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Let f(1)=1, and let f(n) be the number of occurrences of n in a nondecreasing sequence of integers. then the first few values of f(n) are 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, ... ...

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio, called the ratio of magnification ...

Two square matrices A and B that are related by B=X^(-1)AX, (1) where X is a square nonsingular matrix are said to be similar. A transformation of the form X^(-1)AX is called ...

Two triangles are similar if their triples of vertex angles are the same.

A transformation that preserves angles and changes all distances in the same ratio, called the ratio of magnification. A similarity can also be defined as a transformation ...

To multiply the size of a d-D object by a factor a, c=a^d copies are required, and the quantity d=(lnc)/(lna) is called the similarity dimension.

External (or positive) and internal (or negative) similarity points of two circles with centers C and C^' and radii r and r^' are the points E and I on the lines CC^' such ...

The term "similarity transformation" is used either to refer to a geometric similarity, or to a matrix transformation that results in a similarity. A similarity ...

If two similar figures lie in the plane but do not have parallel sides (i.e., they are similar but not homothetic), there exists a center of similitude, also called a ...

The locus of the similitude center of two circles.