CONSTRUCTIBLE NUMBER Meaning and
Definition
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A constructible number refers to a class of mathematical numbers that can be constructed using only a straightedge and compass in a finite number of steps. In other words, it is a real number that can be obtained by starting with the number 1 and performing a series of operations using only the basic tools of a straightedge, which can create lines, and a compass, which can create circles.
Constructible numbers can be thought of as the set of all real numbers that can be calculated by solving a set of geometric problems. These problems involve drawing straight lines and creating circles in order to find the solution. The operations that can be performed include drawing lines through given points, finding the intersection point of two lines, and creating circles with a given radius from a given point.
Generally, constructible numbers are a subset of algebraic numbers, meaning they can be expressed as the solution to a polynomial equation with rational coefficients. However, not all algebraic numbers are constructible. For example, the square root of 2 is algebraic but not constructible.
The concept of constructible numbers has its roots in ancient Greek geometry and the classical geometric constructions that were used to solve mathematical problems. Today, the theory of constructible numbers has applications in fields such as geometry, number theory, and abstract algebra.
Etymology of CONSTRUCTIBLE NUMBER
The term "constructible number" comes from the field of mathematics, specifically from the branch of geometry known as compass and straightedge construction. In this context, a constructible number is a number that can be "constructed" or "drawn" using only a compass and a straightedge.
The etymology of the word "constructible" can be traced back to the Latin word "constructus", the past participle of "construere", meaning "to build" or "to construct". This Latin term is derived from the combination of the prefix "con-" (meaning "together" or "with") and the verb "struere" (meaning "to pile up" or "to build").
Therefore, a constructible number refers to a number that can be "built" or "constructed" using geometric techniques involving a compass and a straightedge.
