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Topic: Circle points segments proof

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	circle
		the pedal of the circle is the limaçon (pedal point not on the circumference) or the cardioid (pedal point on the circumference)
		the circle is the pedal of the hyperbola
		the hyperbolism of the circle is the witch of Agnesi, the serpentine or Kulp's quartic
	www.2dcurves.com /conicsection/conicsectionc.html (1572 words)

	Circle (Site not responding. Last check: 2007-10-08)
		All circles are similar; as a consequence, a circle's circumference and radius are proportional, as are its area and the square of its radius.
		The radius for such a partial circle may be calculated from the length L of a chord, and the distance D from the center of the chord to the nearest point on the circle by various formulas including: image (from a geometric derivation)
		The 3-dimensional analog of the circle is the sphere.
	www.yotor.com /wiki/en/ci/Circle.htm (959 words)

	Circle -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		The segment of a secant bound by the circle is called a (A combination of three or more notes that blend harmoniously when sounded together) chord, and the longest chords are those that pass through the centre, called diameters and divided into two radii.
		The radius for such a partial circle may be calculated from the length L of a chord, and the distance D from the center of the chord to the nearest point on the circle by various formulas including:
		A circle is a kind of ((geometry) a curve generated by the intersection of a plane and a circular cone) conic section, with (Strange and unconventional behavior) eccentricity zero.
	www.absoluteastronomy.com /encyclopedia/c/ci/circle.htm (1084 words)

	Encyclopedia: Circle
		In Euclidean geometry, a circle is the set of all points at a fixed distance, called the radius, from a fixed point, called the centre (center).
		If the circle is centered at the origin (0, 0), then this formula can be simplified to In mathematics and in the sciences, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities.
		Jump to: navigation, search The power of a point P with respect to a circle with center C and radius r is defined as Therefore points inside the circle have negative power, points outside have positive power, and points on the circle have power zero.
	www.nationmaster.com /encyclopedia/Circle (1506 words)

	Nine Point Circle
		of the segments connecting the orthocenter with vertices, lie on a circle, known as the 9 point circle.
		Since the triples come in pairs that comprise six concyclic points, each pair of the triples define the same circle, which exactly means that all three triples - 9 points in all - all lie on the same circle.
		The nine point circle is the circumcirlce of the orthic triangle H
	www.cut-the-knot.org /Curriculum/Geometry/SixPointCircle.shtml (379 words)

	Circle (Site not responding. Last check: 2007-10-08)
		In an x-y coordinate system, the circle with centre (a, b) and radius r is the set of all points (x, y) such that
		The area of a circle cut off by a chord is called a circular segment.
		The radius for such a partial circle may be calculated from the length L of a chord, and the distance D from the center of the chord to the nearest point on the circle by various formulas including: (from a geometric derivation)
	www.usedaudiparts.com /search.php?title=Circle (1085 words)

	ArtLex's Pm-Pom page
		In typography, it is the smallest unit of measurement: although actually.01384 inch, for practical purposes, it is 1/12 of an inch, and twelve points equal one pica.
		A pointing machine is a framework of metal arms which can be fitted around a sculpture to measure the relationship between given points on its surface.
		Pointing machines are especially necessary for the carving of sculptures having complex form which is based on a plastic model.
	www.artlex.com /ArtLex/Pm.html (3451 words)

	Circle (Site not responding. Last check: 2007-10-08)
		---- In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed...
		---- In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, called the centre.
		The radius for such a partial circle may be calculated from the length L of a chord, and the distance D from the center of the chord to the nearest point on the circle by various formulas including: (from a geometric derivation) :
	www.33beat.com /Circle.html (1100 words)

	Dividing a circle into areas
		It will later be useful to know what happens to a set of areas already divided by k lines when you run another line from one end to the other, crossing k lines (see the example, where k = 2).
		This is complicated, because if the k lines intersect each other then we could chose to insert the new line in such a way that it hits the intersection point, resulting in fewer new areas being generated by the division.
		However, there will generally be a path for the new line, such as line {b} which does not involve more than two lines intersecting at any given point (proof?), and in this case it will generally result in the creation of k + 1 (in this case three) new areas.
	www.sciencedaily.com /encyclopedia/dividing_a_circle_into_areas (652 words)

