Comment on I just cited myself.

• rockerface@lemm.ee ⁨5⁩ ⁨months⁩ ago

  pi isn’t even a fraction. like, it’s actually an important thing that it isn’t

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  • I_am_10_squirrels@beehaw.org ⁨5⁩ ⁨months⁩ ago

    pi=c/d

    it’s a fraction, just not with integers, so it’s not rational, so it’s not a fraction.

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• Wandering_Uncertainty@lemmy.world ⁨5⁩ ⁨months⁩ ago

  The problem is, that’s exactly what the … is for. It is a little weird to our heads, granted, but it does allow the conversion. 0.33 is not the same thing as 0.333… The first is close to one third. The second one is one third. It’s how we express things as a decimal that don’t cleanly map to base ten. It may look funky, but it works.

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• force@lemmy.world ⁨5⁩ ⁨months⁩ ago

  Pi isn’t a fraction – it’s an irrational number, i.e. a number with no fractional form in integer bases. Furthermore, it’s a transendental number, meaning it’s never a solution to f(x) = 0, where f(x) is a non-zero finite-degree polynomial expression with rational coefficients. That’s like, literally part of the definition. They cannot be compared to rational numbers like integer ratios/fractions.

  Since |r|<1 => ∑[n=1, ∞] arⁿ = ar/(1-r), and 0.999… is that sum with a = 9 and r = 1/10 (visually, 0.999… = 9(0.1) + 9(0.01) + 9(0.001) + …), it’s easy to see after plugging in, 0.999… = 9(1/10) / (1 - 1/10) = 0.9/0.9 = 1). This was a proof in Euler’s Elements of Algebra.

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• sp3tr4l@lemmy.zip ⁨5⁩ ⁨months⁩ ago

  There are a lot of concepts in mathematics which do not have good real world analogues.

  i, the _imaginary number_for figuring out roots, as one example.

  I am fairly certain you cannot actually do the mathematics to predict or approximate the size of an atom or subatomic particle without using complex algebra involving i.

  It’s been a while since I watched the entire series Leonard Susskind has up on youtube explaining the basics of the actual math for quantum mechanics, but yeah I am fairly sure it involves complex numbers.

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  • myslsl@lemmy.world ⁨5⁩ ⁨months⁩ ago

    i has nice real world analogues in the form of rotations by pi/2 about the origin.

    Since i=exp(ipi/2), if you take any complex number z and write it in polar form z=rexp(it), then multiplication by i yields a rotation of z by pi/2 about the origin because zi=rexp(it)exp(ipi/2)=rexp(i(t+pi/2)) by using rules of exponents for complex numbers.

    More generally since any pair of complex numbers z, w can be written in polar form z=rexp(it), w=uexp(iv) we have wz=(ru)exp(i(t+v)). This shows multiplication of a complex number z by any other complex number w can be though of in terms of rotating z by the angle that w makes with the x axis (i.e. the angle v) and then scaling the resulting number by the magnitude of w (i.e. the number u)

    Alternatively you can get similar conclusions by demoivre’s theorem if you do not like complex exponentials.

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• ccunning@lemmy.world ⁨5⁩ ⁨months⁩ ago

  pie never actually ends

  I want to go to there.

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