Abstract
This chapter presents several excursions that delve more deeply into the geometry of curves, including some of the famous theorems in the field. The theory of curves is an old and extremely well developed mathematical topic. Our aim is simply to describe a few fundamental and interesting highlights.
A planimeter is a drafting instrument that measures the area enclosed in a region. Its design is based on Green’s theorem, one of several global results about curves presented in this chapter.
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Notes
- 1.
To help visualize the function \(\boldsymbol{\psi }\circ \boldsymbol{\alpha }_{s}\) and the degree of this function, a nice animation is available at http://www.mathematik.com/Hopf/index.html
- 2.
We recommend [7] for the history of the longitude problem and John Harrison’s story.
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Tapp, K. (2016). Additional Topics in Curves. In: Differential Geometry of Curves and Surfaces. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-39799-3_2
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DOI: https://doi.org/10.1007/978-3-319-39799-3_2
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Online ISBN: 978-3-319-39799-3
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