	Pythagorean Theorem and its many proofs
		The first proof I merely pass on from the excellent discussion in the Project Mathematics series, based on Ptolemy's theorem on quadrilaterals inscribed in a circle: for such quadrilaterals, the sum of the products of the lengths of the opposite sides, taken in pairs equals the product of the lengths of the two diagonals.
		Douglas Rogers who observed the relationship between the proofs 46-49 also remarked that a square could have been drawn on the smaller legs of the two triangles if the second triangle is drawn in the "bottom" position as in proofs 46 and 47.
		He also pointed out that it is possible to think of one of the right triangles as sliding from its position in proof #46 to its position in proof #48 so that its short leg glides along the long leg of the other triangle.
	www.cut-the-knot.org /pythagoras/index.shtml (6005 words)

	TangentPaper (Site not responding. Last check: 2007-10-08)
		If we are given an arbitrary line, l, with an arbitrary point, p, and an arbitrary circle, O, (with center k) not intersecting the line or point, then we would like to find two circles which are tangent to our given point and circle.
		Now, if we construct a line w parallel to line l through point a, w should be the directrix and point k should be the focus for a parabola opening to the right with its vertex at point f when it is collinear with points a, p, and k.
		Similarly, if we construct a line x parallel to line l through point b, x should be the directrix and k should be the focus for a parabola opening to the right with its vertex at point g when it is collinear with points b, p, and k.
	jwilson.coe.uga.edu /emt669/Student.Folders/Moore.John/tangents/tangentpaper.html (464 words)

	Greek Demonstration: The Return of Odysseus and the Elements of Euclid
		The method of proof which Proclus assumes that Thales used is superposition, not a rigorous deductive method, but still a marginally acceptable procedure in the mathematics of the Elements and entirely diagrammatic in essence.
		By pointing (deiknus) to the map, Aristagoras means to secure the truth of his claim and thus betrays his conviction that Hecataeus' radically geometrical geography proffers evidence of the most irrefutable authority.
		The greek word for "point" in geometry is semeion, a special form of the noun sema, which in the Odyssey names the sign of the olive trunk at the center of Penelope's bed.
	ccat.sas.upenn.edu /awiesner/gkdem.html (13693 words)

	Math Trek: Squaring Circles, Science News Online, Oct. 30, 2004 (Site not responding. Last check: 2007-10-08)
		General interest in the problem was so great and the number of proposed but erroneous proofs so voluminous that, in 1775, the Paris Academy found it necessary to pass a resolution stating that no more purported solutions to the circle-squaring problem would be examined.
		A circle and a square have equal areas only if the ratio of a square's side to a circle's radius equals the square root of pi.
		Mathematicians who studied Tarski's circle problem strongly suspected there is no way to cut up a circle to make a square without losing even a single point out of the circle.
	www.sciencenews.org /articles/20041030/mathtrek.asp (1156 words)

	StudyWorks! Online : Star Polygons (Site not responding. Last check: 2007-10-08)
		Mark m points on the circle such that the circle is divided into equal arcs.
		Repeat this process until you arrive back at the first point or until a closed figure is created.
		It is created by drawing a circle with m points on it and drawing connecting lines between the points every n points.
	www.studyworksonline.com /cda/content/applet/0,,NAV2-21_SAP245,00.shtml (304 words)

	cut on the bias: August 2003 Archives (Site not responding. Last check: 2007-10-08)
		I point out a lot of problems in journalism on this blog, but here is an example of an editor who chose to resign rather than compromise her professional ethics.
		Michele also points out that the coverage of 9/11 by the major media will not be very indepth or comprehensive, which is just incomprehensible to me. I think the reason why must be because of the ambivalence toward the wars in Afghanistan and Iraq that followed.
		The problem is that for the sake of gaining a point, the defense may erode a major protection for teens.
	bias.blogfodder.net /archives/2003_08.html (13952 words)

