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	Conchoid (mathematics) - Wikipedia, the free encyclopedia
		All conchoids are cissoids with a circle centered on O as one of the curves.
		A limaÃ§on is a conchoid with a circle as the given curve.
		The often-so-called conchoid of de Sluze and conchoid of DÃ¼rer do not fit this definition; the former is a strict cissoid and the latter a construction more general yet.
	en.wikipedia.org /wiki/Conchoid_(mathematics) (173 words)

	GEOMETRY - LoveToKnow Article on GEOMETRY
		Between Euclid and Apollonius there flourished the illustrious Archimedes, whose geometrical discoveries are mainly concerned with the mensuration of the circle and conic sections, and of the sphere, cone and cylinder, and whose greatest contribution to geometrical method is the elevation of the method of exhaustion to the dignity of an instrument of research.
		Apollonius was followed by Nicomedes, the inventor of the conchoid; Diodes, the inventor of the cissoid; Zenodorus, the founder of the study of isoperimetrical figures; Hipparchus, the founder of trigonometry; and Heron the elder, who wrote after the manner of the Egyptians, and primarily directed attention to problems of practical surveying.
		The extraordinary mathematical talent which came into being in the 16th and 17th centuries reacted on geometry and gave rise to all those characters which distinguish modern from ancient geometry.
	www.1911encyclopedia.org /G/GE/GEOMETRY.htm (21277 words)

	Category:Curves [Definition] (Site not responding. Last check: 2007-11-04)
		Astroid In mathematics, an astroid is a particular type of curve: a hypocycloid with four cusps, or a super ellipse with n=2/3 and a=b.
		Catenary In mathematics, the catenary is the shape of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight).
		Lemniscate In mathematics, a lemniscate is a type of curve described by a Cartesian equation of the form: Graphing this equation produces a curve similar to.
	www.wikimirror.com /Category:Curves (970 words)

	Nicomedes
		A less certain piece of information comes from Apollonius choosing to name a curve 'sister of the conchoid' which is assumed to be a name he has chosen to compliment Nicomedes' discovery of the conchoid.
		Nicomedes is famous for his treatise On conchoid lines which contain his discovery of the curve known as the conchoid of Nicomedes.
		Nicomedes trisected any rectilinear angle by means of the conchoidal curves, the construction, order and properties of which he handed down, being himself the discoverer of their peculiar character.
	www-history.mcs.st-and.ac.uk /history/Mathematicians/Nicomedes.html (507 words)

	Maybe this Explains the Economic Cycle... best Conchoid (Site not responding. Last check: 2007-11-04)
		Conchoid curve A conchoid is a curve derived from a fixed point O, another curve, and a length...
		Conchoid is a way of deriving a new curve based on a given curve...
		Then the conchoid is defined as the collection of points P (on l) for which PQ is equal to a constant a.
	ascot.pl /th/Fourier3/Conchoid.htm (579 words)

	Cronologie di Psicopolis
		Jabir ibn Aflah writes works on mathematics which, although not as good as many other Arabic works, are important since they will be translated into Latin and become available to European mathematicians.
		Mathematics becomes a compulsory subject for a degree at the University of Paris.
		He proves mathematically that it is impossible to design a walk which crosses each of the seven bridges exactly once.
	www.psicopolis.com /timeline/matemtimeline.htm (5798 words)

	The Helenistic Period of Greek Mathematics
		His mathematical studies of astronomical models required a computation of a table of sines.
		He wrote mathematical monographs and devised mechanical means of finding mean proportions in continued proportion between two straight lines.
		Of all polygons of the same number of sides and equal perimeter the equilateral and equiangular polygon is the greatest in area.
	www.math.tamu.edu /~don.allen/history/helnistc/helnistc.html (1557 words)

	Ancient Greece Mathematics Timeline
		Thales of Miletus (Θαλής ο Μιλήσιος) He brings Babylonian mathematical knowledge to Greece and uses geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore.
		Unable to account otherwise for this agreement, they were led to regard mathematics as the study of ultimate, eternal reality, immanent in nature and the universe, rather than as a branch of logic or a tool of science and technology" (Boyer 1949:1).
		Consequently, when the Pythagoreans developed the theory of geometric magnitudes, by which they were able to compare two surfaces' ratio, they were led, for lack of a system which could handle irrational numbers, to the 'incommensurability problem': Applying the side of a square to the diagonal, no common rational measure is discoverable.
	www.mlahanas.de /Greeks/TLMathematics.htm (2109 words)

	Rene Descarates Contd
		Mathematical language is then seen as a powerful and viable code for aspects of experience, rather than as the sole dictator of truth.
		It is usually mentioned in histories of mathematics that Descartes was the first to classify curves according to the algebraic degree of their equations.
		He was constructing a new method of mathematical representation that responded to both the new symbolic language of his time (algebra) and to the new technology of his time (mechanical engineering).
	www.oswego.edu /multi-campus-nsf/rene_descartes_contd.htm (2445 words)

