J. M.
Reputation
424/400 score
 Aug 26 comment How to approximate/connect two continuous cubic Bézier curves with/to a single one? Just to check: you no longer have the convex hulls of any of the two curves you want to splice to a single one? Aug 26 comment Where does the Pythagorean theorem “fit” within modern mathematics? Tiny nitpick (but otherwise everything here I agree with): the "taxicab norm" is |a|+|b|. Aug 26 revised What is $\sqrt{i}$? edited tags Aug 26 comment Does the number pi have any significance besides being the ratio of a circle's diameter to its circumference? You had my upvote at "it is difficult to know if a circle is not lurking somewhere..." Aug 26 comment Estimates involving sums with binomials jug: Would you mind posting the actual "bigger sum"? Aug 26 comment Does the number pi have any significance besides being the ratio of a circle's diameter to its circumference? I'd rather this be a comment instead, so: $\pi$ turns up in the expression for the so-called "probability integral" (a.k.a. the "error function") among other things. How circles relate to this is a bit of a long-winded explanation though. Aug 26 comment How to convert a hexadecimal number to an octal number? Indeed this is great as a computer algorithm; I however got the impression that he was doing these conversions manually, so I suppose an intermediate conversion to binary is still a nicer approach. Aug 26 comment Why is the number e so important in mathematics? (Very) related: math.stackexchange.com/questions/3006 Aug 26 revised Why is the number e so important in mathematics? edited tags Aug 25 answered What is $\sqrt{i}$? Aug 25 comment How to evaluate Riemann Zeta function There are of course special methods for evaluating $\zeta$ at even (using of course the relation with the Bernoulli numbers) and odd integers. Searching the literature should turn up the methods for $\zeta(2k+1)$. Aug 25 revised On isometric affine transformations linear replaced with affine; added 7 characters in body Aug 25 revised How to evaluate Riemann Zeta function edited tags Aug 25 comment Where does the Pythagorean theorem “fit” within modern mathematics? guest: Well, we use here the definition of "circle" as "the set of all points that are a fixed distance away from a given point". It happens that the "circle" corresponding to the Euclidean norm (as opposed to, say, the Manhattan norm) has an infinite symmetry group (invariant under rotation by any angle with respect to its center, infinitely many axes of symmetry, etc.) which corresponds to the traditional, non-mathematician's concept of a circle. Aug 25 comment Estimates involving sums with binomials It can be expressed in terms of hypergeometric functions according to Mathematica, but I doubt you'd want that closed form. Aug 25 comment “Why do I always get 1 when I keep hitting the square root button on my calculator?” I'd have said raising something to 0 is the same as dividing a number by itself... but that works too. Aug 25 comment How to evaluate Riemann Zeta function On another note, Maple and Mathematica employ Euler-Maclaurin summation for computing $\zeta$; the problem with this of course is that there is the assumption that either you can easily generate or have a large enough cache of Bernoulli numbers (which is not a problem for Maple and Mathematica, but may be inconvenient in other environments). Aug 25 comment How to evaluate Riemann Zeta function Though CRVZ was used for evaluating $\zeta$ at $i-1$ in the paper, some numerical testing I did shows that the method can be unstable for some arguments with negative real part. This is why I recommended using the reflection formula instead for arguments in that region. Aug 25 comment “Why do I always get 1 when I keep hitting the square root button on my calculator?” So, how did you manage to convince yourself that taking square roots of fractions repeatedly has the same behavior? (Just kidding, you replace > with < of course). Aug 25 comment “Why do I always get 1 when I keep hitting the square root button on my calculator?” Qiaochu: Yes, that's why I said "a fixed point", not "the fixed point". But you're right about my forgetting the adjective "attractive".