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The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
Proebsting's paradox apparently shows that the Kelly criterion can lead to ruin. Sleeping Beauty problem: A probability problem that can be correctly answered as one half or one third depending on how the question is approached. Three Prisoners problem, also known as the Three Prisoners paradox: [3] A variation of the Monty Hall problem.
In a more philosophical treatise about the nature of axioms of geometry Richard discusses and rejects the following basic principles: Geometry is founded on arbitrarily chosen axioms - there are infinitely many equally true geometries. Experience provides the axioms of geometry, the basis is experimental, the development deductive.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In mathematical analysis, the staircase paradox is a pathological example showing that limits of curves do not necessarily preserve their length. [1] It consists of a sequence of "staircase" polygonal chains in a unit square , formed from horizontal and vertical line segments of decreasing length, so that these staircases converge uniformly to ...
A single ball is then drawn from the box. In this setting, the question from the original problem resolves to one of two different questions: "what is the probability that a green ball was placed in the box" and "what is the probability a green ball was drawn from the box". These questions ask for the probability of two different events, and ...
Hooper's paradox is a falsidical paradox based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwards get assembled into a rectangle with an area of only 30 units.
One of them includes the geometric progression problem. The story is first known to have been recorded in 1256 by Ibn Khallikan. [3] Another version has the inventor of chess (in some tellings Sessa, an ancient Indian minister) request his ruler give him wheat according to the wheat and chessboard problem. The ruler laughs it off as a meager ...
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