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I am going to deliver some lectures on curvature, envelopes and asypmtotes of curves in $\mathbb{R^2}$. Please recommend me some good books with geometric intuition in this area.

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    $\begingroup$ You have a differential geometry tag here. Curvature is a differential geometry concept (although it can be defined in single-variable calculus for curves in $\Bbb R^2$); asymptotes are a high school precalculus subject. Envelopes naturally require multivariable calculus. Can you be more specific about your background and that of your audience? (That said, I know no source that covers all three of these.) $\endgroup$ Mar 11, 2021 at 5:45
  • $\begingroup$ It's hard to find useful books on applications of those things, because the calculus level stuff is not sufficient to have applications yet. $\endgroup$ Mar 11, 2021 at 5:56
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    $\begingroup$ There is a lot of differences between a course geared towards first-year undergrads and final-year undergrads. $\endgroup$ Mar 11, 2021 at 6:04
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    $\begingroup$ Two books that might have useful things for you: Lines and Curves by Gutenmacher/Vasilyev (2004) and (selected chapters of) Uncommon Mathematical Excursions. Polynomia and Related Realms by Kalman (2009). $\endgroup$ Mar 11, 2021 at 12:12
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    $\begingroup$ Also, don't overlook the many classic calculus texts from the late 1800s which often had a lot of material on these topics, such as Rice/Johnson (1877), Todhunter (1871), Edwards (1892), Byerly (1879), Smith (1898), and many others. $\endgroup$ Mar 11, 2021 at 12:12

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