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Topic: Cycloid

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List of curves

Tautochrone

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Intermediate value theorem

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Calculus of variations

Cauchy integral theorem

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	Cycloid and Ctenoid Scales
		Cycloid and ctenoid scales are found in the majority of bony fishes (the Teleostei).
		Cycloid and ctenoid scales consist of two main regions, a surface "bony" layer, composed of an organic framework impregnated largely with calcium based salts, and a deeper fibrous layer composed mainly of collagen.
		Cycloid and ctenoid scales are derived from ganoid scales that have lost the ganoine and thinned the bony embedded plate.
	www.amonline.net.au /fishes/what/scales/cyccten.htm (323 words)

	Cycloid - LoveToKnow 1911
		The name cycloid is now restricted to the curve described when the tracing-point is on the circumference of the circle; if the point is either within or without the circle the curves are generally termed trochoids, but they are also known as the prolate and curtate cycloids respectively.
		The method by which the cycloid is generated shows that it consists of an infinite number of cusps placed along the fixed line and separated by a constant distance equal to the circumference of the rolling circle.
		The cartesian equation, referred to the fixed diameter and the tangent at B as axes may be expressed in the forms x= a6, y=a(I -cos 0) and y-a=a sin (x/afir); the latter form shows that the locus is the harmonic curve.
	www.1911encyclopedia.org /Cycloid (1248 words)

	Cycloid
		A cycloid is the shape defined by a fixed point on a wheel as it rolls, or, more precisely, the locus of a point on the rim of a circle rolling along a straight line.
		The cycloid was first studied by Nicholas of Cusa[?] and later by Mersenne.
		The cycloid is the solution to the brachistochrone problem and the related tautochrone problem.
	www.ebroadcast.com.au /lookup/encyclopedia/cy/Cycloid.html (0 words)

	Rotary piston machine having cycloid teeth - Patent 6494698
		In contrast to the conventional cycloid construction, the cycloid 6 is generated by rolling a circle along the line of intersection 7 between spherical surface 8 and base surface 4 with the point on this circle describing the cycloid 6 always being located on this spherical surface 8.
		A straight cycloid toothed structure is obtained by a straight generating line moving about a fixed point on the rotary axis of the drive or output shaft 2 along the generating curve 6.
		It is irrelevant to the invention whether the cycloid tooth structure is disposed on the end face of the power component 1 as shown herein, with the corresponding tooth structure disposed on the blocking component 10, or vice versa.
	www.freepatentsonline.com /6494698.html (0 words)

	cycloid - Search Results - MSN Encarta
		Cycloid, a type of curve in plane geometry.
		The most common example of a cycloid is the curve traced by a point on the rim of a wheel moving across...
		Hypocycloid, in geometry, a cusped curve traced by a point on the circumference of a circle that rolls around the inside of another larger circle.
	ca.encarta.msn.com /cycloid.html (110 words)

	[No title]
		The concept of cycloid psychosis applied thus was wider than permitted by the criteria stipulated by Perris and Brockington with respect to the prominence of the mood component.
		Cycloid psychotic disorder: validation of the concept by means of a follow-up and a family study.
		The evolution of the German-Scandinavian concept of cycloid psychosis and of the French concept of 'bouffee delirante' is analyzed.
	www.psycom.net /depression.central.cycloid.html (1785 words)

	Nikon MicroscopyU: Phase Contrast and DIC Comparison Image Gallery - Cycloid Fish Scale
		The deeper fibrous layer is mainly composed of collagen and the outer bony layer is an organic framework saturated primarily with calcium-based salts.
		Cycloid scales grow larger with the fish they cover, which sometimes result in growth rings that are similar to those found in trees.
		Cycloid scales are most often found on advanced fish species, such as trout, herring, and carp.
	www.microscopyu.com /galleries/dicphasecontrast/cycloidsmall.html (244 words)

	Cycloid - Wikipedia, the free encyclopedia
		A cycloid is the curve defined by a fixed point on a wheel as it rolls, or, more precisely, the locus of a point on the rim of a circle rolling along a straight line.
		If its length is equal to that of half the cycloid, the bob of a pendulum suspended from the cusp of an inverted cycloid, such that the "string" is constrained between the adjacent arcs of the cycloid, also traces a cycloid path.
		The cycloid, epicycloids, and hypocycloids have the property that each is similar to its evolute.
	en.wikipedia.org /wiki/Cycloid (472 words)

	The Sundial Primer - Cycloid Polar Sundial
		Cycloid Polar Sundial: a variation of the standard polar sundial in which the gnomon has a cycloid shape, with the result that the hour lines are equally spaced.
		The figure is of a cycloid with its vertex at the origin O, which is the type that is of interest for this particular dial.
		The cycloid template was built using 1/4° movements of the circle turning to calculate the x and y co-ordinates.
	www.mysundial.ca /tsp/cycloid_polar_sundial.html (1283 words)

