Suppose we have a map in which no single territory is made ...

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 ...

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 ...

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

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 ...

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.

Suppose you see a nickel rolling on the sidewalk. Imagine a pen ...

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.

Tessellations, more commonly referred to as tilings, are patterns which are repeated ...

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.

No restrictions on your remixing, redistributing, or making derivative works. Give credit to the author, as required.

Your remixing, redistributing, or making derivatives works comes with some restrictions, including how it is shared.

Your redistributing comes with some restrictions. Do not remix or make derivative works.

Most restrictive license type. Prohibits most uses, sharing, and any changes.

Copyrighted materials, available under Fair Use and the TEACH Act for US-based educators, or other custom arrangements. Go to the resource provider to see their individual restrictions.