Cusp

Cusp may refer to:

Cusp (singularity)

In mathematics a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point on the curve must start to move backward. A typical example is given in the figure. A cusp is thus a type of singular point of a curve.

For a plane curve defined by a differentiable parametric equation

a cusp is a point where both derivatives of f and g are zero, and at least one of them changes of sign. Cusps are local singularities in the sense that they involve only one value of the parameter t, contrarily to self-intersection points that involve several values.

For a curve defined by an implicit equation

cusps are points where the terms of lowest degree of the Taylor expansion of F are a power of a linear polynomial; however not all singular points that have this property are cusps. In some contexts, and in the remainder of this article, one restricts the definition of a cusp to the case where the non-zero part of lowest degree of the Taylor expansion of F has degree two.

Cusp (astrology)

In astrology, a cusp (from the Latin for spear or point) is the imaginary line that separates a pair of consecutive signs in the zodiac or houses in the horoscope.

Because the solar disc has a diameter of approximately half a degree, it is possible for the Sun to straddle the cusp as it moves across the sky. When this occurs at the moment of birth such a person is said to be "born on the cusp" and some believe that their life is influenced by the characteristics of both signs. For example, if an individual was born when the Sun (by convention the point at the centre of the Solar disc) was located at 29 degrees, 50 minutes Gemini, then one might say that he was born on the cusp of Gemini and Cancer. Much of the Solar disc was actually in Cancer even though the centre was in Gemini.

Although the term "cusp" is universally used for the boundaries of signs, not all astrologers agree that an object can ever be included in more than one sign. Many consider relevant only the location of the Sun's centre, which must be entirely in one sign, and would describe the natal Sun in the example as simply being in Gemini. If late degrees of Gemini have a Cancer-like character, they would describe that as simply the nature of that part of Gemini rather than some influence spilling over from the next sign.

Forma

Forma is a Latin word meaning "form". Both the word "forma" and the word "form" are used interchangeably as informal terms in biology:

Formwork

Formwork is the term given to either temporary or permanent molds into which concrete or similar materials are poured. In the context of concrete construction, the falsework supports the shuttering moulds.

Formwork and concrete form types

Formwork comes in several types:

Homogeneous polynomial

In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree. For example, is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial is not homogeneous, because the sum of exponents does not match from term to term. A polynomial is homogeneous if and only if it defines a homogeneous function. An algebraic form, or simply form, is a function defined by a homogeneous polynomial. A binary form is a form in two variables. A form is also a function defined on a vector space, which may be expressed as a homogeneous function of the coordinates over any basis.

A polynomial of degree 0 is always homogeneous; it is simply an element of the field or ring of the coefficients, usually called a constant or a scalar. A form of degree 1 is a linear form. A form of degree 2 is a quadratic form. In geometry, the Euclidean distance is the square root of a quadratic form.

Homogeneous polynomials are ubiquitous in mathematics and physics. They play a fundamental role in algebraic geometry, as a projective algebraic variety is defined as the set of the common zeros of a set of homogeneous polynomials.