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Calculus Curves

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In calculus, a curve is a mathematical object similar to a line, but it doesn’t have to be straight. A curve describes the path of a continuously moving point. As a practical example, an ellipse is a curve describing the motion of planets around a star.
calculus curves

Calculus originates from the study of curves and their properties; without curves, there would be no calculus.


  1. Calculus Curves: Classes
  2. How To Articles
  3. Calculus Curves: A to Z

Calculus Curves: Classes

Many curves studied in calculus belong to certain classes of curves, sharing certain features and properties. In a way, you can think of these curves as the “famous” math curves; they have been studied extensively in ancient or modern times.

Algebraic curves are any curves that can be defined by a polynomial equation [1]. Quartic curves are given by a fourth degree polynomial (e.g. f(x) = x4).

Plane curves lies in a two-dimensional plane. In other words, the points of the curve are all on the same plane; you could draw these curves on a sheet of paper, unlike a 3D shape like a cube (you could draw this on a sheet of paper, but to be accurate you would really need to create a 3D model). In comparison, a space curve’s points do not necessarily all lie on a single plane [2].

Special curves have well-known features. They include circles, ellipses, and hyperbolas. However, there are many more obscure curves that are special. These include the Peano Curve and Quadratix of Hippias.

quadratic special curve

The quadratix of Hippias is a special curve created by a uniform motion.

How To Articles

Calculus Curves: A to Z

Calculus Curves: References

Kepler orbit WillowW, CC BY 3.0 , via Wikimedia Commons
[1] Degree of a Curve. Retrieved February 27, 2022 from:
[2] Montoya, D. & Naves, D. On Plane and Space Curves. Retrieved January 15, 2022 from:

Stephanie Glen. "Calculus Curves" From Calculus for the rest of us!

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