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French curves were used in manual drafting to draw curves of various shapes. In general you would plot various known points on the paper, and seek to join them up on the edge of a French curve.  But why are they the shape they are?  The one on the top left is meant to be good for hyperbolas, top right for ellipses, and the big one for parabolas (all the conic sections except the circle, which can be drawn easily anyway).  Are these shapes somehow optimal for drawing curves? I can’t find any maths to support this.
Feynman did note this property: “the French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal.” This is a joke, as all smooth curves have this property. [more]  [read this book!]

French curves were used in manual drafting to draw curves of various shapes. In general you would plot various known points on the paper, and seek to join them up on the edge of a French curve.  But why are they the shape they are?  The one on the top left is meant to be good for hyperbolas, top right for ellipses, and the big one for parabolas (all the conic sections except the circle, which can be drawn easily anyway).  Are these shapes somehow optimal for drawing curves? I can’t find any maths to support this.

Feynman did note this property: “the French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal.” This is a joke, as all smooth curves have this property. [more]  [read this book!]

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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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