Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.

Formulas for the eccentricity of an ellipse that is expressed in the more general quadratic form are described in the article dedicated to conic sections.

Formulas for expressing the roots of polynomials of degree 2 in terms of square roots have been known since ancient times ( see quadratic equation ), and for polynomials of degree 3 or 4 similar formulas ( using cube roots in addition to square roots ) were found in the 16th century ( see cubic function and quartic function for the formulas and Niccolo Fontana Tartaglia, Lodovico Ferrari, Gerolamo Cardano, and Vieta for historical details ).

For example, a 1901 medical book published for home health use gave the following two " Simple Remedy Formulas " for DYSENTERRY: ( 1 ) Thin boiled starch, 2 ounces ; Laudanum, 20 drops ; " Use as an injection every six to twelve hours "; ( 2 ) Tincture rhubarb, 1 ounce ; Laudanum 4 drachms ; " Dose: One teaspoonful every three hours.

Formulas for addition and multiplication are exactly the same as for the ordinary polynomials, with the only difference that both positive and negative powers of X can be present:

* The Animator's Survival Kit: A Manual of Methods, Principles and Formulas for Computer, Stop-motion, Games and Classical Animators, Faber and Faber, 2002 ( expanded edition 2009, adding ' Internet ' to the subtitle )

Formulas for the other coefficients are much harder to get ; Todd classes of toric varieties, the Riemann – Roch theorem as well as Fourier analysis have been used for this purpose.

Formulas are quite often interpreted as propositions ( as, for instance, in propositional logic ).

Formulas with the form described above are known as 2-CNF formulas ; the " 2 " in this name stands for the number of terms per clause, and " CNF " stands for conjunctive normal form, a type of Boolean expression in the form of a conjunction of disjunctions.

The Animator's Survival Kit: A Manual of Methods, Principles, and Formulas for Classical, Computer, Games, Stop Motion, and Internet Animators.

Formulas for different colors of glass are closely guarded.

Formulas for triose and TP are C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OH and C < sub > 2 </ sub > H < sub > 3 </ sub > O < sub > 2 </ sub >- CH < sub > 2 </ sub > OPO < sub > 3 </ sub >< sup > 2 -</ sup > + 2H < sup >+</ sup >.

Including but not limited to A Moral Code of Ethics, The Sheet of Fives, Pyramid Formulas for Happiness, Harmony and Health, The Ten Stages of Growth and much more.

* Formulas for fast ( er ) matrix multiplication and inversion.

Formulas for Generating Pythagorean Triples

TK Solver is also the platform for engineering applications marketed by UTS, including Advanced Spring Design, Integrated Gear Software, Interactive Roark ’ s Formulas, Heat Transfer on TK, and Dynamics and Vibration Analysis.

* Abramowitz and Stegun, the informal name for Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

Formulas are available to estimate the effective length of a whistle, but an accurate formula to predict sounding frequency would have to incorporate whistle length, scale, gas flow rate, mouth height, and mouth wall area ( see below ).

* The Scale of Einstein, From Faith to Formulas, by Janet Maslin, The New York Times, April 9, 2007.

* Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions ( with Formulas, Graphs and Mathematical Tables ), U. S. Dept.

His most notable works were his ethnographic studies of the Ghost Dance after Sitting Bull's death in 1890, a widespread 19th-century religious movement among various Native American culture groups, and the Cherokee: The Sacred Formulas of the Cherokees ( 1891 ), and Myths of the Cherokee ( 1900 ), all published by the US Bureau of American Ethnology.

* Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, by Milton Abramowitz and Irene A. Stegun ( Eds ), National Bureau of Standards, 1964.

The four titles in this edition were: The Arcane Teaching ( hardback ), The Arcane Formulas, or Mental Alchemy ( pamphlet ), The Mystery of Sex, or Sex Polarity ( pamphlet ), and Vril, or Vital Magnetism ( pamphlet ).

This edition consisted of the following titles ( the three titles marked with an asterix (*) are the volumes that had appeared together as The Arcane Teaching in the previous edition ): The One and the Many * ( hardback ), Cosmic Law * ( hardback ), The Psychic Planes * ( hardback ), The Arcane Formulas, or Mental Alchemy ( binding unknown ), The Mystery of Sex, or Sex Polarity ( binding unknown ), and Vril, or Vital Magnetism ( binding unknown ).

A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables ( Dover: New York, 1972 ), p. 78.

