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In the mathematical field of graph theory, the ladder graph L n is a planar, undirected graph with 2n vertices and 3n – 2 edges. [ 1 ] The ladder graph can be obtained as the Cartesian product of two path graphs , one of which has only one edge: L n ,1 = P n × P 2 .
The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
(i.e. F n is obtained from F n-1 by adjoining a 2 n th root of 2), is an infinite tower. If p is a prime number the p th cyclotomic tower of Q is obtained by letting F 0 = Q and F n be the field obtained by adjoining to Q the p n th roots of unity. This tower is of fundamental importance in Iwasawa theory.
The proposition in probability theory known as the law of total expectation, [1] the law of iterated expectations [2] (LIE), Adam's law, [3] the tower rule, [4] and the smoothing theorem, [5] among other names, states that if is a random variable whose expected value is defined, and is any random variable on the same probability space, then
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
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Crossed ladders of lengths a and b. h is half the harmonic mean of A and B; equivalently, the reciprocals of A and B sum to the reciprocal of h (the optic equation). Given a, b, and h, find w. Two ladders of lengths a and b lie oppositely across an alley, as shown in the figure. The ladders cross at a height of h above the alley floor. What is ...
The tower rule may refer to one of two rules in mathematics: Law of total expectation, in probability and stochastic theory; a rule governing the degree of a field extension of a field extension in field theory