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Enclose a sphere in a cylinder and cut out a spherical segment by slicing twice perpendicularly to the cylinder's axis. Then the lateral surface area of the spherical segment ...

There are at least two results known as "the area principle." The geometric area principle states that (|A_1P|)/(|A_2P|)=(|A_1BC|)/(|A_2BC|). (1) This can also be written in ...

An Argand diagram is a plot of complex numbers as points z=x+iy in the complex plane using the x-axis as the real axis and y-axis as the imaginary axis. In the plot above, ...

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

If f(z) is meromorphic in a region R enclosed by a contour gamma, let N be the number of complex roots of f(z) in gamma, and P be the number of poles in gamma, with each zero ...

The term "Aristotle gap"' is introduced in this work to refer to the angle between the first and last member of a 5-tetrahedral ring. This gap has angle measure theta = ...

An arithmetic function is a function f(n) defined for all n in N, usually taken to be complex-valued, so that f:N->C (Jones and Jones 1998, p. 143). An alternative definition ...

The best known example of an Anosov diffeomorphism. It is given by the transformation [x_(n+1); y_(n+1)]=[1 1; 1 2][x_n; y_n], (1) where x_(n+1) and y_(n+1) are computed mod ...

Take K a number field and L an Abelian extension, then form a prime divisor m that is divided by all ramified primes of the extension L/K. Now define a map phi_(L/K) from the ...

Given a number field K, a Galois extension field L, and prime ideals p of K and P of L unramified over p, there exists a unique element sigma=((L/K),P) of the Galois group ...