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  • 0 posts edited
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  • 13 votes cast
Apr
9
comment What are the distances from a line to the tangents of a circle?
And I finally learned that the area of an arbitrary parallelogram can calculated without any trig (en.wikipedia.org/wiki/Exterior_algebra). This answer would have been far more helpful if any of that had been included.
Apr
9
comment What are the distances from a line to the tangents of a circle?
Ok, I've figured out that ∧ is the "wedge product", so the numerator is the area of the parallelogram with sides AB and AO ... this formula now makes sense to me. So d = ∥AO∥ sin(OAB) ... which should have been obvious to me. This I can calculate.
Apr
5
awarded  Student
Apr
4
comment What are the distances from a line to the tangents of a circle?
I always need both tangents, and in my case the line and circle are usually not disjoint. Anyway, I don't know calculus and or how to solve for the min of f, and I already have a solution that works for me.
Apr
4
comment What are the distances from a line to the tangents of a circle?
I'm not familiar with that notation or how to evaluate d. I was looking for something in terms of trig functions, which is why I tagged this [trigonometry].
Apr
4
comment What are the distances from a line to the tangents of a circle?
@LeonhardtvonM I realized that shortly before I saw your comment. I rotated the two points about the origin and then took y +/- radius. Why did someone downvote this ... I think it's a decent question and such down votes are rather uninviting to people who are inexpert in mathematics. As to what I had tried: I drew lines and circles on paper and tried to construct a solution. That question makes a lot more sense at Stack Overflow.
Apr
3
awarded  Editor
Apr
3
revised What are the distances from a line to the tangents of a circle?
edited tags; edited title
Apr
3
asked What are the distances from a line to the tangents of a circle?
Mar
7
comment Will it become impossible to learn math?
It is already impossible to learn all of math, and always has been. That has nothing to do with the possibility of learning math, any more than it's impossible to learn to read just because you can't read everything.
Dec
17
awarded  Caucus
Oct
10
comment Do mathematicians, in the end, always agree?
"The reason this is so funny" -- What's even funnier is that he's completely wrong about the views of computer scientists. Many results in computational theory depend on such abstractions as "infinite tapes".
Oct
7
comment Incredible Blackjack Hand
No, you don't have to consider his downcard, because you don't know what it is, just like you don't know what the last card in the deck is. Probabilities are a function of known information. What you're trying to do is take it much further than what I wrote in an attempt to avoid its validity. The simple fact is that you took the up card into account to reduce 416 to 415, but not to reduce 13 to 12.8125, and that's simply a mistake.
Oct
7
comment Incredible Blackjack Hand
"asking for the chance that there are 6 straight cards of the same denomination from an 8 deck shoe" -- non-grammatical; "from" should be "in", which is not at all what the OP asked.
Oct
7
comment Incredible Blackjack Hand
Your reading is obviously (based on simple reasoning from clear facts) not "a perfect reasonable interpretation") so ... done. Mere disagreement is useless; you need a rebuttal to simple points like those cards never getting dealt, being split among players, etc. All the other answers got the clear meaning.
Oct
7
comment Incredible Blackjack Hand
It doesn't matter where in the shoe the deal comes from, as long as you haven't seen any of the other cards ... probabilities depend on knowledge. In any case, a run elsewhere in the shoe could go to another player, or get split between players, or never get dealt ... it obviously isn't what the OP is asking about. The OP asked " odds are in getting 6 straight cards" -- "in getting" means being dealt 6 such cards in the manner that happened to the OP, not just having those cards in the shoe somewhere.
Oct
7
comment Incredible Blackjack Hand
This obviously doesn't answer the same question, because the OP is interested in the odds of drawing 6 of the same card, not the odds that there are 6 of the same card in a row somewhere in the shoe.
Oct
7
comment Incredible Blackjack Hand
13 isn't quite right because it's harder to get 6 of the dealer's up-card than to get 6 of the other cards ... so it's about 1 in 589298.
Oct
7
comment Incredible Blackjack Hand
"6,942,219,827,088 ways to get just any six cards" -- only 6,842,091,656,505 because there's a card showing. "13 times more common than above" -- Actually 12.8125 (12 + 13/16) times, because there's a card showing.
Aug
31
comment Are all prime numbers finite?
take the set of inverse squares -- or the set of reciprocals of any other set of natural numbers, e.g., 1, 1/2, 1/3, 1/4, ... or 1/2, 1/3, 1/5, 1/7 ... I would of thought eventually there would be infinitely many zero elements -- how very strange.