Difference between revisions of "Bicylindrics"
From Encyclopedia of Mathematics
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Two closed curves obtained as the intersection of two cylinders the axes of which intersect at right angles. The parametric equations of bicylindrics are | Two closed curves obtained as the intersection of two cylinders the axes of which intersect at right angles. The parametric equations of bicylindrics are | ||
| − | + | $$x=a\cos t,\quad y=\pm\sqrt{b^2-a^2\sin^2t},\quad z=a\sin t,\quad b\geq a,$$ | |
| − | where | + | where $a$ and $b$ are the radii of the cylinders and $t$ is a parameter. If $a=b$, the bicylindrics is a pair of congruent ellipses. |
Latest revision as of 09:40, 5 August 2014
Two closed curves obtained as the intersection of two cylinders the axes of which intersect at right angles. The parametric equations of bicylindrics are
$$x=a\cos t,\quad y=\pm\sqrt{b^2-a^2\sin^2t},\quad z=a\sin t,\quad b\geq a,$$
where $a$ and $b$ are the radii of the cylinders and $t$ is a parameter. If $a=b$, the bicylindrics is a pair of congruent ellipses.
How to Cite This Entry:
Bicylindrics. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bicylindrics&oldid=32719
Bicylindrics. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bicylindrics&oldid=32719
This article was adapted from an original article by E.V. Shikin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article