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Difference between revisions of "Witch of Agnesi"

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$$y(a^2+x^2)=a^3,\quad a>0.$$
 
$$y(a^2+x^2)=a^3,\quad a>0.$$
  
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/w098050a.gif" />
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[[File:Witch of Agnesi.svg|center|400px|Witch of Agnesi]]
 
 
Figure: w098050a
 
  
 
If $a$ is the diameter of a circle with centre at the point $(0,a/2)$, $OA$ is a secant, $CB$ and $AM$ are parallel to the $x$-axis, and $BM$ is parallel to the $y$-axis (see Fig.), then the witch of Agnesi is the locus of the points $M$. If the centre of the generating circle and the tangent $CB$ are shifted along the $y$-axis, the curve thus obtained is called Newton's aguinea and is a generalization of the witch of Agnesi. The curve is named after Maria Gaetana Agnesi (1718-1799), who studied it.
 
If $a$ is the diameter of a circle with centre at the point $(0,a/2)$, $OA$ is a secant, $CB$ and $AM$ are parallel to the $x$-axis, and $BM$ is parallel to the $y$-axis (see Fig.), then the witch of Agnesi is the locus of the points $M$. If the centre of the generating circle and the tangent $CB$ are shifted along the $y$-axis, the curve thus obtained is called Newton's aguinea and is a generalization of the witch of Agnesi. The curve is named after Maria Gaetana Agnesi (1718-1799), who studied it.
 
====References====
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)</TD></TR></table>
 
 
 
  
 
====Comments====
 
====Comments====
 
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The unusual name derives from a misreading of the term ''la versiera'' (from Latin ''versoria'') "rope that turns a sail" as ''l'aversiera'', "witch".
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  J.D. Lawrence,  "A catalog of special plane curves" , Dover, reprint  (1972)</TD></TR></table>
 
  
====Comments====
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* {{Ref|1}} A.A. Savelov,  "Planar curves" , Moscow  (1960)  (In Russian)
The unusual name derives from a misreading of the term ''la versiera'' (from Latin ''versoria'') "rope that turns a sail" as ''l'aversiera'', "witch".
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* {{Ref|a1}} J.D. Lawrence,  "A catalog of special plane curves" , Dover, reprint  (1972)</TD></TR></table>
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* {{Ref|b1}} Ian Stewart, ''Professor Stewart's Cabinet of Mathematical Curiosities'', Profile Books (2010) ISBN 1846683459
  
 
====References====
 
<table><TR><TD valign="top">[b1]</TD> <TD valign="top">  Ian Stewart, ''Professor Stewart's Cabinet of Mathematical Curiosities'', Profile Books (2010) ISBN 1846683459</TD></TR></table>
 
  
 
[[Category:Geometry]]
 
[[Category:Geometry]]

Revision as of 18:50, 16 March 2023

versiera

A plane curve, given in the Cartesian orthogonal coordinate system by the equation

$$y(a^2+x^2)=a^3,\quad a>0.$$

Witch of Agnesi

If $a$ is the diameter of a circle with centre at the point $(0,a/2)$, $OA$ is a secant, $CB$ and $AM$ are parallel to the $x$-axis, and $BM$ is parallel to the $y$-axis (see Fig.), then the witch of Agnesi is the locus of the points $M$. If the centre of the generating circle and the tangent $CB$ are shifted along the $y$-axis, the curve thus obtained is called Newton's aguinea and is a generalization of the witch of Agnesi. The curve is named after Maria Gaetana Agnesi (1718-1799), who studied it.

Comments

The unusual name derives from a misreading of the term la versiera (from Latin versoria) "rope that turns a sail" as l'aversiera, "witch".

References

  • [1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)
  • [a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
  • [b1] Ian Stewart, Professor Stewart's Cabinet of Mathematical Curiosities, Profile Books (2010) ISBN 1846683459
How to Cite This Entry:
Witch of Agnesi. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Witch_of_Agnesi&oldid=34039
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article