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Topic: Eccentricity (mathematics)

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Eccentricity

Ellipse

Conic section

Circumference

Parabola

Orbital energy

Circle

Mathematics

Center of mass

Ferrous

Parabolic reflector

Ramanujan

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	eccentricity - Search Results - MSN Encarta
		Eccentricity, in geometry, a property of a conic section (circle, ellipse, parabola, or hyperbola).
		In mathematics, the eccentricity, denoted e or, is a parameter associated with every conic section.
		A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b.The eccentricity can also be interpreted as the fraction of the distance...
	encarta.msn.com /encnet/refpages/search.aspx?q=eccentricity (190 words)

	AllRefer.com - eccentricity Information
		Physics The distance between the center of an eccentric and its axis.
		Mathematics The ratio of the distance of any point on a conic section from a focus to its distance from the corresponding directrix.
		A circle has an eccentricity of zero; for an ellipse it is less than one; for a parabola it is equal to one; and for a hyperbola it is greater than one.
	www.allrefer.com /eccentricity (236 words)

	Leonhard Euler
		His mathematical genius gained for him a high place in the esteem of Jean Bernoulli, who was at that time one of the first mathematicians in Europe, as well as of his sons Daniel and Nicolas Bernoulli.
		While he was engaged in physiological researches, he composed a dissertation on the nature and propagation of souund, and an answer to a prize question concerning the masting of ships, to which the French Academy of Sciences adjudged the second rank in the year 1727.
		In 1735 a problem proposed by the academy, for the solution of which several eminent mathematicians had demanded the space of some months, was solved by Euler in three days, but the effort threw him into a fever which endangered his life and deprived him of the use of his right eye.
	www.nndb.com /people/954/000048810 (1451 words)

	Ellipse Summary
		The eccentricity: A measure of the relative elongation of an ellipse.
		This angle is the arc cosine of the eccentricity.
		In mathematics, an ellipse (from the Greek for absence) is a the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant.
	www.bookrags.com /Ellipse (2562 words)

	Ellipse LANGUAGE SCHOOL EXPLORER
		In mathematics, an ellipse (from the Greek for absence) is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant.
		An eccentricity of 0 implies that the two foci occupy the same point and that the ellipse is a circle.
		The greater the eccentricity is, the larger the ratio of a to b, and therefore the more elongated is the ellipse.
	www.school-explorer.com /info/Ellipse (1508 words)

	Ellipse Calculator
		As the eccentricity value goes from 0 to 1, the ellipse goes from circular to highly elongated.
		The eccentricity of an ellipse is not such a good indicator of its shape.
		For example, of all the 9 planets the one with the most eccentric orbit is Pluto with an eccentricity value of.245.
	www.1728.com /ellipse.htm (775 words)

	Parabola
		Mathematics is known to heavily borrow its terminology from the common language.
		That is, all conics of the same eccentricity are similar, differing from one another merely in size.
		Since all parabolas have eccentricity 1, all parabolas are similar to one another, differing from one another only in size" [Eves, p.
	www.cut-the-knot.org /ctk/Parabola.shtml (2812 words)

	Hyperbola Summary
		The ratio CF (or CF) is the "eccentricity" and is numerically equal to the eccentricity e in the focus-directrix definition.
		In mathematics, a hyperbola is a type of conic section (Greek ὑπερβολή literally 'overshooting' or 'excess') defined as the intersection between a right circular conical surface and a plane which cuts through both halves of the cone.
		This constant is the eccentricity of the hyperbola.
	www.bookrags.com /Hyperbola (1607 words)

	Category: Mathematics (Site not responding. Last check: )
		Eccentricity is defined, the shape of an ellipse as e approaches 0 and I is observed, and problems are solved using the eccentricity.
		Mathematical content: * estimation: of numbers * number: counting by 2s, 5s, and 10s to 25; number facts of 7 * geometry: solids and their properties cube, cone.
		Project Mathematics: The Story of Pi Although pi is the ratio of circumference to diameter of a circle, it appears in many formulas that have nothing to do with circles.
	home.comcast.net /~m-arendt/mathematics.htm (7874 words)

	Proof and reproof - 09 September 2006 - New Scientist
		Perelman may well be "disillusioned" about mathematics, but that seems to be because he is becoming disillusioned with everything, rather than because of some systematic failure of the subject itself.
		However, the mathematical community is well aware of the issues that you belatedly raise, and has been making strenuous efforts to deal with them for decades.
		It now has a mathematics in medicine initiative, and is about to start up interdisciplinary centres in systems biology (with the biology department and medical school), discrete mathematics (with computer science and business studies), and complex systems (with too many departments to list).
	www.newscientist.com /article/mg19125681.100-proof-and-reproof.html (878 words)

