Cubic Curve
A cubic curve is an Algebraic Curve of degree 3. An algebraic curve over a Field 
is an equation 
,where 
is a Polynomial in 
and 
with Coefficients in , and the degree of 
isthe Maximum degree of each of its terms (Monomials).
Newton 
showed that all cubics can be generated by the projection of the five divergent cubic parabolas. Newton'sclassification of cubic curves appeared in the chapter ``Curves'' in Lexicon Technicum by John Harris published in Londonin 1710. Newton also classified all cubics into 72 types, missing six of them. In addition, he showed that any cubic can beobtained by a suitable projection of the Elliptic Curve
 | (1) |
 | (2) |
 | (3) |
 | (4) |
because it lacked generality. Plückerlater gave a more detailed classification with 219 types. 
Pick a point 
, and draw the tangent to the curve at . Call the point where this tangent intersects the curve 
. Draw another tangent and call the point of intersection with the curve 
. Every curve of third degree has the propertythat, with the areas in the above labeled figure,
 | (5) |
References
Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 114-118, 1991. Newton, I. Mathematical Works, Vol. 2. New York: Johnson Reprint Corp., pp. 135-161, 1967. Wall, C. T. C. ``Affine Cubic Functions III.'' Math. Proc. Cambridge Phil. Soc. 87, 1-14, 1980. Westfall, R. S. Never at Rest: A Biography of Isaac Newton. New York: Cambridge University Press, 1988. Yates, R. C. ``Cubic Parabola.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 56-59, 1952.
- Squarable
- Square
- Square Bracket Polynomial
- Square Cupola
- Square Curve
- Square Cutting
- Squared
- Squared Square
- Square-Free
- Squarefree
- Butterfly Catastrophe
- Butterfly Curve
- Butterfly Effect
- Butterfly Fractal
- Butterfly Polyiamond
- Butterfly Theorem
- Bäcklund Transformation
- Bézier Curve
- Bézier Spline
- C
- C*
- Cable Knot
- Cactus Fractal
- Cake Cutting
- Cal