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In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients and the highest-order terms of F form a polynomial divisible by x2 + y2. More precisely, if
F = Fn + Fn−1 + ... + F1 + F0, where each Fi is homogeneous of degree i, then the curve F(x, y) = 0 is circular if and only if Fn is divisible by x2 + y2.
Equivalently, if the curve is determined in homogeneous coordinates by G(x, y, z) = 0, where G is a homogeneous polynomial, then the curve is circular if and only if G(1, i, 0) = G(1, −i, 0) = 0. In other words, the curve is circular if it contains the circular points at infinity, (1, i, 0) and (1, −i, 0), when considered as a curve in the complex projective plane.
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In geometry, a circularalgebraiccurve is a type of plane algebraiccurve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients...
space and skew curves apply also to real algebraiccurves, although the above definition of a curve does not apply (a real algebraiccurve may be disconnected)...
instance, the zero set of the polynomial below forms a non-circular smooth algebraiccurve of constant width: f ( x , y ) = ( x 2 + y 2 ) 4 − 45 ( x 2...
rational points on the unit circle CircularalgebraiccurveCircular distribution Circular statistics Mean of circular quantities Polygon-circle graph Splitting...
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changes. In classical algebraic geometry, adjectives were often used as nouns: for example, "quartic" could also be short for "quartic curve" or "quartic surface"...
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tautochrone curve or isochrone curve (from Ancient Greek ταὐτό (tauto-) 'same', ἴσος (isos-) 'equal', and χρόνος (chronos) 'time') is the curve for which...
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connection between his algebra and logic was later put on firm ground in the setting of algebraic logic, which also studies the algebraic systems of many other...
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been conjectured that they may be realized by copies of any non-circular simple closed curve in space. In knot theory, the Borromean rings can be proved to...
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