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Topic: Generating trigonometric tables

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	Generating trigonometric tables - Wikipedia, the free encyclopedia
		Tables of trigonometric functions are useful in a number of areas.
		Another important application of trigonometric tables and generation schemes is for fast Fourier transform (FFT) algorithms, where the same trigonometric function values (called twiddle factors) must be evaluated many times in a given transform, especially in the common case where many transforms of the same size are computed.
		Historically, the earliest method by which trigonometric tables were computed, and probably the most common until the advent of computers, was to repeatedly apply the half-angle and angle-addition trigonometric identities starting from a known value (such as sin(π/2)=1, cos(π/2)=0).
	en.wikipedia.org /wiki/Generating_trigonometric_tables (722 words)

	sine (Site not responding. Last check: 2007-09-18)
		In mathematics, the trigonometric functions are functions of an angle important when studying triangles and modeling periodic phenomena.
		The six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin.
		The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 B.C.), who tabulated the lengths of circle arcs (angle A times radius r) with the lengths of the subtending chords (2r sin(A/2)).
	www.yourencyclopedia.net /Sine.html (1944 words)

	Generating trigonometric tables (Site not responding. Last check: 2007-09-18)
		Tables of trigonometric functions are useful in a number of Before the existence of pocket calculators trigonometric tables were essential for navigation science and engineering.
		Interpolation of simple look-up tables of trigonometric are still used in computer graphics where accurate calculations are either not or cannot be made fast enough.
		Another important application of trigonometric tables and schemes is for fast Fourier transform (FFT) algorithms where the same trigonometric values (called twiddle factors) must be evaluated many times in given transform especially in the common case many transforms of the same size are In this case calling generic library routines time is unacceptably slow.
	www.freeglossary.com /Generating_sinus-tables (707 words)

	Generating trigonometric tables (Site not responding. Last check: 2007-09-18)
		Tables of trigonometric function s are useful in a number of areas.
		Table of Elementary Integrals There are basic integral rules and integral formulas.
		Generating Functions Introduction to generating functions with interactive java applets by Alexander Bogomolny.
	www.serebella.com /encyclopedia/article-Generating_trigonometric_tables.html (858 words)

	Generating trigonometric tables - Term Explanation on IndexSuche.Com
		Tables of trigonometric_functions are useful in a number of areas.
		Interpolation of simple look-up tables of trigonometric functions are still used in computer_graphics, where accurate calculations are either not needed, or cannot be made fast enough.
		Another important application of trigonometric tables and generation schemes is for fast_Fourier_transform (FFT) algorithms, where the same trigonometric function values (called ''twiddle factors'') must be evaluated many times in a given transform, especially in the common case where many transforms of the same size are computed.
	www.indexsuche.com /Generating_trigonometric_tables.html (650 words)

	Trigonometric function - Wikipedia, the free encyclopedia
		The computation of trigonometric functions is a complicated subject, which can today be avoided by most people because of the widespread availability of computers and scientific calculators that provide built-in trigonometric functions for any angle.
		In this section, however, we describe more details of their computation in three important contexts: the historical use of trigonometric tables, the modern techniques used by computers, and a few "important" angles where simple exact values are easily found.
		Such tables have been available for as long as trigonometric functions have been described (see History, above), and were typically generated by repeated application of the half-angle and angle-addition identities starting from a known value (such as sin(π/2)=1).
	en.wikipedia.org /wiki/Trigonometric_function (3255 words)

	Trigonometric function
		In mathematics, the trigonometric functions are functionss of an angle, important when studying triangless and modeling periodic phenomena.
		They may be defined as ratios of two sides of a right triangle containing the angle, or, more generally, as ratios of coordinates of points on the unit circle, or, more generally still, as infinite series, or equally generally, as solutions of certain differential equations.
		A few other functions were common historically (and appeared in the earliest tables), but are now little-used, such as the versed sine (versin = 1 − cos) and the exsecant (exsec = sec − 1).
	www.sciencedaily.com /encyclopedia/trigonometric_function (2572 words)

