Curve
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In mathematics, a curve is an object similar to a line, but that does not have to be straight.
Megalithic art from Newgrange showing an early interest in curves
A dragon curve with a positive area
Euclid's Elements
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The Elements is a mathematical treatise written c. 300 BC by the Ancient Greek mathematician Euclid.
Curve
…straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is […] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else…
Papyrus Oxyrhynchus 29, a fragment of Euclid's Elements dated to c. 3rd–4th century AD. Found at Oxyrhynchus, the diagram accompanies Book II, Proposition 5.
Euclid's subdivision of line segment AB into the golden ratio from Book II Proposition 11, with an arc added to the traditional diagram. The construction finds the midpoint E of side AC of square ABCD, intersects line AC at F with a circle of radius EB, and constructs a second square AFGH, whose vertex H is the subdivision point.
The Pythagorean theorem in MS. Vat.gr.190
A woman teaching geometry, from a manuscript (c. 1309–1316) of Adelard of Bath's 12th century translation of the Elements from Arabic into Latin