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Semicubical parabola

Semicubical Sem`i*cu"bic*al, a. (Math.) Of or pertaining to the square root of the cube of a quantity. Semicubical parabola, a curve in which the ordinates are proportional to the square roots of the cubes of the abscissas.

Semicubical Sem`i*cu"bic*al, a. (Math.) Of or pertaining to the square root of the cube of a quantity. Semicubical parabola, a curve in which the ordinates are proportional to the square roots of the cubes of the abscissas.

semicubical parabola

Parabola Pa*rab"o*la, n.; pl. Parabolas. [NL., fr. Gr. ?; -- so called because its axis is parallel to the side of the cone. See Parable, and cf. Parabole.] (Geom.) (a) A kind of curve; one of the conic sections formed by the intersection of the surface of a cone with a plane parallel to one of its sides. It is a curve, any point of which is equally distant from a fixed point, called the focus, and a fixed straight line, called the directrix. See Focus. (b) One of a group of curves defined by the equation y = ax^n where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = 3/2. See under Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.

Parabola Pa*rab"o*la, n.; pl. Parabolas. [NL., fr. Gr. ?; -- so called because its axis is parallel to the side of the cone. See Parable, and cf. Parabole.] (Geom.) (a) A kind of curve; one of the conic sections formed by the intersection of the surface of a cone with a plane parallel to one of its sides. It is a curve, any point of which is equally distant from a fixed point, called the focus, and a fixed straight line, called the directrix. See Focus. (b) One of a group of curves defined by the equation y = ax^n where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = 3/2. See under Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.

- In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve defined by an equation of the form (A) y 2 − a 2 x 3 = 0 , a > 0 ...

- {\vec {c}}(t)=({\tfrac {t^{3}}{3}},{\tfrac {t^{2}}{2}})} describes a semicubical parabola. From c → ′ ( t ) = ( t 2 , t ) {\displaystyle {\vec {c}}'(t)=(t^{2}...

- motion) and four with non-zero torsions (uniform rotation, catenary, semicubical parabola, general case): Case κ 1 = κ 2 = κ 3 = 0 {\displaystyle \kappa _{1}=\kappa...

- Ellipse Parabola Hyperbola Unit hyperbola Cubic parabola Folium of Descartes Cissoid of Diocles Conchoid of de Sluze Right strophoid Semicubical parabola Serpentine...

- include the catenary, circle, cycloid, logarithmic spiral, parabola, semicubical parabola and straight line. The lack of a closed form solution for the...

- of Diocles Conchoid of de Sluze Cubic with double point Strophoid Semicubical parabola Serpentine curve Trident curve Trisectrix of Maclaurin Tschirnhausen...

- the diagram: The blue parabola is an involute of the red semicubic parabola, which is actually the evolute of the blue parabola.) Proof of the last property:...

- integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line x = 0, the curves lying on the right hand...

- An ordinary cusp at (0, 0) on the semicubical parabola x3–y2=0...

- solution of the problem to rectify (i.e., find the length of) the semicubical parabola x3 = ay2, which had been discovered in 1657 by his pupil William...

- {\vec {c}}(t)=({\tfrac {t^{3}}{3}},{\tfrac {t^{2}}{2}})} describes a semicubical parabola. From c → ′ ( t ) = ( t 2 , t ) {\displaystyle {\vec {c}}'(t)=(t^{2}...

- motion) and four with non-zero torsions (uniform rotation, catenary, semicubical parabola, general case): Case κ 1 = κ 2 = κ 3 = 0 {\displaystyle \kappa _{1}=\kappa...

- Ellipse Parabola Hyperbola Unit hyperbola Cubic parabola Folium of Descartes Cissoid of Diocles Conchoid of de Sluze Right strophoid Semicubical parabola Serpentine...

- include the catenary, circle, cycloid, logarithmic spiral, parabola, semicubical parabola and straight line. The lack of a closed form solution for the...

- of Diocles Conchoid of de Sluze Cubic with double point Strophoid Semicubical parabola Serpentine curve Trident curve Trisectrix of Maclaurin Tschirnhausen...

- the diagram: The blue parabola is an involute of the red semicubic parabola, which is actually the evolute of the blue parabola.) Proof of the last property:...

- integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line x = 0, the curves lying on the right hand...

- An ordinary cusp at (0, 0) on the semicubical parabola x3–y2=0...

- solution of the problem to rectify (i.e., find the length of) the semicubical parabola x3 = ay2, which had been discovered in 1657 by his pupil William...

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