Difference between revisions of "Witch of Agnesi"
From Encyclopedia of Mathematics
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A plane curve, given in the Cartesian orthogonal coordinate system by the equation | A plane curve, given in the Cartesian orthogonal coordinate system by the equation | ||
| − | + | $$y(a^2+x^2)=a^3,\quad a>0.$$ | |
| − | + | [[File:Witch of Agnesi.svg|center|400px|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==== | ====References==== | ||
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| + | * {{Ref|1}} A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian) | ||
| + | * {{Ref|a1}} J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) | ||
| + | * {{Ref|b1}} Ian Stewart, ''Professor Stewart's Cabinet of Mathematical Curiosities'', Profile Books (2010) {{ISBN|1846683459}} | ||
| − | + | [[Category:Geometry]] | |
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Latest revision as of 20:28, 15 November 2023
versiera
A plane curve, given in the Cartesian orthogonal coordinate system by the equation
$$y(a^2+x^2)=a^3,\quad a>0.$$
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=18586
Witch of Agnesi. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Witch_of_Agnesi&oldid=18586
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article