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The dual can be visualized as a locus in the plane in the form of the ''polar reciprocal''. This is defined with reference to a fixed conic ''Q'' as the locus of the poles of the tangent lines of the curve ''C''.<ref>{{cite book | author=J. Edwards | title=Differential Calculus
| publisher= MacMillan and Co.| location=London | pages=176| year=1892
|url=
==Properties of dual curve==
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===Dual polygon===
{{Main article|Dual polygon}}
The dual curve construction works even if the curve is [[piecewise linear curve|piecewise linear]] (or [[piecewise differentiable]], but the resulting map is degenerate (if there are linear components) or ill-defined (if there are singular points).
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* {{citation | last1=Arnold|first1=Vladimir Igorevich| title = Geometrical Methods in the Theory of Ordinary Differential Equations| publisher=Springer | year=1988|isbn=3-540-96649-8}}
*{{Citation |title=Plane Algebraic Curves|first=Harold|last=Hilton|publisher=Oxford|year=1920
|chapter=Chapter IV: Tangential Equation and Polar Reciprocation|url=
* {{Citation | last1=Fulton | first1=William | author1-link = William Fulton (mathematician) | title=Intersection Theory | publisher=Springer-Verlag | isbn=978-3-540-62046-4|year=1998}}
* {{Citation | last1=Walker | first1=R.J. | title=Algebraic Curves | publisher=Princeton |year=1950}}
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