	Cycloid
		The cycloid is the locus of a point at distance h from the centre of a circle of radius a that rolls along a straight line.
		The cycloid was first studied by Cusa when he was attempting to find the area of a circle by integration.
		Mersenne gave the first proper definition of the cycloid and stated the obvious properties such as the length of the base equals the circumference of the rolling circle.
	www-groups.dcs.st-and.ac.uk /~history/Curves/Cycloid.html (0 words)

	PlanetMath: cycloid
		The cycloid is the curve a point on the perimeter of a wheel traces when rolling without slipping.
		This is version 2 of cycloid, born on 2005-05-22, modified 2005-05-22.
		Object id is 7100, canonical name is Cycloid.
	planetmath.org /encyclopedia/Cycloid.html (85 words)

	CYCLOID (from Gr. icii... - Online Information article about CYCLOID (from Gr. icii...
		cycloid is now restricted to the curve described when the tracing-point is on the circumference of the circle; if the point is either within or without the circle the curves are generally termed trochoids, but they are also known as the prolate and curtate cycloids respectively.
		companion to the cycloid is a curve so struction, form and equation to the common cycloid.
		locus of P is the companion to the cycloid.
	encyclopedia.jrank.org /CRE_DAH/CYCLOID_from_Gr_iciidws_circle_.html (0 words)

	Olympus Microscopy Resource Center: Specialized Microscopy Techniques - Differential Interference Contrast Image ...
		Both cycloid and ctenoid scales consist of a rigid surface layer primarily composed of calcium-based salts and a fibrous inner layer that is mainly made of collagen.
		Cycloid scales exhibit a smoothly rounded posterior edge, whereas those of the ctenoid variety are characterized by a row of comb-like extensions.
		Cycloid scales are most often found on carps and similar fishes, while ctenoid scales are more common to higher bony fishes, including perch and sunfish.
	www.olympusmicro.com /primer/techniques/dic/dicgallery/cycloidscalesmall.html (0 words)

	Cycloids
		In the case of a regular cycloid, the generating point is on the rim of the disk.
		The shape of the cycloid is determined by two parameters, the first being the radius r of the rolling disk and second the distance d between the generating point and the center of the disk.
		The two sliders Cycloid Discr and Cycloid Length control the number of points of the cycloid curve, that are calculated and the total length of the cycloid respectively.
	www.javaview.de /doc/demo/cycloid.html (0 words)

	Cycloid
		PA is the normal at P. E is a reflection of P through A. The locus of E is the evolute of the cycloid.
		The catacaustic of a cycloid with respect to parallel rays coming beneath its arc are two smaller cycloids.
		The radial of a cycloid is a circle.
	xahlee.org /SpecialPlaneCurves_dir/Cycloid_dir/cycloid.html (0 words)

	Grid Cycloid Arc, Grid Cycloid Arc Batch Processor
		A grid consisting of cycloids (defined by: x = θ - sinθ;, y = 1 - cosθ;, where θ is the angle ranging from 0 to π) is drawn on the image.
		The cycloids must be aligned with their short axes parallell to the vertical axis in the specimen.
		The cycloid height and width are limited by the height or width of the tile, depending on which is the greatest.
	rsb.info.nih.gov /ij/plugins/grid-cycloid-arc.html (1160 words)

	cycloid
		The shape defined by a fixed point on a wheel as it rolls; more precisely, it is the locus of a point on the rim of a circle rolling along a perfectly straight line.
		As well as the ordinary cycloid there is the curtate cycloid, which is the path traced out by a point on the inside of a rolling circle, and the prolate cycloid, which is followed by a point on the outside of the circle.
		A prolate cycloid is traced out, for example, by points on the flange of the wheels of a locomotive, which extends below the top of the tracks.
	www.daviddarling.info /encyclopedia/C/cycloid.html (334 words)

	The Cycloid (Site not responding. Last check: )
		A fascinating property of the cycloid is mentioned in your homework assignment.
		In the photo below, an actual model of a cycloid from the Florence Science Museum is shown, together with a straight rail, built to compare the speeds of a small metal marble rolling down these two curves.
		Another way by which the cycloid curve is derived is obtained by following a point on a boundary on a rolling circle.
	www.case.edu /artsci/math/lonke/cycloids/cyclesa.html (221 words)

	The Cycloid (Site not responding. Last check: )
		A fascinating property of the cycloid is mentioned in your homework assignment.
		In the photo below, an actual model of a cycloid from the Florence Science Museum is shown, together with a straight rail, built to compare the speeds of a small metal marble rolling down these two curves.
		Another way by which the cycloid curve is derived is obtained by following a point on a boundary on a rolling circle.
	www.cwru.edu /artsci/math/lonke/cycloids/cyclesa.html (0 words)

