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

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

Generating the permutations that are solutions of the eight rooks puzzle and then checking for diagonal attacks further reduces the possibilities to just 40, 320 ( that is, 8 !).

While most of the current activity at the site is related to the cleanup project, Hanford also hosts a commercial nuclear power plant, the Columbia Generating Station, and various centers for scientific research and development, such as the Pacific Northwest National Laboratory and the LIGO Hanford Observatory.

When Nikola Tesla, for whom a memorial was later built at Niagara Falls, New York, U. S. A., invented the three-phase system of alternating current power transmission, distant transfer of electricity became possible, as Westinghouse and Tesla had built the AC-power Ames Hydroelectric Generating Plant and proved it effective.

The Annapolis Royal Generating Station has been studied for its various effects, including an accelerated shoreline erosion problem on the historic waterfront of the town of Annapolis Royal, as well as increased siltation and heavy metal and pesticide contamination upstream due to lack of regular river / tidal flushing.

On March 16, 2006 Duke Power announced that a Cherokee County site had been selected for a potential new nuclear power plant, to be called the William States Lee III Nuclear Generating Station.

On-Board Oxygen Generating Systems ( OBOGS ) use zeolites to remove nitrogen from compressed air in order to supply oxygen for aircrews at high altitudes.

President Jimmy Carter leaving Three Mile Island Nuclear Generating Station | Three Mile Island for Middletown, Dauphin County, Pennsylvania | Middletown, Pennsylvania, April 1, 1979.

The Solana Generating Station is scheduled to start providing power for Arizona Public Service in 2013.

* Waterford 3 -- Owned by Entergy Nuclear, Waterford Nuclear Generating Station, also known as Waterford 3, produces roughly 12 % of power for the state of Louisiana.

The coal mined from the Navajo and San Juan mines is used entirely for fuel for the nearby Four Corners Generating Station and San Juan Power Plant to produce electric power.

Alcoa Power Generating continues to generate electricity using four area dams and is working to find new uses for the plant site.

Perry is known for its public schools, whose recent construction was influenced by the nearby Perry Nuclear Generating Station.

The Conservation Law Foundation opposes the permit given to Mirant for the Mirant Kendall Generating Station, an electricity plant near Kendall Square, charging that the water it releases causes blooms of hazardous microorganisms because of its warm temperature.

Generating functions are often expressed in closed form ( rather than as a series ), by some expression involving operations defined for formal power series.

Generating functions for the sequence of square numbers a < sub > n </ sub >

* Main Frame: Strategies for Generating Social Norms News.

The Palo Verde Nuclear Generating Station near Phoenix, Arizona was designed for 100 % MOX core compatibility but so far have always operated on fresh low enriched uranium.

Major employers in Clarington include the Darlington Nuclear Generating Station, General Motors in Oshawa, and several medium-to-large sized manufacturing businesses ; however, most residents travel to points west in Durham Region or to Toronto for employment.

* R. L. Smith " Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed Over Bounded Regions ", Operations Research, Vol.

The SSEB submitted designs for four types of reactor then being considered by HM Government for the next stage of the UK civil nuclear programme: the advanced gas-cooled reactor ( AGR ), the Steam Generating Heavy Water Reactor ( SGHWR ), the Light Water Reactor ( LWR ) and the High Temperature Reactor ( HTR ).

; Generating set: Given a field extension E / F and a subset S of E, we write F ( S ) for the smallest subfield of E that contains both F and S. It consists of all the elements of E that can be obtained by repeatedly using the operations +,-,*,/ on the elements of F and S. If E = F ( S ) we say that E is generated by S over F.

OPG will proceed with a detailed planning phase for the mid-life refurbishment of the Darlington Nuclear Generating Station east of Toronto, with construction expected to start in 2016.

* Confluence, a colloquial term for the tailrace tunnels from the Toronto Power Generating Station

In those oblique coordinate systems the computations of distances and angles is more complicated than in standard Cartesian systems, and many standard formulas ( such as the Pythagorean formula for the distance ) do not hold.

Animation illustrating Pythagorean theorem | Pythagoras ' rule for a right-angle triangle, which shows the algebraic relationship between the triangle's hypotenuse, and the other two sides.

For example, both the Egyptians and the Babylonians were aware of versions of the Pythagorean theorem about 1500 years before Pythagoras ; the Egyptians had a correct formula for the volume of a frustum of a square pyramid ;

Baudhayana ( c. 8th century BCE ) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as:,,,, and as well as a statement of the Pythagorean theorem for the sides of a square: " The rope which is stretched across the diagonal of a square produces an area double the size of the original square.

" It also contains the general statement of the Pythagorean theorem ( for the sides of a rectangle ): " The rope stretched along the length of the diagonal of a rectangle makes an area which the vertical and horizontal sides make together.

However some scholars have disputed the Pythagorean interpretation of this tablet ; see Plimpton 322 for details .</ ref > indicating, in particular, that there was sophisticated understanding on the topic " in Mesopotamia in 1850 BCE.

In particular, for, the generalized mean inequality implies the Pythagorean means inequality as well as the inequality of arithmetic and geometric means.

As noted above this relationship between the three Pythagorean means is not limited to n equals 1 or 2 ; there is a relationship for all n. However, for n

The latter was a result of the Pythagorean theorem and the former the assumption that a + b ≤ c. The contradiction means that it is impossible for both to be true and it is known that the Pythagorean theorem holds.

The Pythagorean theorem and the law of quadratic reciprocity are contenders for the title of theorem with the greatest number of distinct proofs.

Classical scholar Ludwig Edelstein proposed that the oath was written by Pythagoreans, a theory that has been questioned due to the lack of evidence for a school of Pythagorean medicine.

While Pythagorean ratios can provide a rough approximation of perceptual harmonicity, they cannot account for cultural factors.

Han-era mathematical achievements include solving problems with right-angle triangles, square roots, cube roots, and matrix methods, finding more accurate approximations for pi, providing mathematical proof of the Pythagorean theorem, use of the decimal fraction, Gaussian elimination to solve linear equations, and continued fractions to find the roots of equations.

Later, the polis of Rhegion reached great artistic and cultural heights, as is shown by the presence of art, philosophy and science academies, such as the Pythagorean School and also for its well-known poets, historians and sculptors such Ibycus, Ippy and Pythagoras of Rhegium.

In Euclidean geometry, for right triangles it is a consequence of the Pythagorean theorem, and for general triangles a consequence of the law of cosines, although it may be proven without these theorems.

* Pythagorean diet was the name for vegetarianism prior to the nineteenth century

There was a Pythagorean lawgiver of Rhegium known as Phytius, but the early 6th century is too early for this candidate also.

The curvature of space is a mathematical description of whether or not the Pythagorean theorem is valid for spatial coordinates.

Another argument is for the Pythagorean Ratio.

The Sumerian pentagrams served as pictograms for the word " UB " meaning " corner, angle, nook ; a small room, cavity, hole ; pitfall ", suggesting something very similar to the pentemychos ( see below on the Pythagorean use for what pentemychos means ).