Pi question

[Pudgygiant]

I'm reading a book that says the first 10 digits of pi (1415926535) is almost precisely equal to the circumference of the earth, to within inches. Problem is, when I calculate that out I get 268167.9 miles and change, but the exact circumference is 24,901.55 Any idea what I'm doing wrong?

 

[Fencer128]

Originally posted by: Pudgygiant
I'm reading a book that says the first 10 digits of pi (1415926535) is almost precisely equal to the circumference of the earth, to within inches. Problem is, when I calculate that out I get 268167.9 miles and change, but the exact circumference is 24,901.55 Any idea what I'm doing wrong?

What does the book that claims Pi gives you the circumference use as it's measure of the circumference? What units does it use?

Cheers,

Andy

 

[Pudgygiant]

Originally posted by: Fencer128

Originally posted by: Pudgygiant
I'm reading a book that says the first 10 digits of pi (1415926535) is almost precisely equal to the circumference of the earth, to within inches. Problem is, when I calculate that out I get 268167.9 miles and change, but the exact circumference is 24,901.55 Any idea what I'm doing wrong?

What does the book that claims Pi gives you the circumference use as it's measure of the circumference? What units does it use?

Cheers,

Andy

It doesn't say any of that. It just says, simply "Next came pi, the circumference of a circle divided by its diameter, ten decimals of which give the circumference of Earth to the fraction of an inch, thirty decimals the circumference of the known universe to a precision imperceptible to any microscope..."

 

[Fencer128]

It doesn't say any of that. It just says, simply "Next came pi, the circumference of a circle divided by its diameter, ten decimals of which give the circumference of Earth to the fraction of an inch, thirty decimals the circumference of the known universe to a precision imperceptible to any microscope..."

Thanks. As a side note - is this a *spooky coincidence* type text? Could you post the title and author? It's just I don't believe it, and secondly if there is a coinicdence - it's just that, as our units of length are all arbitrary and not based on any rigorous scientific dimension (i.e. diameter of 99.9% probability of H nucleus position in a free H atom, etc.)

Cheers,

Andy

 

[Pudgygiant]

The Seven Mysteries of Life
Guy Murchie

It's actually a really interesting book (albeit nerdy), and very well informed. This is the first mistake I've found and I'm 3/4 of the way through it.

 

[Fencer128]

Originally posted by: Pudgygiant
The Seven Mysteries of Life
Guy Murchie

It's actually a really interesting book (albeit nerdy), and very well informed. This is the first mistake I've found and I'm 3/4 of the way through it.

Yep. I think the author is maybe misinformed (they didn't check this for themselves?)

Cheers,

Andy

 

[kevinthenerd]

It's based on magnitude. Just take the factor error (0.0000000001) and multiply it by the magnitude and you'll get the error.

Example:

What about the orbit of the earth? Let's assume it's round. (It's certainly not.)


93,000,000 miles
2 * 93,000,000 * .0000000001 = .0186 miles error (10 digits of pi)
2 * 9.3*10^6 * 10^-30 = 18.6 * 10^-24 = 1.86 * 10^-23

quite a small error. The first one yields .0186 miles, approximately equal to 98 feet. The second one yields 0.000000000000000001178496 inches.

I memorized pi out to 3.14159265358979323846264338327904288 (may be off in the end), and I did it for the math, not the practicality. It fascinates me.

 

[Smilin]

It all comes down to the unit of measure. If you check the circumfrence in ST's it works out fine.





(SmilinToes for those of you that didn't know)

 

[Jeff7]

Originally posted by: Pudgygiant

Originally posted by: Fencer128

Originally posted by: Pudgygiant
I'm reading a book that says the first 10 digits of pi (1415926535) is almost precisely equal to the circumference of the earth, to within inches. Problem is, when I calculate that out I get 268167.9 miles and change, but the exact circumference is 24,901.55 Any idea what I'm doing wrong?

What does the book that claims Pi gives you the circumference use as it's measure of the circumference? What units does it use?

Cheers,

Andy

It doesn't say any of that. It just says, simply "Next came pi, the circumference of a circle divided by its diameter, ten decimals of which give the circumference of Earth to the fraction of an inch, thirty decimals the circumference of the known universe to a precision imperceptible to any microscope..."

Circumference of the known Universe? When did he get an advanced degree in astrophysics and determine what the exact size of the known Universe even is?

 

[Shalmanese]

Uh, its not talknig about the actual, physical earth in inches or whatever, its an indication of the accuracy. Which means that if you got a hypothetical sphere the exact same size as the earth and had a diameter of 1 earth unit, it would have a circumference of 3.141592654 + or - 0.0000000001 earth units or about an inch.

 

[kevinthenerd]

Originally posted by: Shalmanese
Uh, its not talknig about the actual, physical earth in inches or whatever, its an indication of the accuracy. Which means that if you got a hypothetical sphere the exact same size as the earth and had a diameter of 1 earth unit, it would have a circumference of 3.141592654 + or - 0.0000000001 earth units or about an inch.

exactly my point, but you speak common better than I do.

