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 May 19 comment Is there a general formula for $\sin{(\frac{n \pi}{2})}$? Certainly there is, other than that formula. What other functions would you use? When I was a kid I programmed in BASIC where the built-in functions did include sin but also such things as int and abs... oeis.org is also interesting. Apr 20 comment Is the size of the Online Encyclopedia of Integer Sequences bounded by aleph-null? So, the sequences that exist have the cardinality of the continuum, the sequences that we can ever describe have the cardinality of the integers, and the sequences that we ever have described have finite cardinality? Aleph-two and beth-two for example are entirely out of the question, I think? I'm not 100% clear on uncountables. Nov 9 comment Why is ${x^{\frac{1}{2}}}$ the same as $\sqrt x$? We might think it's equally sensible to define the special case $0^0$ as $0$, but the mathematical convention for that is indeed $0^0 = 1$ in accord with the explanation above. Nov 9 comment What are the most overpowered theorems in mathematics? "The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's lemma?" — Jerry Bona. I like how that joke sums up intuitions (rather than logic) regarding the Axiom of Choice and Zorn's Lemma. Nov 9 comment We know the dimension of the Koch snowflake's perimeter, but does it have a measure? It has a positive and finite Hausdorff measure, am I right? I haven't carefully read and thought through what Hausdorff measure is all about. Nov 9 comment How to put 9 pigs into 4 pens so that there are an odd number of pigs in each pen? Horrible, yes. But logically, what's wrong with questioning the mathematical model that pairs integers with pigs? They can indeed literally disintegrate. Oct 28 comment We know the dimension of the Koch snowflake's perimeter, but does it have a measure? Relevant I think? So, it is quite difficult indeed? dx.doi.org/10.1016/j.amc.2007.01.046 Aug 5 comment Find the smallest $n$ such that the digits in $2^n$ have every digit from $1$ to $9$ Is there a standard definition of "brute force"? Maybe we can claim that there's something clever about doubling decimal digits rather than multiplying them by any other constant. Doubling 1024 obviously produces another number with four distinct digits because 0,1,2,and 4 are all in the lower half of the decimal digits. Aug 1 comment Is it fair to say that Kepler's equation involves squaring the circle? There is much pleasure to be had with such things. If your interest takes you in this direction and you haven't yet looked at these particular points, you may also wish to study 1. the conditions under which it is impossible to square the circle and 2. the interesting proof that it is impossible. Beyond that, from the book Mathematical Cranks I learned that there are some who venture into solving the classic impossibilities and later display serious mental illness. That's not a diagnosis and I'm not a doctor. But if I spent tons of time on this hobby, I hope I'd discuss it with a therapist. Apr 25 comment Could G. H. Hardy make a product of two primes so big he couldn't find out which? Not G.H. Hardy, but "Gauss can factor a two million digit semiprime in his head!" gaussfacts.com/view/Mathematics/825 Mar 18 comment How do I approach the following integral? The antiderivative in software such as Mathematica (thus Alpha) is known as the Risch algorithm. Vaguely I recall that it isn't, or at least didn't used to be, practical to implement the Risch algorithm in full generality, and in the gaps Mathematica tells lies. The Wikipedia article for the algorithm says (citing nothing) that is unknown whether the Risch algorithm has all expressions in the "usual" (meaning?) elementary functions in its domain; and that by Richardson's theorem the expressions in those functions with the addition of the absolute value function are not all in its domain. Feb 28 comment Parametric curve for a tennis ball seam @bubba Thanks, I went on to explain some of the symmetries. So, yes, yes it does. Feb 26 comment Sequence Question from past post Yes, I realize that this question is a follow-up and I don't think it's a duplicate. Feb 22 comment Sequence Question from past post OEIS has the third one. I'll see whether I can do anything with the others. Aha, yes, I can find the previous post that was mentioned. Feb 22 comment Sequence Question from past post These sequence problems are among the many that are collected here: m4maths.com/placement-puzzles.php?SOURCE=IBM Feb 22 comment Sequence Question from past post Related to: math.stackexchange.com/questions/291443/… Dec 21 comment Probability a point will be in a subset of a square The probability is equal to the area, as it says. If the area seems difficult to determine, it may help to draw the picture. Aug 21 comment Ellipse 3-partition: same area and perimeter Hmm, why can't we just 3-partition a circle and project that figure onto a non-orthogonal plane... oh. Because by age 20 we had learned to compute arc length and it doesn't work that way. Apr 4 comment Could G. H. Hardy make a product of two primes so big he couldn't find out which? It's claimed you needn't have the factorization (although Broadhurst does) but as I admitted, I wouldn't actually know. I'm certainly willing to remove the "accepted" status from my answer if we become aware of a flaw, or simply better information. Apr 1 comment Could G. H. Hardy make a product of two primes so big he couldn't find out which? Right, I was looking for a product of exactly two primes for which we may presume that no one knows the factors. This answer addresses an interesting but separate question. Considering the number of votes this answer has received, this other question would be a valuable addition to math.stackexchange.com.