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The conversion of a quadratic polynomial of the form ax^2+bx+c to the form a(x+b/(2a))^2+(c-(b^2)/(4a)), which, defining B=b/2a and C=c-b^2/4a, simplifies to a(x+B)^2+C.

If two numbers b and c have the property that their difference b-c is integrally divisible by a number m (i.e., (b-c)/m is an integer), then b and c are said to be "congruent ...

A number puzzle in which a group of arithmetical operations has some or all of its digits replaced by letters or symbols, and where the original digits must be found. In such ...

A number taken to the power 3 is said to be cubed, so x^3 is called "x cubed." This terminology derives from the fact that the volume of a cube of edge length x is given by ...

The quartic surface resembling a squashed round cushion on a barroom stool and given by the equation z^2x^2-z^4-2zx^2+2z^3+x^2-z^2 -(x^2-z)^2-y^4-2x^2y^2-y^2z^2+2y^2z+y^2=0.

The symbol ∡ABC denotes the directed angle from AB to BC, which is the signed angle through which AB must be rotated about B to coincide with BC. Four points ABCD lie on a ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

A puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

Two cones placed apex to apex. The double cone is given by algebraic equation (z^2)/(c^2)=(x^2+y^2)/(a^2).

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...