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Starting with the circle P_1 tangent to the three semicircles forming the arbelos, construct a chain of tangent circles P_i, all tangent to one of the two small interior ...

All the propositions in projective geometry occur in dual pairs which have the property that, starting from either proposition of a pair, the other can be immediately ...

Let C be a smooth geometrically connected projective curve over F_q with q=p^s a prime power. Let infty be a fixed closed point of X but not necessarily F_q-rational. A ...

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

A special case of Stokes' theorem in which F is a vector field and M is an oriented, compact embedded 2-manifold with boundary in R^3, and a generalization of Green's theorem ...

Buffon's needle problem asks to find the probability that a needle of length l will land on a line, given a floor with equally spaced parallel lines a distance d apart. The ...

In the plane, if a line intersects one side of a triangle and misses the three vertices, then it must intersect one of the other two sides. This is a special case of the ...

Geometry

A path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. A lattice path is therefore a sequence of points P_0, P_1, ...

Draw antiparallels through the symmedian point K. The points where these lines intersect the sides then lie on a circle, known as the cosine circle (or sometimes the second ...