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Given a system of two ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y), (2) let x_0 and y_0 denote fixed points with x^.=y^.=0, so f(x_0,y_0) = 0 (3) g(x_0,y_0) ...

In August 2002, M. Agrawal and colleagues announced a deterministic algorithm for determining if a number is prime that runs in polynomial time (Agrawal et al. 2004). While ...

The self-intersection of a one-sided surface. The word "cross-cap" is sometimes also written without the hyphen as the single word "crosscap." The cross-cap can be thought of ...

The regular heptagon is the seven-sided regular polygon illustrated above, which has Schläfli symbol {7}. According to Bankoff and Garfunkel (1973), "since the earliest days ...

For a general quadrilateral with sides of length a, b, c, and d, the area K is given by (1) where s=1/2(a+b+c+d) (2) is the semiperimeter, A is the angle between a and d, and ...

A circular sector is a wedge obtained by taking a portion of a disk with central angle theta<pi radians (180 degrees), illustrated above as the shaded region. A sector with ...

A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. Let such a pentagon have edge lengths a_1, ..., a_5, and area ...

The diagonal triangle of a complete quadrangle is the triangle formed by its three diagonal points. If the quadrangle is a cyclic quadrilateral, then the circle is the polar ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the B- and C-excircles (with centers J_B and J_C, respectively). Of these, three correspond to the ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the incircle (with center I) and the A-excircle (with center J_A). Of these, three correspond to the ...