A catenary is the curve created by a theoretical representation of a hanging chain or cable held at both ends.

The same object can look completely different depending on which coordinate system is used.

We visualize complex numbers in the same way we visualize an ordered pair on a plane.

Suppose we have a map in which no single territory is made up of disconnected regions. How many colors are needed to color the territories of this map, if all the territories that share a border segment must be of different colors?

This image is an artistic rendering of the Harter-Heighway Curve (also called the Dragon Curve), which is a fractal. It is often referred to as the Jurassic Park Curve because it garnered popularity after being drawn and alluded to in the novel Jurassic Park by Michael Crichton (1990).

This image is a Henon Attractor (named after astronomer and mathematician Michel Henon), which is a fractal in the division of the chaotic strange attractor. This image is a Henon Attractor (named after astronomer and mathematician Michel Henon), which is a fractal in the division of the chaotic strange attractor. This image is a Henon Attractor (named after astronomer and mathematician Michel Henon), which is a fractal in the division of the chaotic strange attractor. This image is a Henon Attractor (named after astronomer and mathematician Michel Henon), which is a fractal in the division of the chaotic strange attractor. This image is a Henon Attractor (named after astronomer and mathematician Michel Henon), which is a fractal in the division of the chaotic strange attractor.

This is an animation of a square rotating in hyperbolic geometry as represented by the Poincaré Disk Model.

This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles.

The image is an example of a Koch Snowflake, a fractal that first appeared in a paper by Swede Niels Fabian Helge von Koch in 1904. It is made by the infinite iteration of the Koch curve.

A Mobius strip, also referred to as a Mobius band, is a surface with only one side and one edge.

Newton's Basin is a visual representation of Newton's Method, which is a procedure for estimating the root of a function.

A parabola is a u-shaped curve that arises not only in the field of mathematics, but also in many other fields such as physics and engineering.

Solar Dishes such as the one shown use a parabolic shape to focus the incoming light into a single collector.

Suppose you see a nickel rolling on the sidewalk. Imagine a pen traced the path of one fixed point on the coin as it rolled. A curve would be created. This curve is called a roulette.

Sierpinski's triangle is a simple fractal created by repeatedly removing smaller triangles from the original shape.

Tessellations, more commonly referred to as tilings, are patterns which are repeated over and over without overlapping or leaving any gaps. Tessellations are seen throughout art history from ancient architecture to modern art.

The vector field shown here represents the velocity of a fluid. Each vector represents the fluid's velocity at the point the arrow begins.