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Difference between revisions of "Viviani curve"

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The curve of intersection of the surfaces of a sphere of radius <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096800/v0968001.png" /> and a certain circular cylinder of radius <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096800/v0968002.png" /> through the centre of the sphere. The part of the solid sphere located inside the cylinder is known as the Viviani solid. So named after V. Viviani (17th century).
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The curve of intersection of the surfaces of a sphere of radius $R$ and a certain circular cylinder of radius $R/2$ through the centre of the sphere. The part of the solid sphere located inside the cylinder is known as the Viviani solid. So named after V. Viviani (17th century).
  
  
  
 
====Comments====
 
====Comments====
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Viviani's window is the set of points in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096800/v0968003.png" /> given by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v096/v096800/v0968004.png" />.
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Viviani's window is the set of points in $E^3$ given by  
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$$
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\{ (x,y,z)\ :\ x^2+y^2+z^2 \le 1\,,\ x^2+y^2 \le x \} \ .
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$$
  
 
====References====
 
====References====
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,  "Geometry" , '''II''' , Springer  (1987)  pp. 84</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Berger,  "Geometry" , '''II''' , Springer  (1987)  pp. 84</TD></TR>
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</table>
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Latest revision as of 19:52, 20 September 2017

The curve of intersection of the surfaces of a sphere of radius $R$ and a certain circular cylinder of radius $R/2$ through the centre of the sphere. The part of the solid sphere located inside the cylinder is known as the Viviani solid. So named after V. Viviani (17th century).


Comments

Viviani's window is the set of points in $E^3$ given by $$ \{ (x,y,z)\ :\ x^2+y^2+z^2 \le 1\,,\ x^2+y^2 \le x \} \ . $$

References

[a1] M. Berger, "Geometry" , II , Springer (1987) pp. 84
How to Cite This Entry:
Viviani curve. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Viviani_curve&oldid=41906
This article was adapted from an original article by E.V. Shikin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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