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Topic: Versine

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	Versine - Wikipedia, the free encyclopedia
		The versed sine, also called the versine and, in Latin, the sinus versus ("flipped sine") or the sagitta ("arrow"), is a trigonometric function versin(θ) (sometimes further abbreviated "vers") defined by the equation:
		This figure also illustrates the reason why the versine was sometimes called the sagitta, Latin for arrow, from the Arabic usage sahem of the same meaning.
		One period (θ = 0..2π) of a versine or, more commonly, a haversine waveform is also commonly used in signal processing and control theory as the shape of a pulse or a window function, because it smoothly (continuous in value and slope) "turns on" from zero to one (for haversine) and back to zero.
	en.wikipedia.org /wiki/Versine (847 words)

	The versed sine also called the versine and in Latin Latin...
		In fact, the earliest surviving trigonometric table, from the 4th 4th–5th century 5th century Siddhantas Siddhantas from India India, was a table of values for the sine and versed sine only (in 3.75-degree increments from 0 to 90 degrees).
		versin from circle versin from circle Sine, cosine, and versine of θ in terms of a unit circle, centered at "O".
		This figure also illustrates the reason why the versine was sometimes called the "sagitta", Latin for arrow arrow, from the Arabic usage "sahem" of the same meaning.
	www.biodatabase.de /Versine (709 words)

	Versine - Biocrawler (Site not responding. Last check: 2007-11-01)
		There are also three corresponding functions: the coversed sine (the versed sine of the complementary angle π/2 − θ, or coversine), the haversed sine or haversine (half the versed sine), and the hacoversed sine (half the coversed sine, also called the hacoversine, the cohaversine, and the havercosine):
		On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc.
		You can find it there under the keyword Versine (http://en.wikipedia.org/wiki/Versine)The list of previous authors is available here: version history (http://en.wikipedia.org/w/index.php?title=Versineandaction=history).
	www.biocrawler.com /encyclopedia/Versine (931 words)

	The Flaw in Newton’s Proof of a = v2/r
		But, the versine is only half the force at the limit, he says [see Prop.
		In Lemma VII, Newton states that at the limit (when the interval between two points goes to zero), the arc, the chord and the tangent are all equal.
		The versine becomes equal to a only if we are considering the arc length from A to b.
	www.wbabin.net /mathis/mathis4.htm (2311 words)

	sine
		Directly derived from the sine are the versine and the haversine.
		The versine is defined as vers(x) = 1 - cos(x); the haversine is defined as hav(x) = 1/2 vers(x).
		The inverse functions of the sine and the cosine are called the arc sine arcsin(x) and the arc cosine arccos(x), respectively.
	www.2dcurves.com /trig/trigs.html (633 words)

	Download Info of - Versine (Site not responding. Last check: 2007-11-01)
		The versed sine, also called the versine and, in Latin, the sinus versus ("flipped sine") or the sagitta ("arrow"), is a trigonometric function versin(θ) (sometimes further abbreviated "vers") defined by the equation: :
		Historically, the versed sine was considered one of the most important trigonometric functions, but it has fallen from popularity in modern times due to the availability of computer s and scientific calculator s.
		In fact, the earliest surviving trigonometric table, from the 4th century – 5th century Siddhantas from India, was a table of values for the sine and versed sine only (in 3.75-degree increments from 0 to 90 degrees).
	versine.en.cwap.org (1663 words)

	Trigonometric function - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-11-01)
		versine (versin θ = 1 − cos θ)
		His works also contain the earliest known tables of sine values and versine (1 − cosine) values (in contrast to the tables of chords earlier produced by Hipparchus and Ptolemy), in 3.75° intervals from 0° to 90°, to an accuracy of 4 decimal places.
		He used the words jya for sine, kojya for cosine, ukramajya for versine, and otkram jya for inverse sine.
	www.arikah.net /encyclopedia/Sine_table (4924 words)

	Trigonometric function - Wikipedia, the free encyclopedia
		Especially in the case of the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically or by other means and then derive these relations.
		A few other functions were common historically (and appeared in the earliest tables), but are now seldom used, such as the versine (1 − cos θ) and the exsecant (sec θ − 1).
		In particular, for a chord AB of the circle, where θ is half of the subtended angle, sin(θ) is AC (half of the chord), a definition introduced in India (see above).
	en.wikipedia.org /wiki/Sine (3785 words)

