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  1. Re: Definition and Examples of Binomial | - Algebra

    https://en.wikipedia.org/wiki/Binomial
  2. Re: Calculate surface area of pyramid

    To find the height of the four isosceles triangles, draw a right triangle from the vertex to the center of the base to the midpoint of one of the sides. If the sides have length A and the overall...
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    Re: Plotting scaled triangle

    Why do you VB* people do everything the hard way? Weakly typed languages for the win. :)

    (Though to be fair, the .NET IDE is really quite nice.)
  4. Re: Calculate instead of simulate?

    Ah, that's far too complicated to hope for an analytic solution. There's also a problem of uniqueness--there are surely quite a few values of your three variables which "on average" with purely...
  5. Re: Calculate instead of simulate?

    More details are needed to give an exact solution; you'll probably end up wanting something like the inverse of a cumulative distribution function.
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    Re: Plotting scaled triangle

    I find the code in post #4 very difficult to interpret--a lot of it doesn't seem to make much sense. The code in post #5 looks pretty close, but I think it should instead be...


    'Assume the Sides...
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    Re: [RESOLVED] Reaaranging expression

    They're not symbol-for-symbol the same, but yes, they're equal, since 3-c is -(c-3), and 12c-6a is -(6a-12c). I had checked to make sure. You can also have Wolfram Alpha check for symbolic equality,...
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    Re: Reaaranging expression

    You're correct, and Wolfram Alpha agrees.
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    Re: Generating parallel lines.

    Minor mistake: "mx = (x2 - x1) / circ2Rad" should be pulled out of the If statement and put right before it. mx is not getting properly reset in the x1=x2 case, which only shows up in the a=0 (or...
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    Re: Solving Triangles

    Note quite. Again the issue is the SSA case, which comes down to the non-invertibility of the sine function on the range 0 to 180. In particular, given a, A, and B, you can compute sin(b), but sin is...
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    Re: Solving Triangles

    You can't do much with just 1 side and its opposite angle. There are certainly many solutions give just those two pieces of information. You should be able to pick a second angle arbitrarily (subject...
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    Re: Solving Triangles

    This is getting at the standard similarity/congruence tests for triangles. Here they are:

    AAA: three angles determine the corresponding sides up to an overall scale factor. Since the angles add up...
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    Re: shellsort and selectionsort code help

    This isn't really a math question. It should be in one of the language-specific forums. There are also a zillion code examples of the zillion and one sorting algorithms out there, though they may not...
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    Re: [RESOLVED] solving equation

    Minor thing: I noticed a typo in my second graph's equation from post #8. I had written y = −x + 21x + 11 instead of y = −x + 21x + 22. This didn't affect the default Wolfram Alpha view of the...
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    Re: solving equation

    Well, y is 0 at the x-intercepts, since the x-intercepts are on the x-axis, and the x-axis is precisely the line consisting of points whose y-coordinate is 0.

    Perhaps this will help? Consider the...
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    Re: solving equation

    I think I'd have to see the question to know what you're trying to do. You again said you needed to "solve for x", and I've told you how to solve for x in terms of y. If you mean you need to solve...
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    Re: solving equation

    You wrote an expression, not an equation, so what do you mean by it "seems insoluble without a value for y"?

    To take a simpler example, start with y=x^2. Doing the same operation, i.e. saying x^2...
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    Re: solving equation

    Well, if you want to solve your equation for x in terms of y, you'll have to use the quadratic formula, and there are two "branches" of solutions in general (the function is not invertible in...
  19. Re: Round-about way to get even distribution using Random functions.

    Oh, I agree my solution is easy to implement with a for loop, it's just cleaner and (potentially) faster to use a linked list/queue style data structure, at least if there are often many unused spots...
  20. Re: Round-about way to get even distribution using Random functions.

    Yeah, I'm not a big fan of the two methods you suggested either. The first would make earlier entities *much* more likely to be chosen than later ones, while the second would make the last entity...
  21. Re: radius of circumcircle from 3 points formula... can someone explain?

    That article is nice and brief, and it gives some notion of what the parts of Heron's formula individually "mean". It does something quite similar to what my proof does, but with the incircle rather...
  22. Re: radius of circumcircle from 3 points formula... can someone explain?