	Towards a History of the Department of Mathematical Sciences
		This is necessary, both to impart to the mind that combined strength and versatility, that peculiar vigor and rapidity of comparison necessary for military action, and to pave the way for progress in the higher military sciences.
		It should be taught gradually to develop its own powers, and as it slowly learns their capacity and the manner of employing them, the increasing lights which are thrown upon its course will enable it to go on for an unlimited extent in the path of improvement.
		Without a background in mathematics it is impossible for one to study properly those sciences with whose principles one must be familiar in order to understand the functioning and operation of modern weapons.
	www.dean.usma.edu /departments/math/people/rickey/dms/talks/RickeyShell.htm (6758 words)

	Mathematical Chronology
		Buffon uses a mathematical and scientific approach to calculate that the age of the Earth is about 75000 years.
		Green publishes Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnets, in which he applies mathematics to the properties of electric and magnetic fields.
		Boole publishes The Mathematical Analysis of Logic, in which he shows that the rules of logic can be treated mathematically rather than metaphysically.
	www-groups.dcs.st-and.ac.uk /~history/Chronology/full.html (8741 words)

	Significant Scots - Alexander Anderson
		How or where he acquired his mathematical education is not known; he probably studied belles lettres and philosophy in his native university.
		This tract refers to the prob1em of inclinations, by which, in certain cases, the application of the curve called the conchoid is superseded.- 2.
		Mathematical genius seems to have been in some degree inherent in the whole family; for through a daughter of Mr David Anderson, it reached the celebrated James Gregory, inventor of the reflecting telescope, who was the son of that lady, and is said to have received, from her, the elements of mathematical knowledge.
	www.electricscotland.com /history/other/anderson_alexander.htm (470 words)

	Durer (Site not responding. Last check: 2007-11-04)
		It is claimed that his self-portrait in a wig made in 1500 has the dimensions of the head constructed proportionally.
		It was not only the mathematical theory of proportion which influenced Dürer's art at this period, but also his mastery of perspective through his study of geometry.
		The first of the four books describes the construction of a large number of curves, including the Spiral of Archimedes, the Equiangular or Logarithmic Spiral, the Conchoid, Dürer's Shell Curves, the Epicycloid, the Epitrochoid, the Hypocycloid, the Hypotrochoid, and the Limaçon of Pascal (although of course Dürer did not use that name!).
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Durer.html (2527 words)

	Trisecting an angle
		The construction of regular polygons using ruler and compass was certainly one of the major aims of Greek mathematics and it was not until the discoveries of Gauss that further polygons were constructed with ruler and compass which the ancient Greeks had failed to find.
		However, most historians of mathematics believe that many of the results given in the Book of Lemmas are indeed due to Archimedes and the result given on trisecting an angle is so much in the spirit of the work On spirals that it is widely accepted that this method is indeed due to Archimedes.
		Pappus tells us that in practice the conchoid was not always actually drawn but that some, for greater convenience, moved a ruler about the fixed point until by trial the intercept was found to be equal to the given length.
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Trisecting_an_angle.html (1997 words)

	A Mathematical Chronology (Site not responding. Last check: 2007-11-04)
		They use Pythagoras 's theorem and use mathematics to extend knowledge of astronomy.
		Pythagoras of Samos moves to Croton in Italy and teaches mathematics, geometry, music, and reincarnation.
		Nicomedes writes his treatise On conchoid lines which contain his discovery of the curve known as the "Conchoid of Nicomedes".
	northonline.sccd.ctc.edu /cvincent/ASL120/a_mathematical_chronology.htm (1039 words)

	[No title]
		Nicomedes is best known for his invention of the curve known as the conchoid [Heath], which serves as the basis for an angle trisection.
		In his discussion of the trisection of an angle, he said, "Nicomedes trisected any rectilineal angle by means of the conchoidal curves, the construction, order and prope rties of which he handed down, being himself the discoverer of their peculiar character.
		The recognition that it was possible to give a proof of impossibility as precise and rigorous as a conventional mathematical solution represents a conceptual turning point for mathematics, and a satisfactory solution of this classical problem was not achieved until the 19th century.
	www.math.rutgers.edu /courses/436/436-s00/Papers2000/jackter.html (2258 words)

	Vincenzo Viviani Mathematicians Mathematics Science
		Vincenzo Viviani, a pupil of Galileo and Torricelli, born at Florence on April 5, 1622, and died there on September 22, 1703, brought out in 1659 a restoration of the lost book of Apollonius on conic sections, and in 1701 a restoration of the work of Aristaeus.
		He explained in 1677 how an angle could be trisected by the aid of the equilateral hyperbola or the conchoid.
		In 1692 he proposed the problem to construct four windows in a hemispherical vault so that the remainder of the surface can be accurately determined; a celebrated problem, of which analytical solutions were given by Wallis, Leibnitz, David Gregory, and James Bernoulli.
	infotut.com /reference/Science/Mathematics/Mathematicians/Viviani,_Vincenzo (128 words)