* The Perfect Sausages ( previously The Perfect Sausage and other Fundamental Formulas ), ISBN 0-439-95901-2 ( areas and volumes, ellipsoids and toruses, number formulas ( e. g. triangle, hexagonal ), speed, acceleration, stopping time, distance, force, gravity, projectiles, Money: percentages ; simple and compound interest, permutations and combinations.

* The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2.

Maroger published The Secret Formulas and Techniques of the Old Masters in 1948.

Redelius was assisting Maroger with a revision of The Secret Formulas and Techniques of the Old Masters before his death in 1962.

Formulas in Calligra Words are provided by the Formula plugin.

Formulas say how to mechanically compute new values from existing values.

*" Basic Concepts and Formulas in Microscopy: Numerical Aperture " by Michael W. Davidson, Nikon MicroscopyU ( website ).

This engine and its legacy drive the SD Trans Ams and Formulas as one of the more, if not the most, desirable Pontiacs ever produced.

Formulas, macros and other objects existed " outside " of the cells, which was intended to make editing much simpler and less error-prone.

Formulas were typed into a separate section, and referred to data through their range, not their physical position in the sheets.

Stirling Numbers of the First Kind., § 24. 1. 3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.

During this period he started supervising Ph. D. students, such as James Halpern ( Contributions to the Study of the Independence of the Axiom of Choice ) and Edgar Lopez-Escobar ( Infinitely Long Formulas with Countable Quantifier Degrees ).

Sacred Formulas of the Cherokees.

Fender later released a 7 " EP, " Four Formulas ", under his own name on XNTRIX records.

All the manuals for setting up vocational courses stress the importance of first making a local survey of skill needs, of estimating the growth of local jobs, and of consulting with local employers on the types of courses and their content.

Chan's method for estimating the mean is numerically unstable when and both are large, because the numerical error in is not scaled down in the way that it is in the case.

Terriberry extends Chan's formulae to calculating the third and fourth central moments, needed for example when estimating skewness and kurtosis:

These can be used for energy meters ( watt-hour meters ) or for estimating the charge of battery or capacitor.

Rising demand for biofuels is expected to be good news for the biotechnology sector, with the Department of Energy estimating ethanol usage could reduce U. S. petroleum-derived fuel consumption by up to 30 % by 2030.

* Presymptomatic testing for estimating the risk of developing adult-onset cancers ;

Some efficient designs for estimating several main effects simultaneously were found by Raj Chandra Bose and K. Kishen in 1940 at the Indian Statistical Institute, but remained little known until the Plackett-Burman designs were published in Biometrika in 1946.

Such a formula for estimating energy typically has relative error of order of 10 %, but can be used to get a rough qualitative idea and understanding of a molecule.

Another method of estimating E < sub > o </ sub > in an overloaded system is to measure the busy-hour call arrival rate, λ ( counting successful calls and blocked calls ), and the average call-holding time ( for successful calls ), h, and then estimate E < sub > o </ sub > using the formula E

This idea is useful for estimating a diffusion length over a heating and cooling cycle, where D varies with temperature.

Joseph Boussinesq ( a mathematician and physicist ) developed theories of stress distribution in elastic solids that proved useful for estimating stresses at depth in the ground ; William Rankine, an engineer and physicist, developed an alternative to Coulomb's earth pressure theory.

Metzger and Aland list the probable date for this manuscript as c. 125 but the difficulty of estimating the date of a literary text based solely on paleographic evidence must allow potentially for a range that extends from before 100 to well into the second half of the 2nd century.

Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable.

In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population.

As Crowley writes, " In estimating the ultimate value of a divinatory judgment, one must allow for more than the numerous sources of error inherent in the process itself.

For historical reasons palaeontology is part of the geology departments of many universities, because in the 19th century and early 20th century geology departments found palaeontological evidence important for estimating the ages of rocks while biology departments showed little interest.

At the same time, as project-scheduling models were being developed, technology for project cost estimating, cost management, and engineering economics was evolving, with pioneering work by Hans Lang and others.

In 1956, the American Association of Cost Engineers ( now AACE International ; the Association for the Advancement of Cost Engineering ) was formed by early practitioners of project management and the associated specialties of planning and scheduling, cost estimating, and cost / schedule control ( project control ).

* estimating the resource requirements for the activities ;

* estimating time and cost for activities ;

The committee was appointed in 1932 by the British Association for the Advancement of Science to investigate the possibility of quantitatively estimating sensory events.