Find a projective change of coordinates
1
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Find a projective change of coordinates that takes the projective completion of the circumference C: $x^2 + y^2 = 1$ to the projective completion of the parabola P: $y^2=2px$, $p geq 0$
(i.e. $x^2 + y^2 = z^2$ to $y^2=2pxz$)
conic-sections coordinate-systems projective-geometry
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
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add a comment |
1
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Find a projective change of coordinates that takes the projective completion of the circumference C: $x^2 + y^2 = 1$ to the projective completion of the parabola P: $y^2=2px$, $p geq 0$
(i.e. $x^2 + y^2 = z^2$ to $y^2=2pxz$)
conic-sections coordinate-systems projective-geometry
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
$endgroup$
$begingroup$
Essentially a duplicate of math.stackexchange.com/q/1273662/265466.
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– amd
Jan 8 at 2:33
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I don’t get the explanation there, it becomes the regular circumference, not its completion.
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– M. Navarro
Jan 8 at 7:47
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It's a change of variables in homogeneous coordinates. You can find the point on the circle that corresponds to the point at infinity $(1, 0, 0)$ on the parabola.
$endgroup$
– Maxim
13 hours ago
add a comment |
1
1
1
$begingroup$
Find a projective change of coordinates that takes the projective completion of the circumference C: $x^2 + y^2 = 1$ to the projective completion of the parabola P: $y^2=2px$, $p geq 0$
(i.e. $x^2 + y^2 = z^2$ to $y^2=2pxz$)
conic-sections coordinate-systems projective-geometry
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
$endgroup$
Find a projective change of coordinates that takes the projective completion of the circumference C: $x^2 + y^2 = 1$ to the projective completion of the parabola P: $y^2=2px$, $p geq 0$
(i.e. $x^2 + y^2 = z^2$ to $y^2=2pxz$)
conic-sections coordinate-systems projective-geometry
conic-sections coordinate-systems projective-geometry
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
asked Jan 7 at 18:53
M. NavarroM. Navarro
858
858
$begingroup$
Essentially a duplicate of math.stackexchange.com/q/1273662/265466.
$endgroup$
– amd
Jan 8 at 2:33
$begingroup$
I don’t get the explanation there, it becomes the regular circumference, not its completion.
$endgroup$
– M. Navarro
Jan 8 at 7:47
$begingroup$
It's a change of variables in homogeneous coordinates. You can find the point on the circle that corresponds to the point at infinity $(1, 0, 0)$ on the parabola.
$endgroup$
– Maxim
13 hours ago
add a comment |
$begingroup$
Essentially a duplicate of math.stackexchange.com/q/1273662/265466.
$endgroup$
– amd
Jan 8 at 2:33
$begingroup$
I don’t get the explanation there, it becomes the regular circumference, not its completion.
$endgroup$
– M. Navarro
Jan 8 at 7:47
$begingroup$
It's a change of variables in homogeneous coordinates. You can find the point on the circle that corresponds to the point at infinity $(1, 0, 0)$ on the parabola.
$endgroup$
– Maxim
13 hours ago
$begingroup$
Essentially a duplicate of math.stackexchange.com/q/1273662/265466.
$endgroup$
– amd
Jan 8 at 2:33
$begingroup$
Essentially a duplicate of math.stackexchange.com/q/1273662/265466.
$endgroup$
– amd
Jan 8 at 2:33
$begingroup$
I don’t get the explanation there, it becomes the regular circumference, not its completion.
$endgroup$
– M. Navarro
Jan 8 at 7:47
$begingroup$
I don’t get the explanation there, it becomes the regular circumference, not its completion.
$endgroup$
– M. Navarro
Jan 8 at 7:47
$begingroup$
It's a change of variables in homogeneous coordinates. You can find the point on the circle that corresponds to the point at infinity $(1, 0, 0)$ on the parabola.
$endgroup$
– Maxim
13 hours ago
$begingroup$
It's a change of variables in homogeneous coordinates. You can find the point on the circle that corresponds to the point at infinity $(1, 0, 0)$ on the parabola.
$endgroup$
– Maxim
13 hours ago
add a comment |
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$begingroup$
Essentially a duplicate of math.stackexchange.com/q/1273662/265466.
$endgroup$
– amd
Jan 8 at 2:33
$begingroup$
I don’t get the explanation there, it becomes the regular circumference, not its completion.
$endgroup$
– M. Navarro
Jan 8 at 7:47
$begingroup$
It's a change of variables in homogeneous coordinates. You can find the point on the circle that corresponds to the point at infinity $(1, 0, 0)$ on the parabola.
$endgroup$
– Maxim
13 hours ago