Shapes & Space

In Euclidean plane geometry, a triangle's interior angles add up to 180 degrees.

A circle's edge stays perfectly equidistant from its center, with no straight sides or corners.

A square, with four equal sides and right angles, counts as a special case of both rectangle and rhombus.

A rectangle's four right angles come with opposite sides that are always equal in length.

A pentagon has five sides and five angles, and also names the US Department of Defense's headquarters building.

The six-sided hexagon appears naturally in the honeycomb structures built by bees.

A polygon is any closed shape of straight segments, named for however many sides it has.

A golden rectangle's sides follow the golden ratio, a proportion often described as especially pleasing.

Area measures the space inside a two-dimensional shape, expressed in square units.

Perimeter totals the distance around a shape's edge by adding up the lengths of every side.

Angles measure the space between two intersecting lines, expressed in degrees or radians.

Parallel lines stay the same distance apart forever, never intersecting no matter how far extended.

A cube's six identical square faces are joined by twelve edges, all equal in length.

A sphere encloses more volume per unit of surface area than any other three-dimensional shape.

A cylinder's two parallel circular bases are joined by a single curved surface.

A cone tapers smoothly from a flat circular base up to a single point called the apex.

A pyramid's triangular faces converge at a single apex above a base that can be any polygon.

Exactly five Platonic solids exist, each built entirely from identical regular polygon faces.

Volume measures the space inside a three-dimensional object, expressed in cubic units.

Tessellations tile a surface with repeating shapes and no gaps, a technique famous in M. C. Escher's art.

The Pythagorean theorem states that a right triangle's two shorter sides squared sum to the hypotenuse squared.

Reflectional symmetry gives matching mirrored halves. Rotational symmetry leaves a figure unchanged after a turn smaller than a full…

Fractals repeat their pattern at every zoom level, a field named and popularized by Benoit Mandelbrot.

A Möbius strip's single twist gives it only one continuous side and a single edge.

A tangram's seven flat pieces can be rearranged into countless different silhouette shapes.

Non-Euclidean geometry's study of curved space helped provide the mathematical basis for general relativity.

The coordinate plane, named for René Descartes, locates points using a horizontal and vertical axis.