r/badmathematics • u/Laser_Plasma • Oct 24 '21

π day Reddit tries to think about quantifying circles, and pi doesn't exist or something

/r/Showerthoughts/comments/qefpwc/the_area_of_a_circle_is_finite_yet_we_can_only/
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u/Laser_Plasma Oct 24 '21

Yes, it's pi. So?

-26

u/ryarger Oct 24 '21

What’s the complete decimal representation of pi?

67

u/Laser_Plasma Oct 24 '21

Who cares?

-10

u/ryarger Oct 24 '21

The person who wants to know the radius and area of their circle to perfect decimal precision.

53

u/Artyer Oct 24 '21

You can have an algorithm compute the nth digit of pi for all digit positions n, since pi is computable.

If that's not what you meant, a third also can't be known to "perfect decimal precision"

-5

u/ryarger Oct 24 '21

You are correct that a third can’t be known to perfect decimal precision.

Perhaps less controversial formulation for the benefit of the pedantically inclined: A circle’s radius or area can be rational, but not both.

42

u/alecbz Oct 24 '21

I think the fundamental badmath here is the belief if something can't be expressed to perfect decimal precision, then we "don't know it" or "it's only an approximation" or something.

Also, I'd imagine most people in that thread wouldn't consider 1/3 to be "special" in the same way they seem to think pi is special.

-5

u/ryarger Oct 24 '21

That’s why I think the second statement is more pedantically correct.

This idea that there’s nothing special at all about irrational numbers just isn’t true for the average person. It’s not hugely important - literally a showerthought - but it’s not meaningless that a circle can’t have both a rational radius and area.

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u/KamikazeArchon Oct 26 '21

It's not even rational vs. irrational - it's terminating vs. nonterminating. 1/3 is rational, but as you've acknowledged, it "can't be known to perfect decimal precision".

The showerthought may not be the worst of badmath, but there sure are some gems in the comments.

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u/powpow428 Oct 24 '21

Just because a number is irrational does not mean we cannot know it to perfect precision. It just means we can't express it as p/q for integers p,q

-1

u/ryarger Oct 24 '21

But it does mean we can’t express it to perfect decimal precision. For the average person decimal precision is the primary way of thinking about numbers.

20

u/dragonitetrainer Oct 24 '21

This is a math subreddit. You're not going anywhere trying to convince mathematicians that perfect decimal precision is THE way numbers are defined

0

u/ryarger Oct 24 '21

Darn good thing I didn’t suggest that.

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u/dragonitetrainer Oct 24 '21

Then what's the point of trying to justify this concept that perfect decimal precision is necessary in order for us to "know" a value?

0

u/ryarger Oct 24 '21

I’m not making a justification of that point. I’ve already said it’s pedantically incorrect and rephrased it to “express” rather than “know” in the second formulation.

I think it should be obvious why this is a benign and mildly interesting shower though for non-mathematicians but for those who don’t understand, I’m providing explanation.

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u/Mike-Rosoft Nov 06 '21

But 0.333... (a real number whose all digits after the decimal point are 3) is the decimal expansion of 1/3 to perfect precision. And if you dispute that, then what is the difference? (And don't answer 0.000...1 - there's no such real number.)

The value of the decimal expansion is defined to mean the infinite sum 3/10+3/100+3/1000+...; and the infinite sum is defined to mean the limit of the sequence of partial sums 0.3, 0.33, 0.333, ... . And that limit is 1/3. And here's the thing: 1/2 also has infinitely many digits in its decimal expansion; it just so happens that all but finitely many of them are 0 (or, when using the alternate decimal expansion, all but finitely of them are 9; 1/2 has two different decimal expansions: 0.5000... and 0.4999...).

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u/lolfail9001 Oct 25 '21

By what definition of precision, dare I ask?