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The exponent laws, also called the laws of indices (Higgens 1998) or power rules (Derbyshire 2004, p. 65), are the rules governing the combination of exponents (powers). The ...

The far-out point F of a triangle DeltaABC is the inverse point of the triangle centroid with respect to the circumcircle of DeltaABC. For a triangle with side lengths a, b, ...

Every finite simple group (that is not cyclic) has even group order, and the group order of every finite simple noncommutative group is doubly even, i.e., divisible by 4 ...

Fermat's sandwich theorem states that 26 is the only number sandwiched between a perfect square number (5^2=25) and a perfect cubic number (3^3=27). According to Singh ...

A reduction system is called finitely terminating (or Noetherian) if there are no infinite rewriting sequences. This property guarantees that any rewriting algorithm will ...

A module M over a unit ring R is called flat iff the tensor product functor - tensor _RM (or, equivalently, the tensor product functor M tensor _R-) is an exact functor. For ...

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Phoenician art from the 9th century BC ...

A graph is a forbidden topological minor (also known as a forbidden homeomorphic subgraph) if its presence as a homeomorphic subgraph of a given graph (i.e., there is an ...

A friendly number is a number that is a member of a friendly pair or a higher-order friendly n-tuple. Numbers that are not friendly are said to be solitary. There are some ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...