	GIS Tips - The Ellipsoid! Part I
		When manipulating the coordinates of an ellipse mathematically, the square of the eccentricity is the most useful number.
		Therefore, it is quite common to specify an ellipse as the equatorial radius and the square of the eccentricity.
		The eccentricity of the Earth is on the order of 0.08, the square of this eccentricity is on the order of 0.0067.
	www.mentorsoftwareinc.com /CC/gistips/TIPS0998.HTM (1255 words)

	EO Library: Milutin Milankovitch
		Born in the rural village of Dalj, Serbia, Milankovitch attended the Vienna Institute of Technology and graduated in 1904 with a doctorate in technical sciences.
		After a brief stint as the chief engineer for a construction company, he accepted a faculty position in applied mathematics at the University of Belgrade in 1909—a position he held for the remainder of his life.
		Milankovitch dedicated his career to developing a mathematical theory of climate based on the seasonal and latitudinal variations of solar radiation received by the Earth.
	earthobservatory.nasa.gov /Library/Giants/Milankovitch (240 words)

	Open Mind
		I’d also like to show the entire impact of eccentricity, precession, and obliquity (the tilt of earth’s axis) on how incoming solar energy is distributed around the planet.
		But since there seems to be a request for the eccentricity piece, I’ll start with just that.
		But one of the lessons of mathematics is that if we’re not careful, the numbers can lead us to the wrong conclusion.
	tamino.wordpress.com (1111 words)

	eccentricity - OneLook Dictionary Search
		Eccentricity : Visionary, for the Study of Vision [home, info]
		Eccentricity : A Glossary of Mathematical Terms [home, info]
		Phrases that include eccentricity: angle of eccentricity, eccentricity perturbations, eccentricity vector
	www.onelook.com /?w=eccentricity (334 words)

	Astronomy Online - Gliese 876
		Using observational data, high-resolution spectroscopy and Keplerian mathematics, it is possible to determine the mass of the star, mass of the planet, the orbital period, and the semi-major axis.
		Where v is the true anomaly, e is the eccentricity and E is the eccentric anomaly.
		In terms of the mathematics involved in solving for the orbit of planets, a two-body system is the only system that can be solved completely [R4].
	astronomyonline.org /Exoplanets/Gliese876.asp?Cate=Exoplanets&SubCate=Gliese876 (5108 words)

	Gauss and Ceres
		The reigning method for calculating orbits assumed that the orbit of a planet was circular, and that the orbit of a comet was parabolic [5]; that is, in both cases the eccentricity of the orbit was taken as known.
		A circle's eccentricity is 0, and the eccentricity of a parabola is 1.
		Appendix: Sketch of the orbits of Ceres and Pallas, by Gauss.
	www.math.rutgers.edu /~cherlin/History/Papers1999/weiss.html (2157 words)

	[No title]
		As the eccentricity varies the foci and shape of the conic change, making a transition from ellipse to hyperbola.
		The computer codes generate an animation that illustrates the shape of the conic as the eccentricity varies.
		This can lead to a further discussion of whether there is a conic for which the eccentricity is exactly equal to 1.
	mathdemos.gcsu.edu /mathdemos/ecc/index.html (416 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: )
		We weren't given the constant of eccentricity, or a directrix of the ellipse.
		I know that eccentricity in a polar conic system is r= 1/[1+ e cos()] where e is eccentricity and () is the angle.
		In practice the eccentricity is known by knowing the lengths of the major and minor axes, so the answer 'Fire the rockets when distance from the planet is a(1 +or- e^2)' is the only realistic solution.
	mathforum.org /library/drmath/view/52019.html (779 words)

	Orbits
		In mathematics, a hyperbola consists of two curves which face each other, each extending into infinity, in a hyperbolic orbit, only one of the curves is dealt with.
		An elliptical orbit is described by several parameters: the length of its semimajor axis, its eccentricity, its inclination, its period, the location of its nodes, and the location of its apsides.
		The eccentricity for ellipses is the ratio of distance between the two foci and the length of the major axis.
	library.thinkquest.org /29033/begin/orbits.htm (1054 words)

	Orbital Description
		Satellites orbit the Earth in elliptical path's with the center of the Earth at one of the ellipse's [mathematical] focus points.
		Eccentricity is computed as the linear eccentricity (the distance from the center of the ellipse to the center of the Earth) divided by the semi major axis.
		A zero eccentricity describes a circular orbit; an eccentricity approaching one describes a highly elliptical orbit.
	www.mindspring.com /~n2wwd/html/body_orbital_description.html (489 words)

