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\left and \right are great, and work just as I expect for and . But when I put them together in a bracket, I'm at a loss what to do. Using an unadorned | gives me . Logically there should be something like \middle or \center, but the first doesn't exist and the second does something totally different. How do I tell LaTeX to automatically adjust the middle line to the correct size? — Keenan Pepper 04:17, 22 January 2008 (UTC)
\newcommand{\braket}[2]{\left\langle{#1}\vphantom{#2}\right|\left.\vphantom{#1}{#2}\right\rangle}
\braket{\frac{tall}{side}}{wide~side}
\Braket{\frac{tall}{side}|wide~side}
JackSchmidt (
talk) 06:08, 22 January 2008 (UTC)I just found out that my LaTeX distribution (TeX Live for Ubuntu) does have \middle and it works exactly as I expect! So, since these other solutions are unacceptable (the first doesn't actually do anything automatically, and the second sounds like a horrible kludge), my new question is: Why doesn't Wikipedia's TeX engine have this irreplaceable command \middle, and when is it going to get it? — Keenan Pepper 13:37, 22 January 2008 (UTC)
\left\langle\left.foo\right|bar\right\rangle
. This sizes the vertical bar based on "foo"; you can of course move the fake "." delimiter to the right end if "bar" is (expected to be) bigger. --
Tardis (
talk) 17:31, 23 January 2008 (UTC)Does anyone have any suggestions on how to solve this non-linear second-order differential equation: where a and b are positive constants, and y is a function of x. Thanks. -- 131.215.166.106 ( talk) 04:20, 22 January 2008 (UTC)
It's the night before my calculus final and I'm about to go to bed, but I'm just really bugged by this problem from a past final that I have no idea how to do:
∫0π/6 sec 2θ tan θ dθ
I know how to take definite integrals of polynomials and indefinite integrals of trigonometric functions, but this! We never learned this ... could anyone please show me at least how to set it up? Thanks so much in advance. —Preceding unsigned comment added by 70.19.20.251 ( talk) 04:37, 22 January 2008 (UTC)
Could you do if it were indefinite?
72.219.143.150 (
talk) 04:40, 22 January 2008 (UTC)
Well, yes, but if you know the antiderivative of the function it is a small step to definite integration...I guess what I'm asking is if the disconnect is just evaluating it. Do you know the antiderivative of the function? Show me that. (oops, forgot to ask---is the tangent's argument 2θ as well? Try a u-substitution. 72.219.143.150 ( talk) 04:49, 22 January 2008 (UTC)
Er, oops. Kinu, you got it. Lapse in my identities. I think the secant should be squared for this integration to be plausible on an exam. 72.219.143.150 ( talk) 04:53, 22 January 2008 (UTC)
(after making a silly mistake) Hm, the arguments are going to present a problem if you can't do u-subs. Your antiderivative is sec(2θ)/2. You'd plug the limits of integration into it and solve it like you would a polynomial expression, ending up with the value sec(/3)/2-sec(0)/2. Since I forget how to parse math stuff, you can calculate those values. 72.219.143.150 ( talk) 05:07, 22 January 2008 (UTC)
What is the largest volume of a tetrahedron that can be inscribed in a sphere? I can do it with a triangle and a circle, but I don't know where to begin when in 3 dimensions. Give me a hint. :) HYENASTE 05:39, 22 January 2008 (UTC)
How do I calculate the inverse color for a color? i.e. if I'm given a color, I want the color best suited for the background color, i.e. most readable.
I have seen many many online inverse color tools that simply assume it's the 256 complement (if I am using that term correctly), so (to use decimal), 10's inverse is 245. But of course then you get the color #808080 (i.e. 128 128 128), and the inverse is not correct at all.