	Computational Kernel (Site not responding. Last check: 2007-09-18)
		The computational kernel of the distributed algorithm carries out all the floating point operations required, except the ones needed for generating the trigonometric tables.
		Since the trigonometric tables are computed only once, their cost is not significant.
		The kernel is based upon the observation that the difference in computations at different stages of the FFT is in the formation of butterflies.
	astro.uchicago.edu /Computing/On_Line/fft/node4.html (125 words)

	Generating trigonometric tables : Generating sinus-tables
		Simple look-up tables of trigonometric functions are now mostly used in computer graphics, where accurate calculations are either not needed, or cannot be made fast enough.
		A quick, but inaccurate, algorithm for calculating a table of N approximations a[n] for sin(2πn/N) and b[n] for cos(2πn/N) is:
		Unfortunately, this isn't a useful algorithm for generating sine tables, for a number of reasons.
	www.fastload.org /ge/Generating_sinus-tables.html (250 words)

	Read This: Briefly Noted, May 2004
		Tables and table-making were, until very recently, a very important part of the practice of mathematics.
		Nowadays, of course, tables have for the most part been replaced by calculators and computers, and the modern equivalent table-making is the creation of efficient numerical algorithms.
		There are chapters on actuarial tables, on tabulation of data, and on various attempts at mechanizing the creation of tables.
	www.maa.org /reviews/brief_may04.html (1728 words)

	Dictionary Ge (Site not responding. Last check: 2007-09-18)
		General Assembly of Unitarian and Free Christian Churches
		General Conference of the Evangelical Baptist Church, Inc.
		General nature of the evidence of Aegean civilization
	www.dictionarydefinition.net /Ge.html (117 words)

	TRIGONOMETRIC FUNCTION FACTS AND INFORMATION (Site not responding. Last check: 2007-09-18)
		The ''Introductio_in_analysin_infinitorum'' (1748) of Euler was primarily responsible for establishing the analytic treatment of trigonometric functions, defining them as infinite series and presenting "Euler's_formula" ''e''
		(See linear_differential_equation.) It turns out that this differential equation can be used not only to define the sine and cosine functions but also to prove the trigonometric identities for the sine and cosine functions.
		, where trigonometric series are used to solve a variety of boundary-value problems in partial differential equations.
	www.bellabuds.com /Trigonometric_function (3879 words)

	Talk:Generating trigonometric tables - Information (Site not responding. Last check: 2007-09-18)
		Unfortunately, that's not a useful algorithm for generating sine tables, for a number of reasons.
		Historical computation of trigonometric tables, before computers were widespread.
		Probably, there should be a separate article on computing trigonometric functions, not necessarily tables per se, but how they are actually done in practice.
	www.book-spot.co.uk /index.php/Talk:Generating_trigonometric_tables (206 words)

	Trigonometric Function Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-09-18)
		Looking For trigonometric function - Find trigonometric function and more at Lycos Search.
		Find trigonometric function - Your relevant result is a click away!
		Such tables have been available for as long as trigonometric functions have been described (see History, below), and were typically generated by repeated application of the half-angle and angle-addition identities starting from a known value (such as sin(π/2)=1).
	www.folkartmuseum.com /encyclopedia/Trigonometric_function (3423 words)

	Learn more about Trigonometric function in the online encyclopedia. (Site not responding. Last check: 2007-09-18)
		Learn more about Trigonometric function in the online encyclopedia.
		Hint: Play with putting spaces before and after your words to see the different results you get.
		These definitions are equivalent to the above given ones because of the theory of Taylor series, and because of the fact that the derivative of sine is cosine and the derivative of cosine is negative sine.
	www.onlineencyclopedia.org /t/tr/trigonometric_function.html (1416 words)

	Lost&Found
		Ptolemy introduced trigonometric tables in his discussions of his concept of epicycles, to explain away the observed anomalies.
		There are two realistic methods for making progress in sciences, Inductive and Deductive (the first based on observations, the second based on axioms from previous experience - generating theorems).
		in the generation following that of Galileo, employed algebra - per the ancient Persians - to encode his thoughts and explorations of algebraic functions within x,y, z space, his important conceptual legacy for modern science.
	sharpgary.org /Lost_Found.html (1072 words)

