They are known as 2 -, alpha -, or α-amino acids ( generic formula H < sub > 2 </ sub > NCHRCOOH in most cases < ref > Proline is an exception to this general formula.

A remarkable early tenth-century document, known as the Burghal Hidage, provides a formula for determining how many men were needed to garrison a borough, based on one man for every of wall.

Eight structural isomers with molecular formula C < sub > 5 </ sub > H < sub > 12 </ sub > O and all alcohols are known:

This formula gives the pairs ( 220, 284 ) for n = 2, ( 17296, 18416 ) for n = 4, and ( 9363584, 9437056 ) for n = 7, but no other such pairs are known.

This formula and the triangular arrangement of the binomial coefficients are often attributed to Blaise Pascal, who described them in the 17th century, but they were known to many mathematicians who preceded him.

The problem of how many variable assignments satisfy a formula, not a decision problem, is in # P. UNIQUE-SAT or USAT or Unambiguous SAT is the problem of determining whether a formula known to have either zero or one satisfying assignments has zero or has one.

The philosopher and astronomer Rabbi Abraham ibn Ezra ( c. 1140 ) established the symmetry of binomial coefficients, while a closed formula was obtained later by the talmudist and mathematician Levi ben Gerson ( better known as Gersonides ), in 1321.

These compounds are also known as organocarbonates or carbonate esters, and have the general formula ROCOOR ′, or RR ′ CO < sub > 3 </ sub >.

The general formula is set out in section 38 ( 1 ), known as the " 7 / 50 formula ", requires: ( a ) assent from both the House of Commons and the Senate ; ( b ) the approval of two-thirds of the provincial legislatures ( at least seven provinces ) representing at least 50 % of the population ( effectively, this would include at least Quebec or Ontario, as they are the most populous provinces ).

The term " deed ", also known in this context as a " specialty ", is common to signed written undertakings not supported by consideration: the seal ( even if not a literal wax seal but only a notional one referred to by the execution formula, " signed, sealed and delivered ", or even merely " executed as a deed ") is deemed to be the consideration necessary to support the obligation.

For example the ester hexyl octanoate, also known under the trivial name hexyl caprylate, has the formula CH < sub > 3 </ sub >( CH < sub > 2 </ sub >)< sub > 6 </ sub > CO < sub > 2 </ sub >( CH < sub > 2 </ sub >)< sub > 5 </ sub > CH < sub > 3 </ sub >.

Solving this, by a process known as completing the square, leads to the quadratic formula

Erlang-B ( sometimes also written without the hyphen Erlang B ), also known as the Erlang loss formula, is a formula for the blocking probability derived from the Erlang distribution to describe the probability of call loss on a group of circuits ( in a circuit switched network, or equivalent ).

:* Escape-time fractals – use a formula or recurrence relation at each point in a space ( such as the complex plane ); usually quasi-self-similar ; also known as " orbit " fractals ; e. g., the Mandelbrot set, Julia set, Burning Ship fractal, Nova fractal and Lyapunov fractal.

The Younger Futhark inscription on the stone bears a commonly seen memorial dedication, but is followed by an encoded runic sequence that has been described as " mysterious ," and " an interesting magic formula which is known from all over the ancient Norse world.

The empirical formula for benzene had been long known, but its highly unsaturated structure was a challenge to determine.

By sorting formulas according to the number of atoms of each element present in the formula according to these rules, with differences in earlier elements or numbers being treated as more significant than differences in any later element or number — like sorting text strings into lexicographical order — it is possible to collate chemical formulas into what is known as Hill system order.

Suppose the formula for some given function is known, but too complex to evaluate efficiently.

Kernite, also known as rasorite is a hydrated sodium borate hydroxide mineral with formula Na < sub > 2 </ sub > B < sub > 4 </ sub > O < sub > 6 </ sub >( OH )< sub > 2 </ sub >· 3 ( H < sub > 2 </ sub > O ).

Molecular spectroscopy deals with the response ( spectrum ) of molecules interacting with probing signals of known energy ( or frequency, according to Planck's formula ).

Tartaglia is also known for having given an expression ( Tartaglia's formula ) for the volume of a tetrahedron ( including any irregular tetrahedra ) as the Cayley – Menger determinant of the distance values measured pairwise between its four corners:

Although originally expressed in Newton's third law, the conservation of linear momentum also holds in special relativity ( with a modified formula ) and, with appropriate definitions, a ( generalized ) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula ( given below ).

