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Let the absolute frequencies of occurrence of an event in a number of class intervals be denoted f_1, f_2, .... The cumulative frequency corresponding to the upper boundary ...

The equation x^p=1, where solutions zeta_k=e^(2piik/p) are the roots of unity sometimes called de Moivre numbers. Gauss showed that the cyclotomic equation can be reduced to ...

There are many mathematical and recreational problems related to folding. Origami, the Japanese art of paper folding, is one well-known example. It is possible to make a ...

In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique ...

The grouping of data into bins (spaced apart by the so-called class interval) plotting the number of members in each bin versus the bin number. The above histogram shows the ...

The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...

Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle. If the class of curves to be considered is limited to smooth ...

The three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...