Unit square
Square with side length one
In mathematics, a unit square is a square whose sides have length 1. Often, the unit square refers specifically to the square in the Cartesian plane with corners at the four points (0, 0), (1, 0), (0, 1), and (1, 1).
01Cartesian coordinates
In a Cartesian coordinate system with coordinates (x, y), a unit square is defined as a square consisting of the points where both x and y lie in a closed unit interval from 0 to 1.
That is, a unit square is the Cartesian product I × I, where I denotes the closed unit interval.
02Complex coordinates
The unit square can also be thought of as a subset of the complex plane, the topological space formed by the complex numbers. In this view, the four corners of the unit square are at the four complex numbers 0, 1, i, and 1 + i.
03Rational distance problem
It is not known whether any point in the plane is a rational distance from all four vertices of the unit square.
Sources and credits
This article is adapted from the Wikipedia article “Unit square”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Unit Square.svg by --pbroks13talk?, CC BY 3.0
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