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A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...

Consider solutions to the equation x^y=y^x. (1) Real solutions are given by x=y for x,y>0, together with the solution of (lny)/y=(lnx)/x, (2) which is given by ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...

k+2 is prime iff the 14 Diophantine equations in 26 variables wz+h+j-q=0 (1) (gk+2g+k+1)(h+j)+h-z=0 (2) 16(k+1)^3(k+2)(n+1)^2+1-f^2=0 (3) 2n+p+q+z-e=0 (4) ...

A general quintic equation a_5x^5+a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 (1) can be reduced to one of the form y^5+b_2y^2+b_1y+b_0=0, (2) called the principal quintic form. Vieta's ...

A mathematical problem, usually not requiring advanced mathematics, to which a solution is desired. Puzzles frequently require the rearrangement of existing pieces (e.g., 15 ...

Finding the height above the bottom of a horizontal cylinder (such as a cylindrical gas tank) to which the it must be filled for it to be one quarter full amounts to plugging ...

Given a straight segment of track of length l, add a small segment Deltal so that the track bows into a circular arc. Find the maximum displacement d of the bowed track. The ...

Relaxation methods are methods of solving partial differential equations that involve splitting the sparse matrix that arises from finite differencing then iterating until a ...

The rhombicosahedron is the uniform polyhedron with Maeder index 56 (Maeder 1997), Wenninger index 96 (Wenninger 1989), Coxeter index 72 (Coxeter et al. 1954), and Har'El ...