By Maggie Koerth-Baker at 12:59 pm Thu, Jan 17, 2013
Pi is much more simple than that.
Pi is exactly 4*sum(-1^n/(2n+1)), for all n >= 0.
Ahhh, yes. Of course.
Maybe it’s nicer to say:
pi = 4 * (1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11 …)
pi = ln(-1) / i
Much easier to work out in your head ;)
I just imagine a circle.
One symbol. Simple!
No, no, you need to imagine a diameter too!
*Sigh* Hoosiers are never going to live that one down.
Until I read the article I figured it was another bill this session by Senator Kruse. it really would not surprise me at this point.
It’s not as if the Indiana state legislature didn’t do due diligence before attempting to define the value of pi. The House sent the bill first to the Committee on Swamp Lands. When they approved it, the Senate referred it to the Committee on Temperance, who also said it seemed OK to them. That’s more consideration and expert attention than many bills get.
PI IS EXACTLY 3
Sorry I had to do that but I need to get your attention.
So, you’re the one to blame for this downward spiral?
Oh, very good!
just for giggles i made an a spreadsheet that does 60k iterations of that formula. At 60,000 the number for pi is 3.141609321. so to even get the first 10 or so digits correct, it’s gonna take ~1 million iterations I would guess? Sure wouldn’t want to do that by hand :)
Limited precision arithmetic can make a series converge to a wrong value. I once wrote a program that failed similarly, and I eventually figured out that, beyond a certain n, some critical operand was rounding down to 0 in the middle of the iteration.
Spreadsheets aren’t good for accurate floating point calculations. http://blogs.office.com/b/microsoft-excel/archive/2008/04/10/understanding-floating-point-precision-aka-why-does-excel-give-me-seemingly-wrong-answers.aspx
Yeah, the additive formula converges very slowly, and perhaps wrongly if you use limited precision, as KWillets points out.
The product formula converges much faster.
Le sigh, “You’re doing it wrong” is the story of my life :)
Worry not – at least you’re doing! Some people don’t even bother trying…
Sure wouldn’t want to do that by hand
If you ever do get the urge for “hands-on pi,” here’s a kinda neat method to hone in on pi’s value (no circles or tricky math required):
You need a bunch of toothpicks, and a wood floor whose slats are as wide as the toothpicks are long. Hold a toothpick at chest level, then drop it onto the floor. Once the toothpick is at rest, record whether or not it crosses a gap between floorboards. Repeat…. The ratio of non-crossings to crossings will approximate pi.
I don’t have enough math to know if this is trolling or just a really cool practical method. But since it’s math, it might be both. Or neither. Or both neither and both. Damn I wish I had more math…
Cut a circle out of paper and weigh it.
Can’t we just say that it’s the ratio of circumference to the diameter of a circle? Humanity…. always trying to put square pegs in 2πR holes…..
Pish. We’ve known all about inconstancy for years. My Granny had inconstancy, so she bought granny diapers.
My Granny had inconstancy as well, which led to my mother having seven or eight stepfathers.
The Bible one is interesting. I wonder how fundamentalists handle that one?
Same as everything else: by applying the bible selectively.
Hey, biblical sig figs. Chill.
Actually there is a semi-logical explanation.
The bit of the Bible in question is in the first book of Kings and describes a vessel in the Temple of Solomon…
He made the [vessel] of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.
If you do the maths on that, Pi equals 3. Derp.
The explanation put forward by people who can’t countenance the idea that the holy-sacred-literal-unalterable-word-of-almighty-god could contain a rough estimate (which is, frankly the most likely explanation) is that the vessel was irregular in shape and flared out a bit at the top. That way the maths works out fine.
Or just that the vessel had non-zero thickness, and “rim to rim” was measuring the vessel’s capacity, and “measure around it” was giving the outer dimension.[edit: this was posted below, and yeah, me wrong.]
Cubits are normally measured with your arm. They may have measured the 30 cubits around using a line, at whatever level of precision they got, but the “10 cubits from rim to rim” is highly unlikely to have been precise enough to distinguish it from 9.5 cubits.
Considering cubits were based on the ruler’s arm length (change of ruler, change of length), surely a short consideration of the unit in question pretty much implies it’s an approximation?
