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My Pi Challenge

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Blayz

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I had pi memorized to 200 decimal places once. Let's see how I go:

What I remember:
3.14159265358979323648905288

Reality:
3.141592653589793238462643383279502884197169

Pairwise alignment:
3.141592653589793238462643383279502884197169
3.14159265358979323---264--8---905288


So about 75%. of 10% Not too shabby after 25 years, or really shabby de-pending on your view point.
 
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AV1611VET

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Resha Caner

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You have a wash basin with the following dimensions:

  1. It's circumference is 30.000 feet.
  2. It's diameter is 10.000 feet.
What is Pi?

Is this an indirect reference to 1 Kings 7:23? If it is, I will say that this verse has generated some of the most ridiculous conversations I've ever heard by people with a very poor understanding of mathematics (both those for and against the Bible).

Something in your quote is improperly (or misleadingly) defined, AV. If you are implying a circle, the 2 numbers cannot be correct. If the wash basin is not a perfect circle, then you should not use the term "diameter."

And yet there is no error in the 1 Kings passage. Pi is an irrational number. Therefore, no matter how many digits you provide, it is an approximation. The only "exact" way to express pi is with the mathematical symbol (the Greek letter, pi). It always freaks people out that things like pi, e, i are actually numbers ... but yes, they are actually numbers. Using other representations (such as 3.14 for pi) is only an approximation of those numbers.

So, the question then become, what is the proper way to approximate pi? You need to specify the number of significant digits and then round. Given that pi approximates as 3.14159265...., it is perfectly acceptable to round it to one digit: 3. The number of significant digits is entirely context dependent, and so there is no problem with 1 Kings approximating pi as 3. Note that the verse never uses the modern notation (the symbol pi), nor does it claim to be exact. There is no error.

However, saying the circumference is 30.000 with a diameter of 10.000 is incorrect. It would be more proper to say the circumference is 30 and the diameter is 10 (i.e. with 1 significant digit). Or, even better, it would be 3.(10)^1 and 1.(10)^1, but the Biblical writers didn't have that type of notation.

If we're going to talk about Biblical "errors," let's try to be sure the challenge isn't so obviously erroneous itself.
 
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Resha Caner

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Tinker Grey

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Hmm. I'm with Tinker on this one. I would have said using "diameter" (major, minor, or otherwise) to describe an ellipse would be erroneous. I have a feeling that's a somewhat colloquial usage, but I could be wrong.

Yeah. QV Lion Hearted Man's post above.
 
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Resha Caner

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Yeah. QV Lion Hearted Man's post above.

Are you saying you now accept that usage? I'm still thinking it's improper. No offense, but the author of the quoted webpage gives no references, and he's a teacher at a junior college. Of course I don't know the guy, but I wouldn't think he hails from the Halls of the Keepers of Math Definitions.

If someone has a more authoritative source, I'll bow. Otherwise, I'm saying it's colloquial usage.

[edit] FWIW I checked my college math texts. In every chapter on conic sections they discuss major & minor axes ... no mention of a major/minor diameter. Further, Wolfram, which I would consider a more authoritative web source for math, makes no mention of it.

Regardless, the OP didn't say "major diameter," but just "diameter," and so remains erroneous. And the Bible verse I quoted remains without error as best I know.
 
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Lion Hearted Man

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Are you saying you now accept that usage? I'm still thinking it's improper. No offense, but the author of the quoted webpage gives no references, and he's a teacher at a junior college. Of course I don't know the guy, but I wouldn't think he hails from the Halls of the Keepers of Math Definitions.

If someone has a more authoritative source, I'll bow. Otherwise, I'm saying it's colloquial usage.

Regardless, the OP didn't say "major diameter," but just "diameter," and so remains erroneous. And the Bible verse I quoted remains without error as best I know.

I'm not a math expert, but to evaluate an ellipse you cannot use one value to describe the diameter -- you must take into account the major diameter (intersection through the center that forms the longest line) and the minor diameter (intersection through the center that forms the shortest line).

But I'm not an expert.
 
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Resha Caner

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I'm not a math expert, but to evaluate an ellipse you cannot use one value to describe the diameter -- you must take into account the major diameter (intersection through the center that forms the longest line) and the minor diameter (intersection through the center that forms the shortest line).

But I'm not an expert.

Note the edit to my previous post. The correct term is major axis, not diameter ... at least as far as I've found so far. But this is only a minor issue. I'm still waiting for the OP to clarify.

P.S. BTW, I'm very familiar with the mathematics of ellipses. In fact, I tried applying it to some problems at work (as well as elliptical integrals, which oddly enough have nothing to do with ellipses).
 
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AV1611VET

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I'm still waiting for the OP to clarify.
I'm not clarifying anything -- the OP stands as written.

You have an ellipse 30 feet in circumference and 10 feet in diameter.

What do you need? a slide ruler to figure out if that diameter is minor or major?
 
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Lion Hearted Man

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Note the edit to my previous post. The correct term is major axis, not diameter ... at least as far as I've found so far. But this is only a minor issue. I'm still waiting for the OP to clarify.

P.S. BTW, I'm very familiar with the mathematics of ellipses. In fact, I tried applying it to some problems at work (as well as elliptical integrals, which oddly enough have nothing to do with ellipses).

All I did was go to Wikipedia to make sure I was somewhat thinking correctly. They used the terms major axis/transverse diameter and minor axis/conjugate diameter. So yeah, you're right.
 
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AV1611VET

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All I did was go to Wikipedia to make sure I was somewhat thinking correctly. They used the terms major axis/transverse diameter and minor axis/conjugate diameter. So yeah, you're right.
From Wikipedia:
The major axis of an ellipse is its longest diameter...
 
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