Does anyone have a better formula? I'm thinking perhaps the color such that new minus old color has the maximum absolute magnitude. Any ideas? Ariel. ( talk) 10:48, 22 January 2008 (UTC)
Is the Ariel asking about complimentary colors as in art and design? Complimentary are the exact opposite of each other and shows the best contrast. It is based on RYB not RGB. 2 complimentary colored paints when mixed will always be black. See http://www.faceters.com/askjeff/answer52.shtml NYCDA ( talk) 23:58, 22 January 2008 (UTC)
(See above for 2 colors that didn't work great with black or white.) All the ideas posted worked pretty well, but I think it can be better. I like the most distant color rule, but I'd like to remove cyan, magenta, and yellow from the options, since those colors aren't the easiest to read. Any ideas? Ariel. ( talk) 15:54, 23 January 2008 (UTC)
NYCDA ( talk) 19:11, 23 January 2008 (UTC)
Alot of people seem to be trying to invert colour mathematically. What is needed here is to invert for the eye. Itensity is not equally effected by the colours. Intensity is generally: (0.299*r) + (0.587*g) + (0.114*b). Opposite intensity = (0.368*r) + (0.080*g) + (0.552*b). So for grey of 128,128,128, the opposite is 47 (0.368*128), 10 (0.080*128), 70(0.552*128), you then invert that to get 208, 245, 185. For gray 32,32,32 the opposite colour is 12,3,17 -> 243,252,238. For red (255,0,0), the opposite itensity is 94,0,0 -> 161,255,255. Opposite of blue (0,0,255) is 0,0,140 -> 255,255,115. Opposite of dark green (0,128,0) is 0,10,0 -> 255,254,255. This is the TRUE opposite. The value I use (0.386,0.080,0.552) are beacuse of the sensitivity of the eye, we see green the most and blue the poorest. Samples: Grey Grey Blue Blue Darkgreen Darkgeen Red Red D.Yellow D.Yellow Green Green I think you will find that no matter what colour you put in, you will get the most pleasing 'opposite' colour for human vision. Note that there is another set of values for computer screens. With these values red and green will be to bright. I know that these are the values for print (newspapers etc) but for computer screens I don't know. I think the green 0.08 is alot higher.-- 155.144.251.120 ( talk) 01:10, 24 January 2008 (UTC)
blackblackwhitewhitegreygreydgreydgreylgreylgreyredredlredlredgreengreenlgreenlgreenbluebluelbluelblueyellowyellowlyellowlyellowindegoindegolindegolindegovioletvioletlvioletlviolet-- Dacium ( talk) 00:24, 25 January 2008 (UTC)
Mathematics desk | ||
---|---|---|
< January 21 | << Dec | January | Feb >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
\left and \right are great, and work just as I expect for and . But when I put them together in a bracket, I'm at a loss what to do. Using an unadorned | gives me . Logically there should be something like \middle or \center, but the first doesn't exist and the second does something totally different. How do I tell LaTeX to automatically adjust the middle line to the correct size? — Keenan Pepper 04:17, 22 January 2008 (UTC)
\newcommand{\braket}[2]{\left\langle{#1}\vphantom{#2}\right|\left.\vphantom{#1}{#2}\right\rangle}
\braket{\frac{tall}{side}}{wide~side}
\Braket{\frac{tall}{side}|wide~side}
JackSchmidt (
talk) 06:08, 22 January 2008 (UTC)I just found out that my LaTeX distribution (TeX Live for Ubuntu) does have \middle and it works exactly as I expect! So, since these other solutions are unacceptable (the first doesn't actually do anything automatically, and the second sounds like a horrible kludge), my new question is: Why doesn't Wikipedia's TeX engine have this irreplaceable command \middle, and when is it going to get it? — Keenan Pepper 13:37, 22 January 2008 (UTC)
\left\langle\left.foo\right|bar\right\rangle
. This sizes the vertical bar based on "foo"; you can of course move the fake "." delimiter to the right end if "bar" is (expected to be) bigger. --
Tardis (
talk) 17:31, 23 January 2008 (UTC)Does anyone have any suggestions on how to solve this non-linear second-order differential equation: where a and b are positive constants, and y is a function of x. Thanks. -- 131.215.166.106 ( talk) 04:20, 22 January 2008 (UTC)
It's the night before my calculus final and I'm about to go to bed, but I'm just really bugged by this problem from a past final that I have no idea how to do:
∫0π/6 sec 2θ tan θ dθ
I know how to take definite integrals of polynomials and indefinite integrals of trigonometric functions, but this! We never learned this ... could anyone please show me at least how to set it up? Thanks so much in advance. —Preceding unsigned comment added by 70.19.20.251 ( talk) 04:37, 22 January 2008 (UTC)
Could you do if it were indefinite?