	[No title]
		Versine is more useful, however, because it is much more accurate near zero.
		Since accuracy is hard to get and easy to lose, the primitive trignometric functions found in your subroutine library should be _versine_ and _arcversine_ instead of _cosine_ and _arccosine_, and those (usually inappropriately) desiring cosine and arccosine can easily construct them as the macros: cos(x) = (1 - vers(x)) acos(x) = (pi/2 - asin(x)).
		Using cd(x), the Pythagoreanness of the formula above is particularly striking: cd(d)^2 = cd(dl)^2 + cos(l1) cos(l2) cd(dL)^2 = cd(dl)^2 + (1-vers(l1)) (1-vers(l2)) cd(dL)^2 The Arab mathematicians circa 1000 AD used the "versed sine", or versine, in addition to the sine and chord.
	www.pipeline.com /~hbaker1/FAQ-lat-long.txt (585 words)

	Plane Trig p 01
		Despite their popularity, because of their excessive round-off errors; these equations involving the cosine should not be employed for numerical calculation.
		Indeed, these equations are the motivation for the original definition of the versine function.
		Definition: A circle is the locus of point at the end of vectors, whose norm is the radius from the point of the center.
	www.geocities.com /ResearchTriangle/2363/trig02.html (3823 words)

	Des4 - repost
		Versine..." the werewolf tried the name out several times, as if tasting it.
		It's just that back in Versine, werewolves are a major threat to the common folk, and since you look exactly like one, I thought..." Mother's Paw was still bandaging him, but he made a sound half way between a sneeze and a snort.
		Destral Minare of Versine, this 'ere is Silent Breeze." Mother's paw pointed at the wolf-man with sand-coloured fur.
	geigercount.net /nurpg/arch/tp3/destral04.htm (7883 words)

	A Correction to the Equation a=v²/r by Miles Mathis
		But, the versine is only half the force, he says [see Prop.
		Once we have found a in this way, there is no need to double it though, since in finding the versine we used the angle θ and the arc length from A to b.
		You may say that the only difference in Newton's method and my correction is that he finds the force over the interval from A to C, whereas I find the force from A to b.
	geocities.com /mileswmathis/avr.html (7591 words)

	versine - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "versine" is defined.
		versine : The American Heritage® Dictionary of the English Language [home, info]
		Versine : Eric Weisstein's World of Mathematics [home, info]
	www.onelook.com /?w=versine (100 words)

	Versine Technologies - Software Consultancy
		Versine Technologies C o m m i t t e d
		Versine Technologies Pvt Ltd is a software development company based in Kolkata, India.
		The niche market that we work in has given us years of specialist knowledge in the semiconductor manufacturing industry - and we are in the process of leveraging this to expand our operations
	www.versine.com (184 words)

	Middle East Open Encyclopedia: Versine (Site not responding. Last check: 2007-11-01)
		This is an extract from The Middle East Open Encyclopedia, made possible through the Wikimedia Foundation.
		Iraq Museum International always displays the most recent published revision of the source article, Versine; all previous versions may be viewed here.
		They link directly to authoring tools for you to start writing a particular article.
	www.baghdadmuseum.org /ref/?title=Versine (971 words)

	Notes on Measures - Angles (Site not responding. Last check: 2007-11-01)
		The three versine functions (which are all positive) were designed with the aim of making calculations easier by removing the need to work with negative numbers.
		Now, whatever the size of angle A, no negative numbers have to be handled.
		Of course it means that the versine values have to be available somewhere.
	www.projects.ex.ac.uk /trol/dictunit/notesa.htm (1475 words)

	versine - wersinus (English to Polish translation glossary) track geometry survey,Tech/Engineering
		versine - wersinus (English to Polish translation glossary) track geometry survey,Tech/Engineering
		The KudoZ network provides a framework for translators and others to assist each other with translations or explanations of terms and short phrases.
		Track quality management is a ne portable system capable of replacing one of the longest survivors of the track geometry manual survey - Horizontal Versine Survey - the so called "Hallade" survey.
	www.proz.com /kudoz/250511 (124 words)

