I guess I've discovered a new pi! Need help with confirmation.

[Fauxen]

Hello Everyone!
I was testing pi by taking circumference of circular objects using a thread, measuring diameter, and taking ratio. BUT, according to my intense reasearch, the pi i always get is: 13.6/4.3 aka 136/43. Doing pi*d with my formula always gives a right circumference which is 1 or 2 milimetre better than the normal pi. "OK, this is totally strange!": i thought at first, but then an idea came into my mind: "what if pi is actually wrong???!!!!". So now my friends, i'll need your help to confirm this (by taking circumference with threads perhaps?). Because the more the reasearch, the better. AND, please don't be very skeptical. Thank you!

 

[ksdhart2]

Uh... uh... I'm just going to go with an all around no on this one. :shock: Pi, by its very nature, literally cannot be "wrong." The ratio of a circle's circumference to its diameter, $\displaystyle \pi=\dfrac{C}{d}$, is the definition of pi. Your value $\displaystyle \dfrac{136}{43} \approx 3.16279$ is an overestimate of pi, which means it will always produce a circumference that is slightly bigger than the real value. I'll be honest, I don't know why you report seeing more accuracy using your poor approximation, except probable measuring error. I'll use several different approximations of pi to calculate the circumference of a circle with diameter 10, to illustrate:

$\displaystyle C=\pi \cdot d$

$\displaystyle \pi \approx 3.14 \implies C=31.4$

$\displaystyle \pi \approx 3.145 \implies C=31.415$

$\displaystyle \pi \approx \dfrac{22}{7} \implies C=\dfrac{220}{7} \approx 31.428571428571428571428571428571$

$\displaystyle \pi \approx \dfrac{136}{43} \implies C=\dfrac{1360}{43} \approx 31.627906976744186046511627906977$

Now, finally, I'll use the most accurate version of pi I know, out to 31 decimal places:

$\displaystyle \pi \approx 3.1415926535897932384626433832795 \implies C=31.415926535897932384626433832795$

The error of each of the above approximations, using the "actual" value outlined above is:

$\displaystyle 31.4 - 31.415926535897932384626433832795 = -0.015926535897932384626433832795$

$\displaystyle 31.415 - 31.415926535897932384626433832795 = -0.000926535897932384626433832795$

$\displaystyle \dfrac{220}{7}-31.415926535897932384626433832795 = 0.01264489267349618680213759577643$

$\displaystyle \dfrac{1360}{43}-31.415926535897932384626433832795 = 0.21198044084625366188519407418174$

As you can clearly see, your estimate is the most inaccurate of any of the ones I've shown, at roughly 21% over the actual value. Thus, it is obviously not, as you claim "a few millimeters better."

 

[lookagain]

AND, please don't be very skeptical. Thank you!

This is exactly the opposite and wrong approach for us to have.

 

[Guatama]

I recall that there was a town in the American midwest during the 20th century that decided to round off pi to 3.

Heck, I thought I had proved Fermat's theorem and any number of lesser theorems (which I hadn't). A good rule of thumb is that if it has passed the scrutiny of millions of mathematicians for thousands of years, you need rigorous proofs, refereed papers published and a Ph.D. in mathematics (and humility) just to begin challenging the most common constant derived by almost every civilization.

However, remember Euclid's "parallel" lines of 300 BC. I believe it was recently (mid-1800s) proved that this axiom does not hold in curved space.

 

[Deleted member 4993]

I recall that there was a town in the American midwest during the 20th century that decided to round off pi to 3.

Heck, I thought I had proved Fermat's theorem and any number of lesser theorems (which I hadn't). A good rule of thumb is that if it has passed the scrutiny of millions of mathematicians for thousands of years, you need rigorous proofs, refereed papers published and a Ph.D. in mathematics (and humility) just to begin challenging the most common constant derived by almost every civilization.

However, remember Euclid's "parallel" lines of 300 BC. I believe it was recently (mid-1800s) proved that this axiom does not hold in curved space.

I believe you are partially correct about the parallel axis "postulates". A whole different set of geometry (hyperbolic geometry) was developed when the fourth postulate (or is it fifth) was not included.

That is quite different from "not holding true" - it is "need not assumed to be true".

 

[Fauxen]

Ok, i understand.

Thanks everyone for clearing up my confusion. I guess my curiousity had made me go way to high.

 

[mmm4444bot]

I recall that there was a town in the American midwest during the 20th century that decided to round off pi to 3.

Some leaders are still trying to pass such a law, as recently as 2010!

 

[mmm4444bot]

You gotta be joking!

It seems like you quoted the wrong part of the OP, Denis. It's not a joke to test the value of pi, by using a thread. I think it's a good way for students to visualize that you need a little more than three diameters to go all the way around a circle. You probably meant to quote the false conclusion that followed. :cool:

 

[Deleted member 4993]

Never talk to pi. He’ll go on forever.