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.

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 estimating the height of mountains, dated Bath, 13 February 1817 Annals of Philosophy, 9 ( March, 1817 ), 251 -- 252.

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 in Calligra Words are provided by the Formula plugin.

Formulas p and q are syntactically equivalent if and only if p ↔ q is a theorem, while p and q are semantically equivalent if and only if p ↔ q is true in every model ( that is, p ↔ q is logically valid ).

Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts.

Formulas are given in SI units and Gaussian-cgs units.

Formulas not involving st ( i. e., formulas of the usual language of set theory ) are called internal, other formulas are called external.

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 ).

Formulas in logic are typically built up recursively from some propositional variables, some number of logical connectives, and some logical quantifiers.

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 ).

Given an MV-algebra A, an A-valuation is a homomorphism from the algebra of propositional formulas ( in the language consisting of and 0 ) into A. Formulas mapped to 1 ( or 0 ) for all A-valuations are called A-tautologies.

Formulas such as XLys, XTrp Analog, XLys, XTrp Maxamaid, XLys, XTrp Maxamum or Glutarex 1 are designed to provide amino acids other than lysine and tryptophan, in order to tentatively prevent protein malnutrition.

Examples of these: ( 1 ) 19th Century American Vice Presidents, ( 2 ) Italian Operas, or ( 3 ) Math Formulas.

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

* TP — Triple play: one for each triple play during which the fielder recorded a putout or an assist

Version numbers 6 through 9 were proposed for various protocol models designed to replace IPv4: SIPP ( Simple Internet Protocol Plus, known now as IPv6 ), TP / IX ( RFC 1475 ), PIP ( RFC 1621 ) and TUBA ( TCP and UDP with Bigger Addresses, RFC 1347 ).

* The Transaction Profile ( TP ) is mandatory for a client to understand his / her transactions.

In 1980, Anderson earned a ' TP de Oro ' Award for ' Best Foreign Actress ' for her role Little House and, in 1981, she earned a Young Artist Award nomination for her performance in the Canadian slasher film Happy Birthday to Me.

Different names, euphemisms and slang terms are used for toilet paper in countries around the world, including " bumf ," " bum wad ," " loo roll / paper ," " bog roll ," " toilet roll ," " dunny roll / paper ," " bathroom / toilet tissue ," " TP ," " arsewipe ," and just " tissue.

Most of the phosphorylation sites for which such a mobility shift has been described fall in the category of SP and TP sites ( i. e. a proline residue follows the phosphorylated serine or threonine residue ).

From 1990 to 1996, Poindexter served as co-founder of TP Systems, Inc., a software development firm specializing in commercial software for the IBM PCs and compatibles ; Poindexter was the chief designer and programmer.

It lies on top of the Tiny TP protocol, so Tiny TP is mandatory for OBEX to work.

As IrLAN lies on top of the Tiny TP protocol, the Tiny TP protocol must be implemented for IrLAN to work.

* ApplicationMaster for the creation of online TP applications

The range of water column TP for Schoodic Lake is 4 – 15 parts per billion ( ppb ) with an average of 9 ppb, while Chla ranges from 2. 1 to 4. 5 ppb with an average of 3 ppb.

The potential for TP to leave the bottom sediments and become available to algae in the water column ( internal loading ) is low to moderate.

* Heron TP, an alternative name for the Eitan ( UCAV ) unmanned aircraft

An early attempt at TP for GCOS 3, the Transaction Processing Executive, assumed that, as in Unix, a new process should be started to handle each transaction, and enjoyed only very limited success.

Another TP system, the Transaction Driven System ( TDS ), was soon developed for GCOS 3, using a single process ( potentially with multiple threads ) to service all transactions.

; TA, TP ( traffic announcement, traffic programme ): The receiver can often be set to pay special attention to this flag and, for example, stop the tape / pause the CD or retune to receive a traffic bulletin.

Let P be a principal H-bundle on M, equipped with a Cartan connection η: TP → g. If g is a reductive module for H, meaning that g admits an Ad ( H )- invariant splitting of vector spaces g = h ⊕ m, then the m-component of η generalizes the solder form for an affine connection.

0 for every vertical vector X ∈ TP.

This was the start of a near annual event where a new TP would be introduced in the first story ...... a handy way of maintaining interest for returning viewers and a convenient way for Price to re-establish the basic premise of the show for new audiences every year.