For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

For output, the machine would have a printer, a curve plotter and a bell.

For some choices of P < sub > 1 </ sub > and P < sub > 2 </ sub > the curve may intersect itself, or contain a cusp.

For Dunedin, George Smith Duncan further developed the Hallidie model, introducing the pull curve and the slot brake ; the former was a way to pull cars through a curve, since Dunedin's curves were too sharp to allow coasting, while the latter forced a wedge down into the cable slot to stop the car.

For example, if u < sub > 1 </ sub > is an eigenvector of A, with a real eigenvalue smaller than one, then the straight lines given by the points along α u < sub > 1 </ sub >, with α ∈ R, is an invariant curve of the map.

For a given quantity of a consumer good, the point on the demand curve indicates the value, or marginal utility, to consumers for that unit.

For elliptic-curve-based protocols, it is assumed that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible.

For current cryptographic purposes, an elliptic curve is a plane curve which consists of the points satisfying the equation

For each of the prime fields, one elliptic curve is recommended.

For each of the binary fields, one elliptic curve and one Koblitz curve was selected.

( For example, dark matter is invoked to explain the galactic rotation curve.

For a population of size n, with a sequence of values y < sub > i </ sub >, i = 1 to n, that are indexed in non-decreasing order ( y < sub > i </ sub > ≤ y < sub > i + 1 </ sub >), the Lorenz curve is the continuous piecewise linear function connecting the points ( F < sub > i </ sub >, L < sub > i </ sub > ), i

For a probability density function f ( x ) with the cumulative distribution function F ( x ), the Lorenz curve L ( F ( x )) is given by:

For a cumulative distribution function F ( x ) with inverse x ( F ), the Lorenz curve L ( F ) is given by:

For a specific demand curve the supply " curve " would be the price / quantity combination at the point where marginal revenue equals marginal cost.

For whatever reasons, after translations and publications of the Instituzioni analitiche ... the curve has become known as the " Witch of Agnesi ".

For example, profit maximization lies behind the neoclassical theory of the firm, while the derivation of demand curves leads to an understanding of consumer goods, and the supply curve allows an analysis of the factors of production.

: For prices above the prevailing price the curve is relatively elastic

: For prices below the point the curve is relatively inelastic

For a randomized experiment, the assumption of unit-treatment additivity implies that the variance is constant for all treatments.

For constant bin width these two expressions can be simplified using:

For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For the analysis to correspond usefully to the actual execution time, the time required to perform a step must be guaranteed to be bounded above by a constant.

For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.

For N to be constant for all values of w, a ' tan w '/ a tan w must also be constant.

For incompressible flows, density remains constant.

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

For example, the first assumption has been tested by observations showing that largest possible deviation of the fine structure constant over much of the age of the universe is of order 10 < sup >− 5 </ sup >.

For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward ( though the equilibrium constant will stay the same ).

For each specific consistent effectively represented axiomatic system for the natural numbers, such as Peano arithmetic, there exists a constant N such that no bit of Ω after the Nth can be proven to be one or zero within that system.

For measurement at constant experimentally controlled volume, the isochoric coefficient of pressure rise with temperature, is defined by

For the mathematical constant, see e ( mathematical constant ).

For example, a thermocouple might be used to help ensure a furnace's temperature remains constant.

For any circle, its circumference, divided by its diameter, is equal to the constant pi, ( approximately 3. 14 ).

For quasistatic processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings.

For systems at constant pressure, the change in enthalpy is the heat received by the system.

For an exothermic reaction at constant pressure, the system's change in enthalpy equals the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings.

For positive integer m the derivative of gamma function can be calculated as follows ( here γ is the Euler – Mascheroni constant ):

For instance, endothermic animals ( mammals and birds ) maintain a constant body temperature, while ectothermic animals ( almost all other organisms ) exhibit wide body temperature variation.

For hydrogen-1, hydrogen-2 ( deuterium ), and hydrogen-3 ( tritium ) the constant must be slightly modified to use the reduced mass of the system, rather than simply the mass of the electron.