Constructible numbers

Constructible numbers are lengths or values that can be obtained using only a straightedge and compass starting from a known segment length, through a finite sequence of geometric steps like drawing circles and lines. In algebraic terms, they are numbers that can be obtained from rational numbers using a series of operations involving addition, subtraction, multiplication, division, and square roots. These numbers correspond to the solutions of certain polynomial equations that can be solved with geometric construction, making them central to classical questions about which lengths can be constructed with simple tools.