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A Continuous Map from a 1-D Space to an $n$-D Space. Loosely speaking, the word ``curve'' is often used to mean the Graph of a 2- or 3-D curve. The simplest curves can be represented parametrically in $n$-D Space as

$\displaystyle x_1$ $\textstyle =$ $\displaystyle f_1(t)$  
$\displaystyle x_2$ $\textstyle =$ $\displaystyle f_2(t)$  
$\displaystyle \vdots$      
$\displaystyle x_n$ $\textstyle =$ $\displaystyle f_n(t).$  

Other simple curves can be simply defined only implicitly, i.e., in the form


See also Archimedean Spiral, Astroid, Asymptotic Curve, Baseball Cover, Batrachion, Bicorn, Bifolium, Bow, Bullet Nose, Butterfly Curve, Cardioid, Cassini Ovals, Catalan's Trisectrix, Catenary, Caustic, Cayley's Sextic, Cesàro Equation, Circle, Circle Involute, Cissoid, Cissoid of Diocles, Cochleoid, Conchoid, Conchoid of Nicomedes, Cross Curve, Cruciform, Cubical Parabola, Curve of Constant Precession, Curve of Constant Width, Curtate Cycloid, Cycloid, Delta Curve, Deltoid, Devil's Curve, Devil on Two Sticks, Dumbbell Curve, Dürer's Conchoid, Eight Curve, Electric Motor Curve, Ellipse, Ellipse Involute, Elliptic Curve, Envelope, Epicycloid, Equipotential Curve, Eudoxus's Kampyle, Evolute, Exponential Ramp, Fermat Conic, Folium of Descartes, Freeth's Nephroid, Frey Curve, Gaussian Function, Gerono Lemniscate, Glissette, Gudermannian Function, Gutschoven's Curve, Hippopede, Horse Fetter, Hyperbola, Hyperellipse, Hypocycloid, Hypoellipse, Involute, Isoptic Curve, Kappa Curve, Keratoid Cusp, Knot Curve, Lamé Curve, Lemniscate, L'Hospital's Cubic, Limaçon, Links Curve, Lissajous Curve, Lituus, Logarithmic Spiral, Maclaurin Trisectrix, Maltese Cross, Mill, Natural Equation, Negative Pedal Curve, Nephroid, Nielsen's Spiral, Orthoptic Curve, Parabola, Pear Curve, Pear-Shaped Curve, Pearls of Sluze, Pedal Curve, Peg Top, Piriform, Plateau Curves, Policeman on Point Duty Curve, Prolate Cycloid, Pursuit Curve, Quadratrix of Hippias, Radial Curve, Rhodonea, Rose, Roulette, Semicubical Parabola, Serpentine Curve, Sici Spiral, Sigmoid Curve, Sinusoidal Spiral, Space Curve, Strophoid, Superellipse, Swastika, Sweep Signal, Talbot's Curve, Teardrop Curve, Tractrix, Trident, Trident of Descartes, Trident of Newton, Trochoid, Tschirnhausen Cubic, Versiera, Watt's Curve, Whewell Equation, Witch of Agnesi



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© 1996-9 Eric W. Weisstein