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May
14
comment Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$?
Celcius to English? What English temperature scales are there? Kelvin would be the closest (although he was Irish by birth and arguably Scottish by adopted), I suppose, but I don't think they teach absolute temperature at that age.
May
8
comment How to merge two poly Bézier curves?
If they were simple polygons, would you be able to do it? Can you find the intersection of two Bézier curves? Can you generate a Bézier curve which is a continuous subset of another Bézier curve?
May
2
comment In how many ways can a number be expressed as a sum of consecutive numbers?
An equivalent statement to that main result is given in the comments on A001227, although without reference.
May
1
comment Graph theory - A type of undirected simple finite graphs
What does the notation $\{a; b\}$ mean? Is that a two-element set, or an uninterrupted range of integers?
Apr
29
comment Intuition and derivation of the geometric mean
And as a point of interest, there are at least two other means which are $f^{-1}(\textrm{arithmetic mean}(f(x_i)))$, namely the harmonic mean ($f(x) = x^{-1}$) and the RMS ($f(x) = x^2$).
Apr
26
comment Why is the Connect Four gaming board 7x6? (or: algorithm for creating Connect $N$ board)
I recall one of the people who solved the game observing that 6x7 is the smallest board which isn't easily shown to be a draw.
Apr
18
comment A sum involving powers of binomial coefficients.
@hkju, see edit.
Apr
18
comment Are computers going to be able to discover and prove important mathematics theorems?
@JonasKibelbek, NP-hard, not NP-complete. There are certainly some theorems whose proof is exponentially larger than the theorem, so theorem proving isn't in NP.
Apr
17
comment A Curious Binomial Coefficient Sum
What do you consider to be a "simple function"? The theory behind Gosper's algorithm will tell you that if the sum exists as a hypergeometric then it's a rational polynomial times the summand.
Apr
16
comment Divide and conquer - Algorithm MYST
FWIW a trivial variant on this algorithm is stooge sort, and the question is equivalent to exercise 8-3 of Introduction to Algorithms by Cormen, Leiserson, and Rivest.
Apr
16
comment Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0, \ldots\}$ without trig?
This can be made more symmetrical as $(1 - n\bmod 4)(1 - n \bmod 2)$
Apr
10
comment Nash equilibria - Why can we calculate a player's strategy without reference to their payoffs?
That seems to be a badly phrased exercise which implicitly relies on being a zero-sum game.
Apr
10
comment What is the tangent plane equation on the 3 spheres?
@you, I missed the "touch each other". Thanks.
Apr
9
comment What is the tangent plane equation on the 3 spheres?
You're going to need to give the radii too...
Apr
3
comment How many 2-card swaps until a “card deck” is close to true random?
This answer doesn't seem to explicitly account for the case where the top card is swapped away and swapped back again. Is there something I'm missing?
Mar
29
comment How would you mathematically represent the master key and 'slave lock' model?
@SNag, the question doesn't say anything about multiple dormitories, so you might want to edit that in. But you can do it by using a few more primes. Let each master key be a prime, each key and lock of which it's a master be the product of that prime with a new one, and the slave lock be the product of all the related primes.
Mar
22
comment Proving that a natural number is divisible by $3$
What on Earth is this doing in a calculus course?
Mar
21
comment Convex Hull Algorithms
@Louis, yes, and both the straight edges are tangent to the circle in the middle, but on opposite sides.
Mar
21
comment Convex Hull Algorithms
I agree that b isn't stated well. As stated, three circles with collinear centres make a counterexample. The intended statement was probably along the lines of "Show that if two non-trivial continuous pieces of a circle C are in the boundary of the convex hull then there is a continuous piece of circle C in the boundary of the convex hull which includes both of them".
Mar
20
comment A problem about the ratio of atoms
@Pureferret, I did define the notation in the second paragraph. $x^\underline{1} = x$; $x^\underline{2} = x(x-1) = x^2 - x$; so $x^2 = x^\underline{2} + x^\underline{1}$.