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

**Contents:**

## 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) = x^{4}).

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.

## How To Articles

- Arc Length Formula
- Area Between Curve and Y-Axis
- Concave Up (Convex), Down
- Curve Sketching
- Find the Area Under the Curve (Excel, Definite Integrals
- Intersections
- Linearization and Linear Approximation
- Normal Line
- Parameterize a Curve
- Quadrifolium
- Riemann Sums
- Secant Line
- Slope of a Curve
- Tangent Lines
- Tangent Vector (Velocity Vector)

## Calculus Curves: A to Z

- Algebraic Curves
- Alysoid
- Ampersand Curve
- Astroid Curve
- Bean Curve
- Gaussian / Bell Curve
- Bow Curve
- Bullet Nose Curve
- Butterfly curve
- Cassini Oval
- Cissoid of Diocles
- Conchoid of Nicomedes
- Cruciform Curve
- Damped Sine Wave
- Deltoid Curve
- Devil’s Curve
- Eight Curve (Leminiscate of Gerono)
- Equiangular Spiral, Spira Mirabilis (Logarithmic Spiral)
- Fish Curve
- Folium of Descartes (Noeud de Ruban)
- Hippopede
- Hypocycloid Curve
- Kampyle of Eudoxus
- Klein Quartic
- Lamé curve
- Level Curve
- Lissajous Curves
- Lituus Curve
- Natural Equation of a Curve
- Nodal Cubic
- Pedal Curve
- Piriform Curve
- Plateau Curve
- Pursuit Curve
- Rectifiable Curve
- Rhodonea Curve (Rose Curve)
- Sawtooth Function (Wave)
- Serpentine Curve
- Simple Closed Curve
- Smooth Curve
- Spiric Section
- Tagaki Curve
- Tractrix Curve
- Trident of Newton
- Trifolium Curve
- Witch of Agnesi

## Calculus Curves: References

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[1] Degree of a Curve. Retrieved February 27, 2022 from: http://assets.press.princeton.edu/chapters/s9665.pdf

[2] Montoya, D. & Naves, D. On Plane and Space Curves. Retrieved January 15, 2022 from: https://web.ma.utexas.edu/users/drp/files/Spring2020Projects/DRP_Final_Project%20-%20Daniel%20Naves.pdf