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Consider the expression 3×7+2^2. This expression has value (3×7)+(2^2)=25 due to what is called operator precedence (or "order of operations"). Precedence of common operators ...

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by ...

A typical vector (i.e., a vector such as the radius vector r) is transformed to its negative under inversion of its coordinate axes. Such "proper" vectors are known as polar ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...

Given a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees ring of R with respect to F is R_+(F)=I_0 direct sum ...

A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i.e., an equilateral parallelogram. The word rhomb is sometimes used ...

A ring homomorphism is a map f:R->S between two rings such that 1. Addition is preserved:f(r_1+r_2)=f(r_1)+f(r_2), 2. The zero element is mapped to zero: f(0_R)=0_S, and 3. ...

One of the three standard tori given by the parametric equations x = (c+acosv)cosu (1) y = (c+acosv)sinu (2) z = asinv (3) with c>a. This is the torus which is generally ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...