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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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Leonardo da Vinci (1452-1519), Italian Renaissance painter from Florence. Engraving by Cosomo Colombini (d. 1812) after a Leonardo self portrait. Ca. 1500.
10 Famous Artworks by Leonardo da Vinci
Calendar showing the month of February
Why Are There Only 28 Days in February?
Prisoners of Buchenwald concentration camp, near Weimar, Germany, April 16, 1945, liberated by American troops of the 80th Division. Elie Wiesel (7th from the left on the middle bunk next to the vertical post) World War II Holocaust
What Is the Origin of the Term Holocaust?
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.
11 Egyptian Gods and Goddesses
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
Inventors and Inventions of the Industrial Revolution
Mona Lisa, oil on wood panel by Leonardo da Vinci, c. 1503-06; in the Louvre, Paris, France. 77 x 53 cm.
Why Is the Mona Lisa So Famous?
The impeachment trial of Pres. Andrew Johnson, illustration from Frank Leslie's Illustrated Newspaper, March 28, 1868.
What If the President Is Impeached?

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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