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An elementary theorem in geometry whose name means "asses' bridge," perhaps in reference to the fact that fools would be unable to pass this point in their geometric studies. ...

The Prelle-Singer method is a semi-decision procedure for solving nonlinear first-order ordinary differential equations of the form y^'=P(x,y)/Q(x,y), where P and Q are ...

The truth of an infinite sequence of propositions P_i for i=1, ..., infty is established if (1) P_1 is true, and (2) P_k implies P_(k+1) for all k. This principle is ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...

The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

The reciprocal of a real or complex number z!=0 is its multiplicative inverse 1/z=z^(-1), i.e., z to the power -1. The reciprocal of zero is undefined. A plot of the ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...