Semicubical parabola for various a In mathematics a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form with a 0 in some Cartesian coordinate system Solving for y leads to the explicit form which imply that every real point satisfies x 0The exponent explains the term semicubical parabola
Semicubical Parabola Mathcurvecom
Neiles Semicubical Parabola MacTutor History of Mathematics
This curve sometimes called the semicubical parabola was discovered by William Neile in 1657 It was the first algebraic curve to have its arc length computed Wallis published the method in 1659 giving Neile the credit The Dutch writer Van Heuraet used the curve for a more general construction William Neile was born at Bishopsthrope in 1637
Semicubic parabola Encyclopedia of Mathematics
The Semicubical Parabola is probably the first curve in our NCB collection whose history is more fascinating than its mathematics William Neile 16371670 discovered and rectified measured its arc length His far more famous professor John Wallis 16161703 published Neiles method in De Cycloide 1659
A brief list of references that should be in most university libraries From the authors of Deposit 80 Bains Manjinder S and J B Thoo The Normals to a Parabola and the Real Roots of a Cubic The College Mathematics Journal 38 4 September 2007 pp 272277 Gray Alfred Modern Differential Geometry of Curves and Surfaces with MATHEMATICA CRC Press 1998 p 1027
Semicubical Parabola Michigan State University
Semicubical Parabola Concept
Semicubical Parabola from Wolfram MathWorld
Semicubic Parabola The Vshaped boundary is the semicubic parabola The dropletshaped boundaries are parallels of a pedal of the semicubic parabola t3t2 with respect to the point 020 semicubicParabolanb History From Robert Yates ay2x3 was the first algebraic curve rectified Neil 1659 Leibnitz in 1687 proposed the problem
DefinitionSemicubical Parabola ProofWiki
The semicubical parabola is a divergent parabola in the case where the polynomial P has a triple root It is the evolute of the parabola and the pedal of the cissoid of Diocles Contrary to the parabola the semicubical parabola can be parametrized by the curvilinear abscissa using rational functions
Semicubical parabola Wikipedia
The semicubical parabola is also known as Neiles parabola after William Neile the cuspidal cubic Also see Results about the semicubical parabola can be found here Historical Note The semicubical parabola was discovered and rectified by William Neile who published his findings in 1657
Semicubical Parabola Concept
The semicubical parabola is the curve along which a particle descending under gravity describes equal vertical spacings within equal times making it an Isochronous Curve The problem of finding the curve having this property was posed by Leibniz in 1687 and solved by Huygens MacTutor Archive The Arc Length Curvature and Tangential Angle are
A semicubic parabola is sometimes called a Neil parabola after W Neil who found its arc length in 1657 Figure s084040a References 1 AA Savelov Planar curves Moscow 1960 In Russian 2 AS Smogorzhevskii ES Stolova Handbook of the theory of planar curves of the third order Moscow 1961 In Russian
The Semicubic Parabola Neiles Parabola National Curve Bank
A semicubical parabola is a curve of the form yax32 1 ie it is half a cubic and hence has power 32 It has parametric equations x t2 2 y at3 3 and the polar equation rtan2thetasecthetaa 4 The evolute of the parabola is a particular case of the semicubical parabola also called Neiles parabola or the cuspidal cubic
Semicubic Parabola xahleeinfo
Neiles Parabola The Semicubical Parabola