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differential geometry: Quick Facts

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An annular strip (the region between two concentric circles) can be cut and bent into a helical strake that follows approximately the contour of a cylinder. Techniques of differential geometry are employed to find the dimensions of the annular strip that will best match the required curvature of the strake.
The curvature at each point of a line is defined to be 1/r, where r is the radius of the osculating, or “kissing,” circle that best approximates the line at the given point.
The normal, or perpendicular, at each point of a surface defines the corresponding tangent plane, and vice versa.
example of straight line not being shortest distance between two points
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Joseph Liouville
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Shiing-shen Chern
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Henry Whitehead
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American mathematician
Louis Nirenberg
Louis Nirenberg
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Shing-Tung Yau
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