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Was (wer) ist gap theorem - definition
Gap theorem
THEOREM THAT THERE ARE ARBITRARILY LARGE COMPUTABLE GAPS IN THE HIERARCHY OF COMPLEXITY CLASSES
In computational complexity theory, the Gap Theorem, also known as the Borodin–Trakhtenbrot Gap Theorem, is a major theorem about the complexity of computable functions.
Fabry gap theorem
MATHEMATICAL THEOREM
Fabry's gap theorem
In mathematics, the Fabry gap theorem is a result about the analytic continuation of complex power series whose non-zero terms are of orders that have a certain "gap" between them. Such a power series is "badly behaved" in the sense that it cannot be extended to be an analytic function anywhere on the boundary of its disc of convergence.
Three-gap theorem
![In the [[Fibonacci word]], an example of a [[Sturmian word]], there are four distinct length-3 subsequences (in left-right order): 010, 100, 001, and 101.](https://commons.wikimedia.org/wiki/Special:FilePath/Fibonacci word cutting sequence.png?width=200 "In the [[Fibonacci word]], an example of a [[Sturmian word]], there are four distinct length-3 subsequences (in left-right order): 010, 100, 001, and 101.")
![End-on view of a plant stem in which consecutive leaves are separated by the [[golden angle]]](https://commons.wikimedia.org/wiki/Special:FilePath/Goldener Schnitt Blattstand.png?width=200 "End-on view of a plant stem in which consecutive leaves are separated by the [[golden angle]]")
![Tones of the [[Pythagorean tuning]] as points of the [[chromatic circle]]. Edges indicate the [[perfect fifth]]s used to construct the tuning; the two longer gap lengths between consecutive points represent [[semitone]]s, and the short gap where the [[dodecagram]] fails to close up is the [[Pythagorean comma]].](https://commons.wikimedia.org/wiki/Special:FilePath/PythagoreanTuningGeometric.png?width=200 "Tones of the [[Pythagorean tuning]] as points of the [[chromatic circle]]. Edges indicate the [[perfect fifth]]s used to construct the tuning; the two longer gap lengths between consecutive points represent [[semitone]]s, and the short gap where the [[dodecagram]] fails to close up is the [[Pythagorean comma]].")
![Points spaced at the golden angle along a [[Fermat spiral]] (center) are more uniformly spaced than for other angles.](https://commons.wikimedia.org/wiki/Special:FilePath/Sunflower spiral.png?width=200 "Points spaced at the golden angle along a [[Fermat spiral]] (center) are more uniformly spaced than for other angles.")
ON POINTS ON A CIRCLE PLACED AT ANGLES OF Θ, 2Θ, 3Θ ... FROM THE STARTING POINT
Three distance theorem; Steinhaus conjecture; Three gap theorem
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places points on a circle, at angles of , , , ... from the starting point, then there will be at most three distinct distances between pairs of points in adjacent positions around the circle.
