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An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2). (3) If the ...

The Fano plane is the configuration consisting of the two-dimensional finite projective plane over GF(2) ("of order two"), illustrated above. It is a block design with nu=7, ...

Draw lines P_AQ_A, P_BQ_B, and P_CQ_C through the symmedian point K and parallel to the sides of the triangle DeltaABC. The points where the parallel lines intersect the ...

The envelope of the plane lx+my+nz=c, (1) where c is the speed of propagation of a wave in the direction (l,m,n) (i.e., l, m, and n are the direction cosines) is known as the ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...

The Gaussian integral, also called the probability integral and closely related to the erf function, is the integral of the one-dimensional Gaussian function over ...

A geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

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 ...