The standard gravitational parameter GM appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of light caused by gravitational lensing, in Kepler's laws of planetary motion, and in the formula for escape velocity.

To illustrate how one may use Newton's formula in actual practice, consider the first few terms of the Fibonacci sequence f = 2, 2, 4 ... One can find a polynomial that reproduces these values, by first computing a difference table, and then substituting the differences which correspond to x < sub > 0 </ sub > ( underlined ) into the formula as follows,

Note that this formula ( equivalent to Newton's law of heat flow ) is analogous to, and much older than, Ohm's law of electric flow:

The " conditions " are a formula ( or several ) that represent reality, often something arising from a physical law like Newton's second law, the force-acceleration equation:

Newton's formula is of interest because it is the straightforward and natural differences-version of Taylor's polynomial.

Newton's formula is Taylor's polynomial based on finite differences instead of instantaneous rates of change.

Newton's form has the simplicity that the new points are always added at one end: Newton's forward formula can add new points to the right, and Newton's backwards formula can add new points to the left.

When so doing, it uses terms from Newton's formula, with data points and x values renamed in keeping with one's choice of what data point is designated as the data point.

Newton's formula for kinetic energy, given as, is only an approximation for the kinetic energy of an object, reasonably accurate for speeds well below c, approximately 3 × 10 < sup > 8 </ sup > m s < sup >− 1 </ sup >.

* July 5-Isaac Newton's Principia ( full title Philosophiae Naturalis Principia Mathematica ) is published, in which Newton describes his theory of universal gravitation, explains the laws of mechanics, gives a formula for the speed of sound and demonstrates that Earth is an oblate spheroid.

The solutions to this equation are called the roots of the quadratic polynomial, and may be found through factorization, completing the square, graphing, Newton's method, or through the use of the quadratic formula.

where the first equality is Newton's second law, and the second line uses Hamilton's equations and the equipartition formula.

The recurrence formula of the secant method can be derived from the formula for Newton's method

One way of calculating and is to use Newton's method to find a solution for the equation, giving the recursive formula

The above formula is applicable only for Newton's rings obtained by reflected light.

Introducing the ideal gas law per unit volume for the osmotic pressure, the formula becomes identical to that of Einstein's.

The formula that yields this temperature is based on the first law of thermodynamics and takes note of the fact that the heat of combustion is used entirely for heating the fuel, the combustion air or oxygen, and the combustion product gases ( commonly referred to as the flue gas ).

The first law gives rise to the following formula:

In sum, Radbruch's formula argues that where statutory law is incompatible with the requirements of justice " to an intolerable degree ", or where statutory law was obviously designed in a way that deliberately negates " the equality that is the core of all justice ", statutory law must be disregarded by a judge in favour of the justice principle.

The 19th century saw development in groundwater hydrology, including Darcy's law, the Dupuit-Thiem well formula, and Hagen-Poiseuille's capillary flow equation.

From the law of excluded middle, formula ✸ 2. 1 in Principia Mathematica, Whitehead and Russell derive some of the most powerful tools in the logician's argumentation toolkit.

In case u and v commute, this formula reduces to the familiar exponential law.

Variations on this basic formula describe the magnetic force on a current-carrying wire ( sometimes called Laplace force ), the electromotive force in a wire loop moving through a magnetic field ( an aspect of Faraday's law of induction ), and the force on a particle which might be traveling near the speed of light ( relativistic form of the Lorentz force ).

This formula represents a physical law that radio devices use.

However, the subsequent discovery of the Kuiper belt, and in particular of the object, which is larger than Pluto yet does not fit Bode's law, have further discredited the formula.

Note the similarity of the above formula to the ideal gas law and also that osmotic pressure is not dependent on particle charge.

Melanchthon made the distinction between law and gospel the central formula for Lutheran evangelical insight.

Snell's law ( also known as the Snell – Descartes law and the law of refraction ) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass.

Although this law remains constant, the formula for fusion strongly suggests that it is in fact, not an accurate measure at all.

Wren was unconvinced, Hooke did not produce the claimed derivation although the others gave him time to do it, and Halley, who could derive the inverse-square law for the restricted circular case ( by substituting Kepler's relation into Huygens ' formula for the centrifugal force ) but failed to derive the relation generally, resolved to ask Newton.

In Canadian labour law, the Rand formula ( also referred to as automatic check-off ) is a workplace situation in which the payment of trade union dues is mandatory, regardless of the worker's opinion about the union.