hyperosculating parabola - traducción al ruso
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hyperosculating parabola - traducción al ruso

Cuspidal cubic; Neile's parabola; Semi-cubic parabola; Semicubic parabola; Neile parabola; Neile's Parabola
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hyperosculating parabola      

математика

гиперсоприкасающаяся парабола

semicubical parabola         

общая лексика

полукубическая парабола

parabola         
PLANE CURVE: SYMMETRICAL CONIC SECTION
X squared; Parabolas; Parabolic Equation; Conic section/Proofs; Derivations of Conic Sections; Parabola/Proofs; Derivation of parabolic form; Derivations of conic sections; Parabolic curve; Lambert's Theorem; Parabolae; Parabolic motion

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общая лексика

парабола

существительное

математика

парабола

Definición

Parabola
·noun One of a group of curves defined by the equation y = axn where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = /. ·see under Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.
II. Parabola ·noun 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.

Wikipedia

Semicubical parabola

In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form

y 2 a 2 x 3 = 0 {\displaystyle y^{2}-a^{2}x^{3}=0}

(with a ≠ 0) in some Cartesian coordinate system.

Solving for y leads to the explicit form

y = ± a x 3 2 , {\displaystyle y=\pm ax^{\frac {3}{2}},}

which imply that every real point satisfies x ≥ 0. The exponent explains the term semicubical parabola. (A parabola can be described by the equation y = ax2.)

Solving the implicit equation for x yields a second explicit form

x = ( y a ) 2 3 . {\displaystyle x=\left({\frac {y}{a}}\right)^{\frac {2}{3}}.}

The parametric equation

x = t 2 , y = a t 3 {\displaystyle \quad x=t^{2},\quad y=at^{3}}

can also be deduced from the implicit equation by putting t = y a x . {\textstyle t={\frac {y}{ax}}.}

The semicubical parabolas have a cuspidal singularity; hence the name of cuspidal cubic.

The arc length of the curve was calculated by the English mathematician William Neile and published in 1657 (see section History).

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