Properties (52)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Mathematical Concept
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| gptkbp:application |
Used in classical constructions in geometry.
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| gptkbp:characteristics |
The set of constructible numbers is closed under addition.
The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of a power of 2 and a distinct Fermat prime. The set of constructible numbers can be used to construct squares. The set of constructible numbers can be used to construct regular octagons. The set of constructible numbers can be used to solve certain geometric problems. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of a power of 2 and a prime number. The set of constructible numbers is a subset of real numbers. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a power of 2. The set of constructible numbers can be used to construct lengths. The set of constructible numbers can be used to construct regular hexagons. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of distinct prime factors. All constructible numbers are real numbers. The set of constructible numbers is closed under taking square roots. The set of constructible numbers can be represented as points on a number line. The set of constructible numbers is countable. Can be expressed as a sum, difference, product, or quotient of integers and square roots. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of distinct composite factors. The set of constructible numbers can be used to construct regular polygons. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of distinct composite numbers. The set of constructible numbers is closed under multiplication. The set of constructible numbers can be used to construct angles. The set of constructible numbers is not closed under taking cube roots. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of a power of 2 and a composite factor. The set of constructible numbers can be used to construct triangles. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of a power of 2 and a composite number. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of a power of 2 and an odd prime. The set of constructible numbers can be used to construct regular dodecagons. The set of constructible numbers can be generated from the rational numbers. The set of constructible numbers can be used in compass and straightedge constructions. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of distinct prime numbers. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of a power of 2 and a prime factor. The set of constructible numbers includes all numbers of the form a + b√c. The set of constructible numbers can be used to construct regular polygons with a number of sides that is a product of distinct odd primes. The set of constructible numbers includes all rational numbers. The set of constructible numbers can be used to construct circles. Constructible_numbers_can_be_represented_as_coordinates_on_a_plane. The_set_of_constructible_numbers_can_be_used_to_construct_regular_polygons_with_a_number_of_sides_that_is_a_product_of_distinct_Fermat_primes. |
| gptkbp:defines |
Numbers that can be constructed using a finite number of steps with a compass and straightedge.
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| gptkbp:examples |
The number (1 + √5)/2 is constructible.
The number 1 is constructible. The number √2 is constructible. |
| gptkbp:historicalSignificance |
Related_to_problems_of_ancient_Greek_mathematics.
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| https://www.w3.org/2000/01/rdf-schema#label |
Constructible Numbers
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| gptkbp:isAttendedBy |
The number e is not constructible.
The number π is not constructible. |
| gptkbp:relatedPatent |
gptkb:Algebraic_Numbers
Field Extensions Galois Theory |
| gptkbp:relatedTo |
Field of Geometry
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| gptkbp:result |
A number is constructible if and only if it can be obtained from the rational numbers by a finite number of operations involving addition, subtraction, multiplication, division, and taking square roots.
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