Constructible Number
A number which can be represented by a Finite number of Additions, Subtractions, Multiplications, Divisions, and Finite Square Rootextractions of integers. Such numbers correspond to Line Segments which can be constructed usingonly Straightedge and Compass.
All Rational Numbers are constructible, and all constructible numbers are AlgebraicNumbers (Courant and Robbins 1996, p. 133). If a Cubic Equation with rational coefficients has norational root, then none of its roots is constructible (Courant and Robbins, p. 136).
In particular, let 
be the Field of Rational Numbers. Now construct an extensionfield 
of constructible numbers by the adjunction of 
, where 
is in , but is not,consisting of all numbers of the form 
, where 
. Next, construct an extension field 
of by the adjunction of 
, defined as the numbers 
, where 
, and 
is anumber in for which does not lie in . Continue the process 
times. Then constructible numbersare precisely those which can be reached by such a sequence of extension fields 
, where is a measure of the``complexity'' of the construction (Courant and Robbins 1996).
References
Courant, R. and Robbins, H. ``Constructible Numbers and Number Fields.'' §3.2 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 127-134, 1996.
- Lie Commutator
- Lie Derivative
- Lie Group
- Lie Groupoid
- Lie Product
- Lie-Type Group
- Life
- Life Expectancy
- Lift
- Lifting Problem
- Ligancy
- Likelihood
- Likelihood Ratio
- Limaçon
- Limaçon Evolute
- Limaçon of Pascal
- Limit
- Limit Comparison Test
- Limit Cycle
- Limit Point
- Lindeberg Condition
- Lindeberg-Feller Central Limit Theorem
- Lindelof's Theorem
- Lindemann-Weierstraß Theorem
- Lindenmayer System