Difference between revisions of "Paraboloid"
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A non-closed non-central [[Surface of the second order|surface of the second order]]. The canonical equations of a paraboloid are | A non-closed non-central [[Surface of the second order|surface of the second order]]. The canonical equations of a paraboloid are | ||
| − | + | $$ | |
| + | |||
| + | \frac{x ^ {2} }{p} | ||
| + | + | ||
| + | \frac{y ^ {2} }{q} | ||
| + | = 2z,\ \ | ||
| + | p, q > 0, | ||
| + | $$ | ||
for an [[Elliptic paraboloid|elliptic paraboloid]], and | for an [[Elliptic paraboloid|elliptic paraboloid]], and | ||
| − | + | $$ | |
| + | |||
| + | \frac{x ^ {2} }{p} | ||
| + | - | ||
| + | \frac{y ^ {2} }{q} | ||
| + | = 2z,\ \ | ||
| + | p, q > 0, | ||
| + | $$ | ||
for a [[Hyperbolic paraboloid|hyperbolic paraboloid]]. | for a [[Hyperbolic paraboloid|hyperbolic paraboloid]]. | ||
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====Comments==== | ====Comments==== | ||
| − | |||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''II''' , Springer (1987) pp. Chapt. 15</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> D. Pedoe, "Geometry" , Dover, reprint (1988) pp. 135, 398</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> M. Berger, "Geometry" , '''II''' , Springer (1987) pp. Chapt. 15</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> D. Pedoe, "Geometry" , Dover, reprint (1988) pp. 135, 398</TD></TR></table> | ||
Latest revision as of 08:05, 6 June 2020
A non-closed non-central surface of the second order. The canonical equations of a paraboloid are
$$ \frac{x ^ {2} }{p} + \frac{y ^ {2} }{q} = 2z,\ \ p, q > 0, $$
for an elliptic paraboloid, and
$$ \frac{x ^ {2} }{p} - \frac{y ^ {2} }{q} = 2z,\ \ p, q > 0, $$
for a hyperbolic paraboloid.
Comments
References
| [a1] | M. Berger, "Geometry" , II , Springer (1987) pp. Chapt. 15 |
| [a2] | D. Pedoe, "Geometry" , Dover, reprint (1988) pp. 135, 398 |
How to Cite This Entry:
Paraboloid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Paraboloid&oldid=48110
Paraboloid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Paraboloid&oldid=48110
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article