Is Pi = 3.1415 or 3.33 ?

[alexander]

just something i saw on the news a while back, i think that the closest approximation of pi was done by some japanese scientists who calculated pi to the nearest forty billionth place... now here's a situation where 10000 digit make the other number still seem a bit superfluous...

[Guadalupe]

How about dividing the circumference of a circle with it's radius?

 

Hi! Tormod :lol:

 

My math is a little rusty but here goes nothing. I put this equation together, hoping, that it may help, in answering your question.

 

Example: The circumference of a circle is 10 centimeters. What is the radius?

 

Solution using Pi = 3.1415.

 

r = (C ÷ Pi) ÷ 2 r

C = 10 cm ÷ 3.1415

d = 3.18 cm ÷ 2 r

r = 1.59 cm

 

Checking my work.

 

(r x 2) Pi = C

3.18 x 3.1415 = C

9.9899 cm = C

9.98 cm = C

 

:hihi: Close :lol:

 

 

Solution using Pi = 3.3333

 

r = (C ÷ Pi) ÷ 2 r

C = 10 cm ÷ 3.3333

d = 3.00 cm ÷ 2 r

r = 1.50 cm

 

Checking my work.

 

(r x 2) Pi = C

3 x 3.3333 = C

9.9999 cm = C

9.99 cm = C

 

:) Closer :P

 

 

Is this right? Or does it really matter?

 

:)

[Tormod]

radius r = (circumference c / 2)

 

C = Pi ^ diameter d

 

10 = 3.1415 ^ d

 

10 / 3.1415 = d

 

d = 3,183

 

r = 1,5915

[Tormod]

And the reverse:

 

C = 2 x Pi x r

 

r = 1,5915

d = r x 2 = 3,183

c = 3,183 x 3,1415 = 9,99935

 

The accuracy will depend on the amount of digits you choose to use for Pi.

 

 

Using 3,3333 gives you a larger error:

 

c = 3,183 x 3,333 = 10,6089

[Guadalupe]

Hi! Tormod

 

I went over my math and I found no error.

 

This is my original answer:

 

C = 3 x 3,333 = 9.99 :naughty:

 

From where are you getting this answer?

 

c = 3,183 x 3,333 = 10,6089 :doh:

 

 

:confused:

[Tormod]

From where are you getting this answer?

 

c = 3,183 x 3,333 = 10,6089 :confused:

 

My calculator?

[C1ay]

Solution using Pi = 3.3333

 

r = (C ÷ Pi) ÷ 2 r

C = 10 cm ÷ 3.3333

d = 3.00 cm ÷ 2 r

r = 1.50 cm

 

Checking my work.

 

(r x 2) Pi = C

3 x 3.3333 = C

9.9999 cm = C

9.99 cm = C

 

Is this right? Or does it really matter?

 

No, it's wrong and yes, it matters. Just because you can divide the circumference of a circle by some arbitrary value does not mean the result is the circle's radius and working the problem backwards does not prove it equals the radius.

[Bo]

i propose you put pi=1 and get 100% accuracy, no matter what

(or in other words, as clay said: you should only do things that make sense)

(however it might be fun to do nonsense)

 

Define infinity=0

1/inf=0=inf=1/0

 

Woohoo consistency!

a=a+0=a+inf=inf (if a is finite)

so if 0 is infinite, all numbers are infinite (this makes sense of course)

 

however it is nonsense :confused:

 

Bo

[CraigD]

Here’s a Math riddle (not a hard or deep one, just some trick linguistic abuse, and an implied misconception about rational and real numbers, and an outright false statement) involving the geometric definition of Pi:

 

Suppose we define Pi, as usual, as the ratio of circumference to diameter of a circle (Pi = c/d = c/(2*r)). Rather than scribing circles with a compass on a plane, however, let’s do it on a sphere, using a string rather than a divider-type compass. Then:

 

Piplane > Pisphere >= 0

 

When the radius ® of the scribed circle is small relative to the circumference of the globe (G), Pisphere approaches Piplane. As the radius approaches G/2, Pisphere approaches 0.

 

Clearly, for some R, Pisphere is 1, giving a circle of circumference R. However, a circular cross-section of the sphere corresponding to every point of the circle has circumference Piplane*2*R2, where R2 is the radius of the cross section.

 

How can circumference R, clearly a rational number, = Piplane*2*R2, clearly a transcendental real number?

[Agen]

If anyone is interested in accuracy, here you go :confused:

 

http://3.141592653589793238462643383279502884197169399375105820974944592.com/

[cnfsdnlostinside]

i'm sorry, I must now ask a silly question- how, when and from what exactly was Pi (3.14159...)derived? I understand that Pi= c/d=c/2r... what is the practical application of the circumfrance of a sphere divided by the diameter?

 

 

 

(for some reason, I feel a horribly simple reply coming on...oh well. my excuse is that it's early)

[Rincewind]

22/7 :confused:

A better easy to remember ratio for rough calculation is 355/113 (just remember 113355):

[font=Courier New]Pi      = 3.14159265...
22/7    = 3.14285714... <-- accurate to 2 decimal places
355/113 = 3.14159292... <-- accurate to 6 decimal places[/font]

[Bo]

i'm sorry, I must now ask a silly question- how, when and from what exactly was Pi (3.14159...)derived? I understand that Pi= c/d=c/2r... what is the practical application of the circumfrance of a sphere divided by the diameter?

 

as said before: these immensely accurate values for pi are calculated from mathematical sequences http://mathworld.wolfram.com/PiFormulas.html gives a list.

 

the practcial applications are HUGE. realy realy huge.

The most simple thing is: a radius (1 dimensional thing) is easy to measure, an area or a volume ared difficult. pi let's you relate one to the other.

 

Bo

[Turtle]

A better easy to remember ratio for rough calculation is 355/113 (just remember 113355):

[font=Courier New]Pi      = 3.14159265...
22/7    = 3.14285714... <-- accurate to 2 decimal places
355/113 = 3.14159292... <-- accurate to 6 decimal places[/font]

 

___Here's a twister for you; rewrite 22/7 in base twelve notation & do the division longhand. You end up with a repeating decimal!

:evil:

[Guadalupe]

I like to thank you all for showing an interest in this post. Again, thank you. :Glasses:

 

:naughty:

[Kriminal99]

Whats the point of calculating that many decimal places of Pi lol... Theres no such thing as a perfect circle, ie a circle where you have a mathematical point, then an infinitely small change and angle, another mathematical point and so on. Any thing we see that looks like a circle is going to have a point of precision past which its not going to look like a circle any more and so using values of pi more precise than that is pointless anyways.

[CraigD]

Whats the point of calculating that many decimal places of Pi lol...

Like much Math, what a particular rational approximation of Pi is is usually less interesting that how one approximates it. The real achievement in these very precise approximations is not how many decimal places are calculated, but how little arithmetic processing is required for a given number of decimal places.

 

Approaches to approximation of Pi provide algorithms and insights into generating all sorts of useful sequences. They also raise some profound information theory questions.