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constructible numbers
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(Definition)
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Given an integer $m$ consisting of $k$ digits $d_1, \dots, d_k$ in base $b$ let $$j = \sum_{i = 1}^{k} d_i,$$ then $j$ is the digit sum of $m$ Iterating this operation on the digits of $j$ until $j < b$ gives the digital root or repeated digit sum of $m$ The digit sum and digital root of a number are the same only if the additive persistence of the digital root is 1.
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"constructible numbers" is owned by CWoo. [ full author list (2) | owner history (1) ]
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See Also: Euclidean field, compass and straightedge construction, theorem on constructible angles, theorem on constructible numbers
| Also defines: |
ruler and compass operation, compass and ruler operation, compass and straightedge operation, straightedge and compass operation, constructible number, constructible from, constructible, field of constructible numbers, field of real constructible numbers |
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Cross-references: algebra, one-to-one correspondence, positive elements, Euclidean plane, lengths, rational number, compass, ruler, real number, points, ruler and compass construction, algorithm, extension, binary, finite sequence, operation, unary, square root, binary operations, complex number, contains, conversely, numbers, subset, field, properties, Euclidean, subfield
There are 10 references to this entry.
This is version 14 of constructible numbers, born on 2007-06-13, modified 2007-06-25.
Object id is 9583, canonical name is ConstructibleNumbers.
Accessed 6025 times total.
Classification:
| AMS MSC: | 12D15 (Field theory and polynomials :: Real and complex fields :: Fields related with sums of squares ) |
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Pending Errata and Addenda
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