72.219.143.150 (
talk) 04:40, 22 January 2008 (UTC)
Well, yes, but if you know the antiderivative of the function it is a small step to definite integration...I guess what I'm asking is if the disconnect is just evaluating it. Do you know the antiderivative of the function? Show me that. (oops, forgot to ask---is the tangent's argument 2θ as well? Try a u-substitution. 72.219.143.150 ( talk) 04:49, 22 January 2008 (UTC)
Er, oops. Kinu, you got it. Lapse in my identities. I think the secant should be squared for this integration to be plausible on an exam. 72.219.143.150 ( talk) 04:53, 22 January 2008 (UTC)
(after making a silly mistake) Hm, the arguments are going to present a problem if you can't do u-subs. Your antiderivative is sec(2θ)/2. You'd plug the limits of integration into it and solve it like you would a polynomial expression, ending up with the value sec(/3)/2-sec(0)/2. Since I forget how to parse math stuff, you can calculate those values. 72.219.143.150 ( talk) 05:07, 22 January 2008 (UTC)
What is the largest volume of a tetrahedron that can be inscribed in a sphere? I can do it with a triangle and a circle, but I don't know where to begin when in 3 dimensions. Give me a hint. :) HYENASTE 05:39, 22 January 2008 (UTC)
How do I calculate the inverse color for a color? i.e. if I'm given a color, I want the color best suited for the background color, i.e. most readable.
I have seen many many online inverse color tools that simply assume it's the 256 complement (if I am using that term correctly), so (to use decimal), 10's inverse is 245. But of course then you get the color #808080 (i.e. 128 128 128), and the inverse is not correct at all.
Does anyone have a better formula? I'm thinking perhaps the color such that new minus old color has the maximum absolute magnitude. Any ideas? Ariel. ( talk) 10:48, 22 January 2008 (UTC)
Is the Ariel asking about complimentary colors as in art and design? Complimentary are the exact opposite of each other and shows the best contrast. It is based on RYB not RGB. 2 complimentary colored paints when mixed will always be black. See http://www.faceters.com/askjeff/answer52.shtml NYCDA ( talk) 23:58, 22 January 2008 (UTC)
(See above for 2 colors that didn't work great with black or white.) All the ideas posted worked pretty well, but I think it can be better. I like the most distant color rule, but I'd like to remove cyan, magenta, and yellow from the options, since those colors aren't the easiest to read. Any ideas? Ariel. ( talk) 15:54, 23 January 2008 (UTC)
NYCDA ( talk) 19:11, 23 January 2008 (UTC)
Alot of people seem to be trying to invert colour mathematically. What is needed here is to invert for the eye. Itensity is not equally effected by the colours. Intensity is generally: (0.299*r) + (0.587*g) + (0.114*b). Opposite intensity = (0.368*r) + (0.080*g) + (0.552*b). So for grey of 128,128,128, the opposite is 47 (0.368*128), 10 (0.080*128), 70(0.552*128), you then invert that to get 208, 245, 185. For gray 32,32,32 the opposite colour is 12,3,17 -> 243,252,238. For red (255,0,0), the opposite itensity is 94,0,0 -> 161,255,255. Opposite of blue (0,0,255) is 0,0,140 -> 255,255,115. Opposite of dark green (0,128,0) is 0,10,0 -> 255,254,255. This is the TRUE opposite. The value I use (0.386,0.080,0.552) are beacuse of the sensitivity of the eye, we see green the most and blue the poorest. Samples: Grey Grey Blue Blue Darkgreen Darkgeen Red Red D.Yellow D.Yellow Green Green I think you will find that no matter what colour you put in, you will get the most pleasing 'opposite' colour for human vision. Note that there is another set of values for computer screens. With these values red and green will be to bright. I know that these are the values for print (newspapers etc) but for computer screens I don't know. I think the green 0.08 is alot higher.-- 155.144.251.120 ( talk) 01:10, 24 January 2008 (UTC)
blackblackwhitewhitegreygreydgreydgreylgreylgreyredredlredlredgreengreenlgreenlgreenbluebluelbluelblueyellowyellowlyellowlyellowindegoindegolindegolindegovioletvioletlvioletlviolet-- Dacium ( talk) 00:24, 25 January 2008 (UTC)