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Difference between revisions of "Bicylindrics"

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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
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161401.png" /></td> </tr></table>
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$$x=a\cos t,\quad y=\pm\sqrt{b^2-a^2\sin^2t},\quad z=a\sin t,\quad b\geq a,$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161402.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161403.png" /> are the radii of the cylinders and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161404.png" /> is a parameter. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b016/b016140/b0161405.png" />, the bicylindrics is a pair of congruent ellipses.
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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
This article was adapted from an original article by E.V. Shikin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article