	Trigonometric Function (Site not responding. Last check: 2007-09-18)
		Explorer Technology, when an algorithm uses a sine function, the tool...
		Alternatively, all of the basic trigonometric functions can be defined in terms of a unit circle centered at O (shown above right), and similar such geometric definitions were used historically.
		The next significant development of trigonometry was in India, in the works known as the Siddhantas (4th-5th century A.D.), which first defined the sine as the modern relationship between half an angle and half a chord.
	www.wikiverse.org /trigonometric-function (2466 words)

	[No title]
		The code generator is described in the paper "A Fast Fourier Transform Compiler", by M. Frigo, to appear in the `Proceedings of the 1999 ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI), Atlanta, Georgia, May 1999'.
		The storage space required is minimal, proportional to the logarithm of the sizes the `wisdom' was generated from.
		The following is a brief example in which the `wisdom' is read from a file, a plan is created (possibly generating more `wisdom'), and then the `wisdom' is exported to a string and printed to `stdout'.
	www.mit.edu /afs/athena/software/grace_v5.1.18/info/fftw.info-1 (5681 words)

	Sines (Site not responding. Last check: 2007-09-18)
		Eli Maor, Trigonometric Delights (http://www.pupress.princeton.edu/books/maor/) (Princeton Univ. Press, 1998).
		"Trigonometric functions (http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Trigonometric_functions.html)", MacTutor History of Mathematics Archive.
		Dave's Short Trig Course (http://babbage.clarku.edu/~djoyce/java/trig/) uses interactive java applets that are very helpful for learning about trig functions on the unit circle, as well as being useful more generally for students of trigonometry.
	www.freecaviar.com /search.php?title=Sines (3303 words)

	[No title]
		1-5 Master Table of Contents (ver 1.0; March 6, 1995) Derived from source material created by David Kirk, Paul Heckbert and Alan Paeth Notes: some titles have been truncated; page numbers must be rechecked.
		This table also serves as an index to the code in the FTP collection.
		Note that every article has text that appears in the book but not in the FTP archive, and some articles contain no C or C++ code.
	www.geom.uiuc.edu /software/cglist/cglib/AllGems.TOC (436 words)

	Trigonometry Formula on Almondnet
		A formula is a concise way of expressing information symbolically or a general relationship between quantities.
		Shop at Amazon for general books like "Pocket Book of Integrals and Mathematical Formulas" by J. Ronald Tallarida at Amazon.co.uk.
		They can appear with in the tags listed in table Places of Mathematical Formulas...
	www.commercial-mortgage-rates.co.uk /mortgages/trigonometry_formula.html (450 words)

	Generating trigonometric tables (Site not responding. Last check: 2007-09-18)
		Generating trigonometric tables
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Generating trigonometric tables article at Free Euro Online Encyclopedia

It uses material from the wikipedia article Generating trigonometric tables.

www.eurofreehost.com /ge/Generating_trigonometric_tables.html (268 words)

	Generating trigonometric tables : Generating sinus-tables (Site not responding. Last check: 2007-09-18)
		Generating trigonometric tables : Generating sinus-tables
		bgcolor='#FFFF33' bordercolor='fl' summary='layout' cellspacing=0 cellpading=0 border=1 rows=1>
Generating trigonometric tables : Generating sinus-tables article at Free Euro Online Encyclopedia

It uses material from the wikipedia article Generating trigonometric tables : Generating sinus-tables.

www.eurofreehost.com /ge/Generating_sinus-tables_2.html (116 words)

	The QBasic Forum
		we've covered this sort of thing on the forum, and the general answer is yes, it's doable.
		Bitmap file formats are much more complex JPEG for example compress its data via a complex means of doing discrete cosine transform on 8 by 8 pixel blocks then 2 tables are generated for luminance and chrominance.
		the two table are used to quantize dct coefficients.
	www.network54.com /Forum/viewall?forumid=13959&it=12 (8908 words)

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