: Mathematics: constructible number

geometry > geometric drawing > constructible number

number > algebraic number > constructible number

constructible number

In geometry and algebra, a real number ${\\displaystyle r}$ is constructible if and only if, given a line segment of unit length, a line segment of length ${\\displaystyle |r|}$ can be constructed with compass and straightedge in a finite number of steps. Equivalently, ${\\displaystyle r}$ is constructible if and only if there is a closed-form expression for ${\\displaystyle r}$ using only integers and the operations for addition, subtraction, multiplication, division, and square roots. The geometric definition of constructible numbers motivates a corresponding definition of constructible points, which can again be described either geometrically or algebraically. A point is constructible if it can be produced as one of the points of a compass and straight edge construction (an endpoint of a line segment or crossing point of two lines or circles), starting from a given unit length segment. Alternatively and equivalently, taking the two endpoints of the given segment to be the points (0, 0) and (1, 0) of a Cartesian coordinate system, a point is constructible if and only if its Cartesian coordinates are both constructible numbers. Constructible numbers and points have also been called ruler and compass numbers and ruler and compass points, to distinguish them from numbers and points that may be constructed using other processes.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Constructible_number)

http://data.loterre.fr/ark:/67375/PSR-B2H0L954-0

RDF/XML TURTLE JSON-LD Created 8/4/23, last modified 10/18/24

Loterre