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Divine Proportions does not assume much in the way of mathematical background in its readers, but its many long formulas, frequent consideration of finite fields, and (after part I) emphasis on mathematical rigour are likely to be obstacles to a popular mathematics audience. Instead, it is mainly written for mathematics teachers and researchers.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
I just created this article, because Wildberger clearly needed an article, as he has made an important contribution to mathematics with his new subject known as "rational trigonometry."Dratman 01:56, 17 September 2011 (UTC) I think there have been changes since the Wikipedia:Articles for deletion/Norman J. Wildberger discussion. Wildberger is ...
The elements of this field are precisely those that may be expressed as a formula in the original points using only the operations of addition, subtraction, multiplication, division, complex conjugate, and square root, which is easily seen to be a countable dense subset of the plane. Each of these six operations corresponding to a simple ...
All 12 orthogons, when formed together, create an entire unit: a square that is developed into a double square. [ 14 ] Perhaps the most popular among the ortogons is the auron or golden rectangle , which is produced by projecting the diagonal that goes from the middle point of a side of a square to one of the opposite vertexes, until it is ...
For instance, if Δ is the boundary of the octahedron, then its f-vector is (1, 6, 12, 8), and if Δ is the first simplicial complex pictured above, its f-vector is (1, 18, 23, 8, 1). A complete characterization of the possible f -vectors of simplicial complexes is given by the Kruskal–Katona theorem .
In mathematics, the supergolden ratio is a geometrical proportion close to 85/58. Its true value is the real solution of the equation x 3 = x 2 + 1. The name supergolden ratio results from analogy with the golden ratio, the positive solution of the equation x 2 = x + 1. A triangle with side lengths ψ, 1, and 1 ∕ ψ has an angle of exactly ...
Graph showing relationships between the rule of twelfths (coloured bars), a sine wave (dashed blue curve) and a clockface, if high tide occurs at 12:00. The rule of twelfths is an approximation to a sine curve. It can be used as a rule of thumb for estimating a changing quantity where both the quantity and the steps are easily divisible by 12 ...