	Math History (Site not responding. Last check: 2007-11-04)
		The MacTutor History of Mathematics archive has biographies of hundreds of mathematicians, organized in both chronological and alphabetical order.
		This article takes issue with histories of mathematics as we know it today, which tend to portray the discovery of mathematics as a steady, progressive growth of ideas.
		Instead, this article takes an interesting approach of relating the history of mathematics to an evolutionary process, in which mathematical ideas evolve, and are "naturally" selected by people who accept them, refine them, and pass them along to their descendents.
	mcraeclan.com /links/InfoMathHistory.htm (387 words)

	Conchoid - TheBestLinks.com - Glass, Mineral, Disambig, Conchoid (mineralogy), ...
		Conchoid - TheBestLinks.com - Glass, Mineral, Disambig, Conchoid (mineralogy),...
		Conchoid curve, an equation discovered by the Greek mathematician Nicomedes
		Conchoidal fracture, a breakage pattern characteristic to certain minerals and glasses.
	www.thebestlinks.com /Conchoid.html (119 words)

	Historiske kurver
		The conchoid has x = b as an asymptote and the area between either branch and the asymptote is infinite.
		The conchoid was used in the construction of ancient buildings.
		The vertical section of columns was made in the shape of the loop of the conchoid.
	www.odder-gym.dk /matematik/LN/HistKurver.html (615 words)

	Timeline of civilisation, science and technology (Site not responding. Last check: 2007-11-04)
		Thabit ibn Qurra makes important mathematical discoveries such as the extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic geometry, and non-euclidean geometry.
		Pacioli publishes Summa de arithmetica, geometria, proportioni et proportionalita which is a review of the whole of mathematics covering arithmetic, trigonometry, algebra, tables of moneys, weights and measures, games of chance, double-entry book-keeping and a summary of Euclid's geometry.
		It is the first published work on probability theory, outlining for the first time the concept called mathematical expectation based on the ideas in the letters of Fermat and Pascal from 1654.
	www.mtvdance.com /scitrance/shivatech/timeline.htm (10325 words)

	Folium of Descartes (Site not responding. Last check: 2007-11-04)
		"Conchoid" implies the shape of a sea shell.
		Arguably his most significant contribution to mathematics was to found analytic geometry.
		Bell, E. Men of Mathematics, Chapter 3 in various editions and publishers.
	curvebank.calstatela.edu /calculusfolium/calculusdescartes.htm (180 words)

	Xah: Special Plane Curves: References
		The emergence of non-Euclidean geometries in the beginning of the nineteenth century represents one of the dramatic episodes in the history of mathematics.
		The course can serve either as the one undergraduate geometry course taken by mathematics majors in general or as a sequel to college geometry for prospective or current teachers of secondary school mathematics.
		Here's the description from the back cover: This is a genuine introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences.
	xahlee.org /SpecialPlaneCurves_dir/Intro_dir/references.html (2675 words)

	NSW HSC ONLINE - Mathematics
		These are designed for mathematics classes working in a computer laboratory.
		Solutions and graphs for a broad range of mathematical questions are presented at this dynamic and interactive site.
		This powerful tool could be used as an exercise checker and self tutorial for students or as a generator of exercises.
	hsc.csu.edu.au /maths/student_resources/2383/online/reviews/site_reviews.html (790 words)

	Timeline related to Greek Science and Technology 1/2
		He brings Babylonian mathematical knowledge to Greece and uses geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore.
		Other paradoxes made the same or opposite points, but, in fact, mathematical analysis shows that infinite aggregates and the nature of the continuum are not self-contradictory but only counter to intuition.
		About 370-360 BC Eudoxus of Cnidus invented a model of twenty-seven concentric spheres by which he was able to calculate the sun's annual motions through the zodiac, the moon's motion including its wobble, and the planets' retrograde motion.
	www.mlahanas.de /Greeks/HistoricEvents.htm (5114 words)

	Trisecting an angle
		The problem is therefore to trisect an arbitrary angle and the aim is to make the construction using ruler and compass (which is impossible) but failing that to devise some method to trisect an arbitrary angle.
		So as a practical problem there was little left to do although the Greeks still were not satisfied in general with mechanical solutions from a purely mathematical point of view they did not find them.
		The ruler has a fixed distance marked on it and one mark is kept on a given line while the other traces the conchoid curve.
	www-groups.dcs.st-and.ac.uk /~history/PrintHT/Trisecting_an_angle.html (1995 words)

	History of Mathematics (Site not responding. Last check: 2007-11-04)
		Some years down the line, the mathematics department at this same university plays host to an astonishingly comprehensive website dedicated to the history of this subject (www-groups.dcs.st-andrews.ac.uk/~history/).
		Edmund Robertson, head of the School of Mathematics and Statistics at the University of St. Andrews, and a colleague at the department, Dr. John O'Connor, created the History of Mathematics website as part of teaching software they had developed: the MacTutor System.
		This feature, which includes curves enigmatically named Conchoid of de Sluze and the Witch of Agnesi, provides drawings of 66 famous "curves," their history and associated mathematical curves.
	fathom.lse.ac.uk /Features/35516 (493 words)

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