in a finite way; every

decimal place is 3 , but, AFAIK, there is no finite description of π.

 

[Bacle2]

Still, by the same token, shouldn't today, 3/16 be "square root of 10 day", and

February 23 , 2/23 be "square root of five day"?

 

[Number Nine]

But I think there is an important difference: 1/3 can be described in a finite way; every

decimal place is 3 , but, AFAIK, there is no finite description of π.

Yes there is: [itex]\pi[/itex].
This is just as valid a representation as 1/3. What you mean is that [itex]\pi[/itex] has no finite decimal expansion, but a decimal expansion is just one way of representing a number. It's not the number itself.

 

[Bacle2]

Yes there is: [itex]\pi[/itex].
This is just as valid a representation as 1/3. What you mean is that [itex]\pi[/itex] has no finite decimal expansion, but a decimal expansion is just one way of representing a number. It's not the number itself.

Right, I should have said that the decimal representation of π does not have, AFAIK
a finite description, i.e., if I wanted to know the digit in any place on the expansion
of π , there is none (AFAIK) rule for determining it. The decimal expansion of 1/3 is infinite,
but it can be fully described by the statement that every term is equal to 3.

 

[ramsey2879]

Ah! But then the length is ill-defined! Because ##1=0.999999...##, it appears that ##1## has both finite and infinite length! :tongue2:

Every integer but zero can be expressed as an infinite number, but the length of an integer is technically speaking "the highest power of 10 less or equal to the absolute value of the integer", plus 1.

 

[Bachelier]

The biggest misconception about ##\pi## is that ##\pi = \frac{22}{7}##. Maybe the originator of this idea intended it to be an approximation (a very bad one, one may add) but Internet forums are infested with this response.

 

[ramsey2879]

The biggest misconception about ##\pi## is that ##\pi = \frac{22}{7}##. Maybe the originator of this idea intended it to be an approximation (a very bad one, one may add) but Internet forums are infested with this response.

There was a court case in the US Patent and Trademark Office where the Judges disregarded the argument of an attorney and ruled that the court would use the "more precise value of 22/7" in its calculations.

 

[Bachelier]

There was a court case in the US Patent and Trademark Office where the Judges disregarded the argument of an attorney and ruled that the court would use the "more precise value of 22/7" in its calculations.

Sometimes I know not whether to believe that the Courts are here to promote the rights of the people or to demise them. For Mathematicians, this so called case shall ergo be equivalent to the "Dred Scott v. Sandford" case.

 

[HallsofIvy]

There was a court case in the US Patent and Trademark Office where the Judges disregarded the argument of an attorney and ruled that the court would use the "more precise value of 22/7" in its calculations.

I see nothing wrong with this. They are simply saying that, instead of the more common "3.14", the court, for this particular case, will use the "more precise value of 22/7" which, to three decimal places, is 3.143, slightly more accurate.

The words "more precise" themselves indicate that this is not intended to be an exact value but only a slightly better approximation.