"The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal." All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal.

Back in the day, before approximation methods like splines became vogue in my line of work, one way of computing the area under an empirically drawn curve was to painstakingly sketch it on a piece of graphing paper (usually with the assistance of a French curve) along with the axes, painstakingly cut along the curve, weigh the cut pieces, cut ...

$\begingroup$ Yes, you can buy a french curve, they are good for making pretty curves of different curvature. But the aesthetics of your cubic curves are ultimately less important than having the shape approximately right. i.e. Identifying where is the curve upward sloping and where is it downward sloping. $\endgroup$ –

2021年11月19日 · What is a French curve, as mentioned by Feynman? 4. Calculating values for cubic Bezier curve. 1.

2020年3月5日 · What is a French curve, as mentioned by Feynman? 29. How to verify if a curve is exponential by eyeballing? 0.

2016年9月18日 · When the French mathematician Gilles de Roberval first found the area under the sine and cosine curves in 1635, this was a very challenging problem that required a great deal of ingenuity. If we didn’t have the benefit of the Fundamental Theorem of Calculus, we would have to compute a difficult limit of sums using obscure trigonometric ...

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The curve in question is the "folium of Descartes", so called as Descartes sent this curve to Fermat as a challenge to the latter's claim for a method of determining slopes of tangent lines. Fermat handled it successfully, something made a bit more impressive by the fact that he accomplished it in 1638, prior to the more formal development of ...

2021年12月21日 · $\newcommand{\R}{\mathbb{R}}$ My preferred approach is to derive the Frenet-Serret equations from scratch without assuming arclength parameterization.

2019年12月10日 · If $(a_n)$ traverses a compact curve $\Gamma$ then there is a convergent subsequence $(b_n)$. But since (a_n) and (b_n) both traverse the same curve, they should converge to the same limit. But this is very counterintuitive. For example, I would not expect a sequence along some of the wilder space filling curves to converge, so I doubt my ...