Is there a rational parametrization of Quadric surfaces?
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Does there exists a rational parametrization of quadratic surfaces? In particular, I want to parametrize hyperboloid of one sheet $frac{x^2}{b}+frac{y^2}{4b}-frac{z^2}{4b}=1$ where $b$ is rational. (https://en.wikipedia.org/wiki/Hyperboloid).
In the above link, it says that plane section of hyperboloid is conic (or lines) and we can parametrize the conics rationally. Will this generate all the rational solutions on my hyperboloid? Is there any good reference on this stuff?
analytic-geometry
asked Dec 6 '18 at 18:19
ershersh
334112
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add a comment |
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Does there exists a rational parametrization of quadratic surfaces? In particular, I want to parametrize hyperboloid of one sheet $frac{x^2}{b}+frac{y^2}{4b}-frac{z^2}{4b}=1$ where $b$ is rational. (https://en.wikipedia.org/wiki/Hyperboloid).
In the above link, it says that plane section of hyperboloid is conic (or lines) and we can parametrize the conics rationally. Will this generate all the rational solutions on my hyperboloid? Is there any good reference on this stuff?
analytic-geometry
asked Dec 6 '18 at 18:19
ershersh
334112
$endgroup$
1
$begingroup$
A web search for “rational parameterization of quadric” turns up some interesting-looking sources.
$endgroup$
– amd
Dec 6 '18 at 20:21
add a comment |
$begingroup$
Does there exists a rational parametrization of quadratic surfaces? In particular, I want to parametrize hyperboloid of one sheet $frac{x^2}{b}+frac{y^2}{4b}-frac{z^2}{4b}=1$ where $b$ is rational. (https://en.wikipedia.org/wiki/Hyperboloid).
In the above link, it says that plane section of hyperboloid is conic (or lines) and we can parametrize the conics rationally. Will this generate all the rational solutions on my hyperboloid? Is there any good reference on this stuff?
analytic-geometry
asked Dec 6 '18 at 18:19
ershersh
334112
$endgroup$
Does there exists a rational parametrization of quadratic surfaces? In particular, I want to parametrize hyperboloid of one sheet $frac{x^2}{b}+frac{y^2}{4b}-frac{z^2}{4b}=1$ where $b$ is rational. (https://en.wikipedia.org/wiki/Hyperboloid).
In the above link, it says that plane section of hyperboloid is conic (or lines) and we can parametrize the conics rationally. Will this generate all the rational solutions on my hyperboloid? Is there any good reference on this stuff?
analytic-geometry
analytic-geometry
asked Dec 6 '18 at 18:19
ershersh
334112
asked Dec 6 '18 at 18:19
ershersh
334112
asked Dec 6 '18 at 18:19
ershersh
334112
asked Dec 6 '18 at 18:19
ershersh
334112
asked Dec 6 '18 at 18:19
ershersh
334112
334112
1
$begingroup$
A web search for “rational parameterization of quadric” turns up some interesting-looking sources.
$endgroup$
– amd
Dec 6 '18 at 20:21
add a comment |
1
$begingroup$
A web search for “rational parameterization of quadric” turns up some interesting-looking sources.
$endgroup$
– amd
Dec 6 '18 at 20:21
1
1
$begingroup$
A web search for “rational parameterization of quadric” turns up some interesting-looking sources.
$endgroup$
– amd
Dec 6 '18 at 20:21
$begingroup$
A web search for “rational parameterization of quadric” turns up some interesting-looking sources.
$endgroup$
– amd
Dec 6 '18 at 20:21
add a comment |
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A web search for “rational parameterization of quadric” turns up some interesting-looking sources.
$endgroup$
– amd
Dec 6 '18 at 20:21