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curvature
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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. curved space-time intrinsic curvature of a surface
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An ancient egyptian hieroglyphic painted carving showing the falcon headed god Horus seated on a throne and holding a golden fly whisk. Before him are the Pharoah Seti and the goddess Isis. Interior wall of the temple to Osiris at Abydos, Egypt.
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A Factory Interior, watercolor, pen and gray ink, graphite, and white goache on wove paper by unknown artist, c. 1871-91; in the Yale Center for British Art. Industrial Revolution England
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Photos

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.
curved space-time
intrinsic curvature of a surface
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Related Topics and References

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Key People

Gaspard Monge, detail of an oil painting by Jean Naigeon, 1811; in the Museum of Fine Arts, Beaune, France.
Gaspard Monge, count de Péluse
French mathematician and public official