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Jan
17
comment Eccentricity is invariant for ellipse defined by intersection between plane and ellipsoid [can't be correct]??
For a tilted ellipse, a and b only give you the x and y intercepts of the ellipse. These are no longer the end points of the major and minor axes of the ellipse.
Jan
17
comment Minimizing a quadratic function of 2 variables in quadratic region
Partial derivatives and boundary condition checking?
Jan
17
comment Eccentricity is invariant for ellipse defined by intersection between plane and ellipsoid [can't be correct]??
I'm not sure I'm following this, but realize the ellipse you create no longer has the x and y axes as its major and minor axes. The ellipse is now "tilted" and you need to rotate your x and y axes to find the major and minor ellipse axes and thus find the eccentricity.
Jan
17
comment Solving $x^2 + y^2 = 1 + z^4$ with (x,y,z) = 1 and z < x < y
Possible hint: rewrite the equation to use difference of squares.
Jan
16
answered On the sum of the reciprocals of square roots.
Jan
16
comment Finding elements of a set that is itself a group under addition.
If p is in the group, all multiples of p must also be in the group, and p*q is certainly a multiple of p.
Jan
16
comment Finding elements of a set that is itself a group under addition.
Actually, I think any three elements in the set will generate a group (as will any 3 integers). You need to find a group that contains 3 of the elements of the set but does NOT contain the other 2. In other words, exactly 3 are in the group.
Jan
16
comment Finding elements of a set that is itself a group under addition.
More like trial and error, I'd say.
Jan
16
comment Finding elements of a set that is itself a group under addition.
I was just giving a hint. If you choose q as a generator, you can't have p or p+q, and you can't have p^q since p^q is not a multiple of q, and all elements in the group generated by q must be multiples of q.
Jan
16
comment Finding elements of a set that is itself a group under addition.
Note that if p is in the group, p+p+p...+p (q times) is also in the group (thus p*q), and that p^q is also in the group since you can generate it by adding p to itself a sufficient number of times.
Jan
15
comment Method for Counting the Number of “Unique” Vertices in a Grid?
So the input to your function would be, effectively, a finite list of non-overlapping rectangles? I can think of a computer algorithm to solve that, which is a function of sorts, but I'm not sure how a purely mathematical description of the function would look like. It's effectively the cardinality of the set of all corner points for all of the rectangles.
Jan
14
comment Compute the angle between a line and a plane if the line forms the angles of 45 degrees and 60 degrees with two perpendicular lines lying in the plane
Possible hint: if you have two perpendicular lines in a plane, you can regard them as the x and y axes of a Cartesian coordinate system.
Jan
14
comment Calculating Down Range and Cross Range Coordinates
Cosine is an even function. The cosine of 45 degrees is the same as the cosine of -45 degrees. You may be computing it wrong in the negative case.
Jan
13
comment Stochastic Convergence
math.stackexchange.com/questions/837902/…
Jan
12
comment Stochastic Convergence
Given any finite series of numbers, there exists a polynomial p such that p(1), p(2), p(3), ... generates those series of numbers. Is that what you're looking for?
Jan
12
comment Least squares problem: am I solving it correctly?
OK, I think I'm misunderstanding the question. To me, least squares means you are given fewer equations than variables and you have to maximize some sort of function within those constraints.
Jan
12
comment Calculating Down Range and Cross Range Coordinates
What results do you get and what results does the model get?
Jan
11
comment Calculating Down Range and Cross Range Coordinates
At first glance, this looks ok to me. Why do you think it's wrong?
Jan
11
comment Least squares problem: am I solving it correctly?
Trick question: the system is inconsistent (if I'm understanding correctly)
Jan
10
comment Probability of having 2 cards in hand knowing the probability of having 1
But if you see a 'ONE' card in the opponent's hand, isn't it more likely he has 2 'ONE' cards than having only 1 'ONE' card?