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The Kakeya needle problems asks for the plane figure of least area in which a line segment of width 1 can be freely rotated (where translation of the segment is also ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...

The approximation for pi given by pi approx sqrt((40)/3-2sqrt(3)) (1) = 1/3sqrt(120-18sqrt(3)) (2) = 3.141533.... (3) In the above figure, let OA=OF=1, and construct the ...

Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then ds_N^2=ds_T^2+ds_B^2, (1) where ds_N^2 = ...

The latitude of a point on a sphere is the elevation of the point from the plane of the equator. The latitude delta is related to the colatitude (the polar angle in spherical ...

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, ...

Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by ...

The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set S=sum_(k)(a_k,b_k) containing disjoint intervals, ...

The Lemoine ellipse is an inconic (that is always an ellipse) that has inconic parameters x:y:z=(2(b^2+c^2)-a^2)/(bc):(2(a^2+c^2)-b^2)/(ac): (2(a^2+b^2)-c^2)/(ab). (1) The ...

Consider a game where everyone in a classroom picks a number between 0 and 100. The person closest to half the average wins. Obviously, picking a number over 50 would be ...