	Steve Sailer-Articles & Blog on Human Biodiversity, Genetics, Sports, Race, Gender, Immigration, IQ, Mexico, ...
		But the key point is this: the IQ gap between the white majority in France and the Muslims appears to be at least as large as the IQ difference between whites and African-Americans—which causes so many problems in this country.
		A reader points out that libertarian Congressman Ron Paul, definitely one of the more fun members of the House, suggested we issue them after 9/11 as a free-enterprise solution to terrorism.
		Still, as The Clash pointed out, "The future is unwritten." Fifty years ago white Americans thought of African-Americans the way they think of Hispanics today: as trustworthy servants.
	www.isteve.com (11658 words)

	BuzzMachine... by Jeff Jarvis
		But he first makes an important point about the future of media and the necessity of links: We depend on our blog friends to find the good stuff for us and if they don't, we aren't likely to read it.
		The point of this would be to garner realistic details for the novel and to create a convincing character who thinks and behaves like a young, Western-educated Iranian blogger....
		She said: I wish the flag of Islam rise all over the globe; as a proof of globalization of Islam, you see that women in France also wear head scarves.
	www.buzzmachine.com /archives/2004_02.html (14850 words)

	NCTM : Illuminations (Site not responding. Last check: 2007-10-08)
		Create a customized circle graph with your own data, or display a circle graph from an included set of data.
		Create equivalent fractions by dividing and shading squares or circles, and match each fractions to its location on the number line.
		Construct a figure that illustrates the sum of the angles in a triangle, quadrilateral or pentagon.
	illuminations.nctm.org /tools/index.aspx (902 words)

	Analysis, Convergence, Series, Complex Analysis - Numericana
		thus converges and its limit is the function f defined over [0,1] which is zero everywhere except at point 1, where f(1)=1.
		This means (and it's important for the rest) that the Fourier series converge to the half-sum of the left limit and the right limit at such points of discontinuity, in particular the value at point 0 is
		At a point x where a function f has a jump discontinuity, any partial sum of its Fourier series adds up to a function that has an "overshoot" (i.e., a dampened oscillation) whose initial amplitude is about 9% of the value of the jump
	home.att.net /~numericana/answer/analysis.htm (3995 words)

	Recurrence relation - Wikipedia, the free encyclopedia
		If you consider the Taylor series of the solution to a linear differential equation:
		you see that the coefficients of the series are given by the n-th derivative of f(x) evaluated at the point a.
		The differential equation provides a linear difference equation relating these coefficients.
	en.wikipedia.org /wiki/Recurrence_relation (841 words)

	Social Software
		The effect of the attack is relatively simple: if moderators mod the crapflood down, they will use up their mod points (each moderator can affect no more than five comments.) If the moderator points are used up in moderating the crap down, they can never flag the good stuff.
		Rick Bruner does make the case that there are lots of businesses using blogs in the consumer market and points out this is like the web in 1995 and where the weblog as publishing market is headed.
		Never mind the false positives, the point is that your average F500 employee spends 3-4 hours per day using email, almost 50% of email is spam and 30% is occupational spam.
	www.corante.com /many/20030801.shtml (13358 words)

	Eschaton (Site not responding. Last check: 2007-10-08)
		This Nov.4, there will be a bond election on the next segment of rail to be built.
		I mean, from a liberal's point of view we had no minority voting rights (that is, no minorites voting), racial covenants restricting home sales to fls, jews, etc...
		Tarek rightly points out that the momentum was going "our way." Still, from a purely partisan practical perspective (wow, what alliteration), if this thing gets postponed 'till March it's hard to imagine that being a net Bad Thing.
	atrios.blogspot.com /2003_09_14_atrios_archive.html (6850 words)

	The Corner on National Review Online
		“Islam is untouchable: to criticize or be suspicious of it is a proof of racism.
		Blogging away from Austria, the invaluable Bill Dawson links to a fascinating speech Merkel made recently and highlights a couple of key segments, one on the question of Islamic head scarves in schools (a source of considerable controversy in a number of European countries) and, another on Germany’s relationship with the United States.
		And, as a sign of progress, he points out that when he is offered tea now the tiny glasses overflow and stand in a saucer full of spilled liquid.
	www.nationalreview.com /thecorner/03_11_02_corner-archive.asp (11969 words)

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