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Is the percentage of sunlight 'blocked' by a weave of material. How is this calculated using widths and gaps? -- 124.182.160.177 ( talk) 08:59, 28 April 2010 (UTC)
/ * * \ / * * G Wc * * / \ * * * * * \ Wt \ * * * * * /
Wc = Wt + G
100×G²/Wc²
100 - (100×G²/Wc²)
100 × (Wt² + 2G×Wt)/Wc²
I don't understand how the cross ratio answers when 4 points in projective line are projectivly equivalent. According to my book, "if z_1,z_2,z_3,z_4 and w_1,w_2,w_3,w_4 are two sets of 4 points, the are projectivly equivalent if their cross ratios are the same". The explanation is "since the cross ratio of z_1,z_2,z_3,z_4 is the image of the (unique) projective transformation carrying z_1 to 1, z_2 to infinity and z_3 to 0". How can the cross ratio, a scalar, be the image of a map on the projective line, a point defined by two coordinates? Thanks m uchly. —Preceding unsigned comment added by 122.109.239.224 ( talk) 10:01, 28 April 2010 (UTC)
Any triple of distinct points on the line is "equivalent" to any other, so the shape of a tuple of four points is just a matter of where you put the fourth point, and that is expressed by a scalar. Michael Hardy ( talk) 03:28, 29 April 2010 (UTC)
Thanks but how exactly? I thought that may be the scalar represents the point in affine coordinates, but what exactly does it mean to multiply and divide two points in the projective line? Could you give a proof that the cross ratio is the image of z_4? There isn't a proof in Wikipedia, so I'm not sure. All I got is if z_3=az_1+bz_2, then if z_1 is sent to (x,0) and z_2 is sent to (0,y) (just looking at the transformation on affine space) z_3 is sent to (ax,by). Thanks muchly. —Preceding unsigned comment added by 122.109.239.224 ( talk • contribs)
I couldn't think of a better title. I thought this article was very interesting considering I am a mathmetically challenged. Does anyone have any more to add to this list? -- Reticuli88 ( talk) 12:59, 28 April 2010 (UTC)
123/10 = 12.3 123/100 = 1.23 123/1000 = .123 123/10000 = .0123 <- Add leading zero 123/100000 = .00123 "
960364.
Mathematics desk | ||
---|---|---|
< April 27 | << Mar | April | May >> | April 29 > |
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. |
Is the percentage of sunlight 'blocked' by a weave of material. How is this calculated using widths and gaps? -- 124.182.160.177 ( talk) 08:59, 28 April 2010 (UTC)
/ * * \ / * * G Wc * * / \ * * * * * \ Wt \ * * * * * /
Wc = Wt + G
100×G²/Wc²
100 - (100×G²/Wc²)
100 × (Wt² + 2G×Wt)/Wc²
I don't understand how the cross ratio answers when 4 points in projective line are projectivly equivalent. According to my book, "if z_1,z_2,z_3,z_4 and w_1,w_2,w_3,w_4 are two sets of 4 points, the are projectivly equivalent if their cross ratios are the same". The explanation is "since the cross ratio of z_1,z_2,z_3,z_4 is the image of the (unique) projective transformation carrying z_1 to 1, z_2 to infinity and z_3 to 0". How can the cross ratio, a scalar, be the image of a map on the projective line, a point defined by two coordinates? Thanks m uchly. —Preceding unsigned comment added by 122.109.239.224 ( talk) 10:01, 28 April 2010 (UTC)
Any triple of distinct points on the line is "equivalent" to any other, so the shape of a tuple of four points is just a matter of where you put the fourth point, and that is expressed by a scalar. Michael Hardy ( talk) 03:28, 29 April 2010 (UTC)
Thanks but how exactly? I thought that may be the scalar represents the point in affine coordinates, but what exactly does it mean to multiply and divide two points in the projective line? Could you give a proof that the cross ratio is the image of z_4? There isn't a proof in Wikipedia, so I'm not sure. All I got is if z_3=az_1+bz_2, then if z_1 is sent to (x,0) and z_2 is sent to (0,y) (just looking at the transformation on affine space) z_3 is sent to (ax,by). Thanks muchly. —Preceding unsigned comment added by 122.109.239.224 ( talk • contribs)
I couldn't think of a better title. I thought this article was very interesting considering I am a mathmetically challenged. Does anyone have any more to add to this list? -- Reticuli88 ( talk) 12:59, 28 April 2010 (UTC)
123/10 = 12.3 123/100 = 1.23 123/1000 = .123 123/10000 = .0123 <- Add leading zero 123/100000 = .00123 "
960364.