(I find it hard to get out of geek mode.)

 

[Fencer128]

Originally posted by: Shalmanese
Uh, its not talknig about the actual, physical earth in inches or whatever, its an indication of the accuracy. Which means that if you got a hypothetical sphere the exact same size as the earth and had a diameter of 1 earth unit, it would have a circumference of 3.141592654 + or - 0.0000000001 earth units or about an inch.

so all you're saying really is:

circumference = 2 x pi x radius = pi x diameter

diameter = 1

circumference = pi

Is that a spooky coincidence or just a fact?

I'm confused now, this seems "normal" - nothing strange here. Unless its saying the very fact that there's a mathematical relationship containing pi that relates the circumference to the radius of a circle is strange. That would be a silly arguement though IMHO.

Cheers,

Andy

 

[Shalmanese]

No, were talking about accuracy figures here.

Pi is 3.1415926536..... etc.

whereas Pi to 10 sig figs is 3.141592654000000.... etc.

What the passage was trying to say is that 3.141592654000... is accurate to within a few inches of 3.1415926536... on an earth sized scale.

 

[Fencer128]

Originally posted by: Shalmanese
No, were talking about accuracy figures here.

Pi is 3.1415926536..... etc.

whereas Pi to 10 sig figs is 3.141592654000000.... etc.

What the passage was trying to say is that 3.141592654000... is accurate to within a few inches of 3.1415926536... on an earth sized scale.

Right. I see where you're coming from now. I still don't see what is special or spooky about that though? You use a number to a precision of 9 dp and then say that if you use the number to a precision of 10dp, any formulae where you compare using both numbers only differ in their result by very small amounts.

Cheers,

Andy

 

[kevinthenerd]

Originally posted by: Fencer128
There's no point in entering a debate unless all concerned entertain the possibility they could be incorrect. Otherwise it's just bigotry.

Everybody, thing and action has positive and negative aspects, although these are seldom balanced. Failure to acknowledge both these sides indicates fanaticism.

sweet sig!

 

[Fencer128]

Originally posted by: kevinthenerd

Originally posted by: Fencer128
There's no point in entering a debate unless all concerned entertain the possibility they could be incorrect. Otherwise it's just bigotry.

Everybody, thing and action has positive and negative aspects, although these are seldom balanced. Failure to acknowledge both these sides indicates fanaticism.

sweet sig!

Cheers - I made it myself :beer:

Andy

 

[Shalmanese]

I don't know what book pudygiant is reading but an educated guess sayis its something like "The Idiots guide to Pi" or something and the context surrounding the quote would be something like "Although people have memorised Pi to over 10,000 places and computers have calculated it to several billion, in reality, no more than about 20 places are ever needed. the first 10 digits of pi (1415926535) is almost precisely equal to the circumference of the earth, to within inches. The first 20 digits is equal to the diameter of the universe to within an atom..."

 

[Smilin]

Pi*R^2

Pie are square? Fools everyone knows Pies are round!

 

[RossGr]

Since the initial definition of a meter is 1/10 million th the distance from the north pole to the equator the diameter of the earth is (4/ pi) x10e7m. In this sense Pi is built into the meter when used as a measure of the earths dimensions.

 

[Jeff7]

Originally posted by: Shalmanese
Uh, its not talknig about the actual, physical earth in inches or whatever, its an indication of the accuracy. Which means that if you got a hypothetical sphere the exact same size as the earth and had a diameter of 1 earth unit, it would have a circumference of 3.141592654 + or - 0.0000000001 earth units or about an inch.

Just to be annoying now - which circumference of Earth? Around the poles or equator? It's bigger around the equator than the poles.

 

[Shalmanese]

Just to be equally annoying, I am referring to a hypothetical sphere so it wouldnt matter .

 

[dmw16]

Well....the fact of the matter is, the earth is not a sphere. It is "fatter" at its center do to its spin and some other factors. Also, any correlation between Pi and a circumfrence of the earth is totally coincidence....Pi isnt spooky...its just Pi.
-doug

 

[Shalmanese]

Yes, I know the earth is not a sphere. But I am referring to a HYPOTHETICAL sphere the same size as the earth. The fact that its Pi is not a co-incidence, its definitional.

 

[RossGr]

Guess the question would be.... How many digits of PI are needed to show that the earth is NOT a shpere?

 

[ET2nuke]

Originally posted by: dmw16
Well....the fact of the matter is, the earth is not a sphere. It is "fatter" at its center do to its spin and some other factors. Also, any correlation between Pi and a circumfrence of the earth is totally coincidence....Pi isnt spooky...its just Pi.
-doug

Read that good explanation again- I think you missed the meat of it this time around. Took me a couple tries, too.