    @boops boops: for what it's worth, I made an effort to avoid Heron's formula since it seemed like its use just pushes the problem farther down the line--why is Heron's formula true? On the other hand...
  23. Re: radius of circumcircle from 3 points formula... can someone explain?

    First, here's why the circumcenter exists. Take two sides of a triangle and consider their perpendicular bisectors. Since the sides are not parallel, neither are the perpendicular bisectors, so they...
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    Re: drawing random triangle

    Just to be clear, my comment about precision was directed at how precisely you wanted to draw "the maximum sized scale triangle within the bounding rectangle [subject to some given angles]", rather...
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    Re: drawing random triangle

    The complexity of what you want depends a lot on how precise you want it all to be and what you're willing to say is "good enough". For instance, your "acute" case in post #1 allows non-acute...
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    Re: Rotating 3d Object by Axis

    @dday9: cool beans.



    Totally understandable, though in this case there was a very easy check besides looking at the original source code. The matrix form of the operation needed to have...
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    Re: Rotating 3d Object by Axis

    I see one big mistake still in #3, namely the "- x" should be "+ x". That would produce extremely erratic results.

    I disagree with passel in that I think the integer-based coordinates for your...
  28. Re: Gaussian Sigma and Pascal's Triangle

    You seem to be referring to the fact that the rows of Pascal's triangle, when plotted after normalization, look very much like a normal distribution, especially as you take longer and longer rows....
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    Re: [RESOLVED] Average from percentage?

    Ah, my mistake. That makes the computation easier. Since 0 < N < 100, we may evidently assume every such sequence terminates, since a non-terminating sequence occurs with 0 probability. Each sequence...
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    Re: [RESOLVED] Average from percentage?

    Unless I'm really, really misunderstanding your question, it's not (N/100)M times. For instance, at N=100, this gives M, but as you say it should obviously give infinity. As I understand it, you...
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    Re: Maximum Yards Returned

    x is a value between 0 and 1 (a float), but you're making it an int. You could also make x use percentages, I suppose.
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    Re: Maximum Yards Returned

    You want what's called a "linear interpolation". If p and q are two numbers and x is a parameter between 0 and 1, you can get values in between p and q based on x using the standard formula F(x) =...
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    Re: Three guys rent a room for $30

    I agree with passel. The guys each have $-9 at the end, the bellhop has $2, and the manager has $25. -9*3 = 27 = 2+25, which makes perfect sense. The "$1 discrepancy" is just coming from confusing +...
  34. Re: [RESOLVED] Expression Evaluator - Parenthesis and Negatives

    I had a more iterative approach in mind for the lexer. That is, you run through the code character by character adding tokens to a queue as you go. It's fundamentally similar to what you're doing,...
  35. Re: Expression Evaluator - Parenthesis and Negatives

    RPN probably isn't an option here since that would force users to enter unusual syntax.

    The shunting-yard algorithm is probably what you're after here. The example and description at the link are...
  36. Re: Expression Evaluator - Parenthesis and Negatives

    I feel I should have a disclaimer at the top of this post. Namely, you probably shouldn't have to write your own parser nowadays and should instead be able to use someone else's; if you do have to...
  37. Re: [RESOLVED] reliable decimal to fraction converter

    I don't work in VB anymore, though the Python translation of that code fails on the example I gave earlier, and the VB version should be similar. Specifically, given



    def dec2frac(f):
    u =...
  38. Re: reliable decimal to fraction converter

    The trouble is your code is assuming the decimal representation infinitely repeats. For instance, for 6/5 = 1.2, you're assuming it's really 1.2222222... = 11/9. But it's not, it's 1.200000.... I...
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    Re: Logarithmic question

    I can't really understand your revised version, sorry. What I know so far: if A (the random number) is > 0.9, compute N = ceil((1+log10(1-A))/log10(0.9)), which is the smallest N such that 0.1*0.9^N...
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    Re: Logarithmic question

    Say x is the random number. If x < 0.1, you want to know when 0.1*0.9^y = x (essentially); this occurs for y = log_(0.9) (x/0.1) = (1+log10(x))/log10(0.9). For instance, if x = 0.0324, this gives...
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