	Cycloid Summary
		A cycloid is the curve defined by a fixed point on a wheel as it rolls, or, more precisely, the locus of a point on the rim of a circle rolling along a straight line.
		The cycloid was first studied by Nicholas of Cusa and later by Mersenne.
		The cycloid, epicycloids, and hypocycloids have the property that each is similar to its evolute.
	www.bookrags.com /Cycloid (694 words)

	Cycloid - Search Results - ninemsn Encarta
		Cycloid, a type of curve in plane geometry.
		The most common example of a cycloid is the curve traced by a point on the rim of a wheel moving across...
		Herring, common name for several fishes characterized by a single short dorsal fin in the middle of the back and by an anal fin similarly located...
	au.encarta.msn.com /Cycloid.html (0 words)

	The Cycloid
		The cycloid is a famous curve traced by a point on the edge of a rolling wheel.
		Geometrically, the cycloid is formed by tracing a point on the edge of a circle B of radius b that is concentric to a circle A of radius a, as circle A rolls without slipping along the x-axis.
		If the radius of B is less than that of A, then the cycloid is said to be curtate.
	www.math.hmc.edu /~gu/curves_and_surfaces/curves/cycloid.html (88 words)

	The Helen of Geometers
		The curve traced out by a point on the rim of a rolling circle is called a cycloid, and we've seen that this curve described gravitational free-fall, both in Newtonian mechanics and in general relativity (in terms of the free-falling proper time).
		Mersenne publicized the cycloid among his group of correspondents, including the young Roberval, who, by the 1630's had determined many of the major properties of the cycloid, such as the interesting fact that the area under a complete cycloidal arch is exactly three times the area of the rolling circle.
		Thus he had discovered that the cycloid is the tautochrone, i.e., the curve for which the time taken by a particle sliding from any point on the curve to the lowest point on the curve is the same, independent of the starting point.
	www.mathpages.com /rr/s8-03/8-03.htm (1364 words)

	cycloid (Site not responding. Last check: )
		Huygens used the insight that the involute of a cycloid is the same cycloid (of course also valid for the evolute).
		Jakob and Johann Bernoulli showed (1692) that the cycloid is the catacaustic of a circle, where light rays come from the circumference.
		Sometimes the meaning of cycloid and trochoid is interchanged: trochoid for the general case, cycloid only for the situation that the starting point is lying on the circle.
	www.2dcurves.com /roulette/roulettec.html (1239 words)

	Cycloid Inflates Market Niche
		When Pittsburgh-based Cycloid Company began developing an automatic tire inflation system back in 1993, the company knew it was poised to leverage a niche in the trucking industry that would have a dramatic impact on a trucking firm's bottom line and general safety.
		Cycloid was able to develop and deliver its product to the marketplace in relatively short period of time through a unique "virtual" operation.
		Cycloid's Cranberry Township offices engineer and market the product, while it subcontracts the manufacturing to C&J Industries in Meadville, Pa. The air pressure system is then sold through distributors, including Euclid Industries in Ohio.
	news.pghtech.org /teq/teqstory.cfm?id=186 (0 words)

	Cycloid \| World of Mathematics
		The cycloid is a planar curve, defined as the trajectory traveled by a marked point on the rim of a wheel as it rolls without slipping along a level surface.
		The cycloid resembles a series of arches, with cusps at the beginning and end of each arch.
		The cycloid is part of a general class of curves called roulettes (curves produced by rolling) and was one of the first curves whose arc length was computed exactly.
	www.bookrags.com /research/cycloid-wom (288 words)

	Scientific career - Quadrature of the cycloid curve
		From the nature of the cycloid is derived the property that its base AB is equal to the periphery of the generating circle AC.
		The space included between the cycloid and the straight line forming its base is the triple of the generating circle or one and a half times the triangle having the same base and height.
		Let there be given the cycloid ABC, described by the point C of the circle CDEF when it rotates on the fixed base AF.
	galileo.imss.firenze.it /multi/torricel/etorat32.html (0 words)

	Cycloids
		A cycloid is the path traced out by a point on the circumference of a circle as the circle rolls (without slipping) along a straight line.
		A cycloid can be drawn by a pencil (chalk or marker) attached to a circular lid which is rolled along a ruler.
		It is relative easy to explain what the cycloids are and then it is exciting and informative to see them plotted.
	mathdemos.gcsu.edu /mathdemos/cycloid-demo/index.html (999 words)

	Count On (Site not responding. Last check: )
		The curve we obtain of a fixed point on the circumference of a circle rolling on a line is called the Cycloid - but in general, as we shall see, there are many types of cycloid and we need to consider different cases of the base curve.
		The Cycloid has been studied by many famous mathematicians, and was probably first conceived by Mersenne and Galileo in 1599.
		Other cycloids are formed by points which are rigidly attached to a circle but not on it.
	www.mathsyear2000.org /explorer/circles/cycloids (0 words)

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