square

Also known as 2-orthoplex, bicross, 2-cube, 2-cross-polytope, regular quadrilateral

In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal sides. As with all rectangles, a square's angles are right angles (90 degrees, or Pi|/2 radians), making adjacent sides perpendicular. The area of a square is the side length multiplied by itself, and so in algebra, multiplying a number by itself is called squaring.

AI overview

A square is a four-sided shape where all sides are equal in length and all corners form right angles (90 degrees). Squares matter because they're fundamental in geometry and mathematics—their properties are used to calculate area, and the concept of "squaring" a number (multiplying it by itself) is named after this shape's mathematical importance.

AI-generated from the Wikipedia summary — may contain errors.

Key facts

Polygon.name: Square
Polygon.image: Square with offset tick marks.svg
Polygon.caption: A square. The blue ∟ annotations mark equal right angles at its vertices and the red // annotations mark equal side lengths.
Polygon.edges: 4
Polygon.symmetry: order-8 dihedral
Polygon.area: side2
Polygon.angle: /2 (90°)
Polygon.perimeter: 4 · side

via Wikipedia infobox

Wikidata facts

Image: Regular polygon 4 annotated.svg

Show 3 more facts

Unicode character: ⬛
Commons category: Square (geometry)
Schläfli symbol: {4}

Sources (6)

via Wikidata · CC0

~33 min read

Article

17 sections

Contents

Definitions and characterizations
Properties
Measurement
Symmetry
Inscribed and circumscribed circles
Applications
Constructions
Coordinates and equations
Compass and straightedge
Related topics
Inscribed squares
Area and quadrature <span class="anchor" id="Squaring the circle"></span>
Tiling and packing
Counting
Other geometries
See also
References

Equal squares can tile the plane edge-to-edge in the square tiling. Square tilings are ubiquitous in tiled floors and walls, graph paper, image pixels, and game boards. Square shapes are also often seen in building floor plans, origami paper, food servings, in graphic design and heraldry, and in instant photos and fine art.