I wonder if there’s a web site somewhere that tells you what various constants’ values are in different numbering systems…
/Yes, I’m pretty sure there is at least fifty of ’em.
For the longest time I’ve seriously wanted Patricia Luisa Vasquez’ “spacetime multi-meter” for taking local readings of values like pi, /h, gravitational constant, c, ratio of proton mass to electron mass, etc. ‘Cuz, ya know, how do you really know they’re constants unless you keep an eye on ’em?
(Holy crap! It’s been 27 years since Eon was published. Old man!)
I heard someone explain the pi=3 bible thing as when you measure across you are taking an interior measurement but when you measure around you are taking an external measurement so the thickness of the vessel makes the bible description possible to be correct without making pi=3
It never occurs to them the Bible isn’t an engineering document.
Except that 30 cubits (implying pi=3) is less than the 31.415… cubits it should be. Measuring the circumference around the external measurement when the diameter is measured internally would give you a ratio even bigger than pi, not less.
Maybe I got the details reversed, but I think I found the explanation:
In First Kings, Hiram made a big bowl. How big was it? Ten cubits across. Thirty cubits around. Pretty big for a bowl. That was the point.
I can’t even claim this is a cheap shot. There are Christians who would argue that pi must be 30 / 10 because the Bible says so. As someone who takes the Bible seriously, I get really embarrassed when (a few of) my co-religionists try to tease out God’s hidden scientific truths in the Scripture.
If someone posted here saying something so clearly wrong, that because the bible says so, pi must be equal to 3, then by Poe’s law it would be impossible to tell whether they meant it anyway.
I prefer to give all such statements the benefit of the doubt and assume they are jokes.
The US certainly does have the most comedic political and criminal justice systems in the world. It must be so much fun to live there!
Indian tried that in 1897; 115 years ago and it never passed. And please cite where the Bible says Pi is 3. I can’t find anything to support that. A lot of misinformation just being flung around here.
Try reading the rest of the thread. Like the comment directly above yours.
Kings 7:23 (as stated in the article everyone is commenting about)
It’s about significant digits.
A result of circumference 30 and diameter 10 is consistent with pi when you consider that they are just rounding to the nearest unit. Did their number system even have a way of representing complicated fractions?
For example 9.65 cubits and 30.32 cubits might be the actual measurements that agree with a true value of pi but rounded off they would give 10 and 30.
Do we suppose that anyone seeing this structure had a cubit tape measure accurate to 100ths? More likely they made a quick measure so they could describe the size of it.
It isn’t as if the writer of that passage is making a huge error. The error is not recognizing how the writer was using numbers.
I agree entirely. Its not as if this book is meant to be the word of God.
From the size of the thing, I think they were really going for “It was Huge” rather than “here are it’s exact measurements and a description of the exact casting processes so you can make one at home”
Apparently the story about Indiana trying to define pi as 3 is not accurate either.
Aside from the fact that voting to reject a bill is rather different from “trying to” do something, the rejected bill was to make pi equal to 3.2, not 3.
Isn’t that worse than trying to define pi as 3? If you’re rounding to the nearest whole number, then 3.1415… would be 3. If you’re rounding to the first decimal place, then 3.1415… would be 3.1.
I didn’t realize that Indiana voted on this in 1897… a tidbit not mentioned above. It doesn’t excuse the now deceased legislators that brought it forward though.
Surely the value of Pi depends on your geometry? For example, in a spherical geometry, the ratio of a circle’s diameter to its radius isn’t a constant:
Well, it is possible to take any two apparently contradictory statements in the bible and interpret each in a way that makes them consistent. It’s also possible to interpret pairs of statements in the Bible in ways that make them irreconcilably contradictory.
Neither occupation is a good use of anyone’s time. Compared to say, feeding the poor, forgiving people for offending you, and attending to your own sins and errors rather than those of others. It’s just a book after all.
Even if the various authors of the books of the Bible were divinely inspired, implausibly good at conveying what was revealed to them, and always correctly translated, the book itself says God made the whole *universe*. Next to that the Bible is a *negligible* fraction of the works of God that are there for our understanding.
Word of God. Infallible. Inerrant.
These words apparently do not mean as much to Christians who supposedly believe them as they do to atheists who don’t.
math neil deGrasse Tyson physics pi Science
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