	My Story of Quadong (Site not responding. Last check: 2007-11-01)
		And to make this more clear, he drew some kind of wavy line on the board to represent mathematical progress vs. time (approximation shown here), where the versine was invented in one of the low spots.
		He goes on to say that versine is stupid because it is no more useful than sticking any other random functions together and giving it a new name.
		Note: versine is not actually defined in Mathematica, but Wolfram notes its existance: see
	gridley.res.carleton.edu /~straitm/quadongstory.html (279 words)

	Railway Survey and Measurement Trolleys from Consillia (Site not responding. Last check: 2007-11-01)
		Consillia's range of survey trolleys are designed to measure a range of track and trackside parameters simultaneously.
		Standard measurements include: gauge, cross level, twist, left and right versine, horizontal alignment and topography.
		Additional measurement such as platform and conductor rail positions, sleeper height and true location can also be recorded with the option of extra transducers.
	trackgeometry.co.uk /railway_survey_trolleys.htm (141 words)

	EN World - Morrus' D&D / d20 News & Reviews Site - D&D: Kazadar Empire (OOC)
		Of late, Kazadar's interest in conquest has shifted to the elven nation inside the sprawling Versine Forest.
		The Versine just happens to be directly south of the Karad Mountains, and rests entirely inside the Empire.
		Over the last six years, Kazadar has launched major attacks on the elven nation in the Versine three times, and has had countless minor skirmishes.
	www.enworld.org /printthread.php?t=61204&pp=50 (2465 words)

	Portable Track Survey Trolley for the measurement of rail parameters (Site not responding. Last check: 2007-11-01)
		The PTST-C is a hand pushed track recording trolley designed to measure a variety of track and trackside parameters simultaneously.
		The standard unit will measure Cross-Level, Twist, Left and Right Vertical and Horizontal Versine and Topography.
		Additional transducers can be added as options to provide measurements of platform geometries, conductor rail parameters, sleeper height and true location.
	www.trackgeometry.co.uk /track_survey_trolley.htm (158 words)

	Ninth Generation (Site not responding. Last check: 2007-11-01)
		Mildred Versine Corey and John Kalin were married.
		Mildred Versine Corey and Fred K Tonkin were married.
		Send mail to webmaster@coryfamsoc.com with questions or comments about this web site.
	www.coryfamsoc.com /william/william/b2627.htm (29 words)

	ROBEL Bahnbaumaschinen GmbH: 82.06 - Versine Measuring Device (Site not responding. Last check: 2007-11-01)
		For easily determining the versine in horizontal track curves
		Measuring chord adjustable to the rail height and from side to side
		Call for more information about this machine and our whole product range.
	www.robel.info /produkte/e_detail.asp?id=298 (41 words)

	Definition of versine - Merriam-Webster Online Dictionary (Site not responding. Last check: 2007-11-01)
		Click here to search for another word in the Merriam-Webster Online Dictionary.
		For More Information on "versine " go to Britannica.com
		Get the Top 10 Search Results for "versine "
	www.bonus.com /contour/merriam_webster/http@@/www.m-w.com/dictionary/versine (56 words)

	Math Forum Discussions (Site not responding. Last check: 2007-11-01)
		Replies: 3 Last Post: Oct 8, 2002 1:05 AM
		Does anybody use the VERSINE, COVERSINE, HAVERSINE, or EXSECANT functions anymore
		I found reference to them in an old CRC math table book.
	mathforum.org /kb/thread.jspa?threadID=86871&messageID=424528 (111 words)

	Track Parameter Measurement Trolley for Gauge, Crosslevel, Twist, Top and Versine Recording (Site not responding. Last check: 2007-11-01)
		Track Parameter Measurement Trolley for Gauge, Crosslevel, Twist, Top and Versine Recording
		The system comprises a measuring frame onto which all of the transducers are attached together with the battery propelled propulsion unit.
		Gauge, Crosslevel, Twist, Rail Top (both rails), Versine over 3m chord (both rails)
	www.trackgeometry.co.uk /railway_track_recording_trolley.htm (108 words)

	[No title]
		result: versine REAL(SGL), INTENT (IN) :: X !
		result: versine REAL(DBL), INTENT (IN) :: X !
		compute inverse versine (rad) END FUNCTION DAVERS !----------------------------------------------------------------------------------------------------------------------------------- !
	home.att.net /~david.g.simpson/Software/auxtrig_f90.txt (1142 words)

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