	History and Philosophy of Western Astronomy
		Most comet orbits have large eccentricities (some are so eccentric that the aphelion is around 100,000 AU while the perihelion is less than 1 AU!).
		The eccentricity of the ellipses increases from top left to bottom left in a counter-clockwise direction in the figure but the semi-major axis remains the same.
		As the eccentricity increases, the Sun's position is closer to one side of the elliptical orbit, but the semi-major axis remains the same.
	www.astronomynotes.com /history/s7.htm (1569 words)

	AllRefer.com - ellipse (Mathematics) - Encyclopedia
		The vertices are the two points of intersection of the major axis with the curve.
		The eccentricity of an ellipse, a ratio of two lengths, is a measure of its flatness; it is the distance from the center to either focus divided by the distance from the center to either vertex.
		The circle may be considered an ellipse of eccentricity zero, i.e., one in which the center and the two foci all coincide.
	reference.allrefer.com /encyclopedia/E/ellipse.html (267 words)

	Astronomical Astronomy Glossary Dictionary Terminology meanings
		Eccentricity The eccentricity of an orbit is a measure of its departure from a circle.
		Elliptical orbits have an eccentricity >0 and <1, parabolic paths have an eccentricity =1, and hyperbolic paths have an eccentricity >1.
		They are the semi-major axis (a), the eccentricity (e), the inclination to the reference plane (i), the mean anomaly (M), the argument of the pericentre (w), and the longitude of the ascending node (W).
	www.aoe.com.au /astronomical_glossary.html (6593 words)

	[No title] (Site not responding. Last check: )
		Eccentricity of a vertex in a graph at distance (graph theory)
		Eccentric (mechanism), a wheel that rotates on an axle that is displaced from the focus of the circle described by the wheel
		Orbital eccentricity, in astrodynamics, calculated from orbital state vectors as an absolute value of eccentricity vector or using other methods based on orbital energy and angular momentum.
	stron.frm.pl /wiki.php?title=Eccentricity (160 words)

	Special Plane Curves: Conic Sections
		F is called the focus of the conic, d the directrix, and e the eccentricity.
		The set of all such points is a hyperbola, shaped and positioned so that its vertexes is located at the ellipse's foci, and foci is on the ellipse's vertexes, and the plane it resides is orthogonal to the ellipse's.
		The corresponding hyperbolas's eccentricities are 1/.3, 1/.7, and 1/.9 respectively.
	www.xahlee.org /SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html (1839 words)

	Moments of the Distance from the Force Center in a Two-Body Kepler Orbit
		For most people, once they have thought about it, the "average" distance of the earth from the sun would probably be calculated by measuring the distance every day for one full year and then dividing the sum of these measurements by the number of days in a year.
		Hence, for small eccentricities, the mean position of a planet averaged over true anomaly is approximately half way between the center of the ellipse and the focus (sun).
		To the numerical accuracy of the calculation this value of the eccentricity gave an “exact” linear fit with a correlation coefficient equal to –1.
	matcmadison.edu /alehnen/kepler/kepler.htm (5351 words)

	The use of Newtonian Mechanics to explain cyclic temperature variations
		The variations in the Earth's orbital motion, specifically its variations in: obliquity, quasi-periodic precession index, and orbital eccentricity, each govern a cyclic portion of the climatic variation (Hays, Imbrie, and Shackleton 1131).
		Because of its 3 dimensional complexity, the mathematics employed in Benumof's paper looks extremely complicated; however, he is just applying the technique of variation of parameters to a more complex system.
		This is not to say the mathematics is trivial -- if you are tempted to wade through it, bring a large pad of paper, several pencils, a large dose of patience, and plenty of time!
	www.users.nac.net /pschoch/spst435/gravity.html (482 words)

	Eccentricity of Conics -- Mudd Math Fun Facts
		A circle has eccentricity 0, an ellipse between 0 and 1, a parabola 1, and hyperbolae have eccentricity greater than 1.
		Surprise: the eccentricity is equal to the sine of the angle of this tilt!
		If students are puzzled why the circle has eccentricity zero, you might explain that its directrix is the line "at infinity" in the projective plane.
	www.math.hmc.edu /funfacts/ffiles/20003.2.shtml (373 words)

	Pion abstract (Site not responding. Last check: )
		In three experiments schematic faces were used as stimuli, involving seven levels of iris eccentricity crossed with three levels of face eccentricity.
		All results showed clear and consistent effects of both iris and face eccentricity on perceived gaze direction.
		These web-based abstracts are provided for ease of seaching and access, but certain aspects (such as as mathematics) may not appear in their optimum form.
	www.perceptionweb.com /ecvp04/0387.html (221 words)

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