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	Malfatti circles
		In 1803 the Italian mathematician Giovanni Malfatti (1731-1807) posed the following problem: Given a triangle, find three non-overlapping circles inside it such that the sum of their areas is maximal.
		Malfatti and many other mathematicians thought that the solution is given by the three circles each of which is tangent to the other two and also to two sides of the triangle.
		The third circle is inscribed either in the same angle or in the middle angle of the triangle, depending on which of them has the bigger area.
	www.daviddarling.info /encyclopedia/M/Malfatti_circles.html (184 words)

	Circles - FUTEF
		In mathematics, a unit circle is a circle with a unit radius, i.e., a circle whose radius is 1.
		Frequently, especially in trigonometry, "the" unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in t...
		In geometry, a circular segment (also circle segment) is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant or a chord.
	futef.com /search?query=cats:[Circles] (480 words)

	Journal of Computer-Generated Euclidean Geometry 2007 No 32
		The Inner Apollonius circle of the Excircles is the Nine-Point Circle, and the Inner Apollonius triangle of the Excircles is the Feuerbach triangle.
		The Outer Apollonius circle of the Excircles is the Apollonius Circle.
		The Tangential Triangle and the Outer Apollonius Triangle of the Triad of the Incircles of the Triangulation Triangles of the Center of the Inner Soddy Circle are perspective with perspector the Perspector of the Intouch Triangle and the Tangential Triangle.
	www.dekovsoft.com /j/2007/32 (4799 words)

	Malfatti Circles -- from Wolfram MathWorld
		Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the
		The Malfatti configuration appears on the cover of Martin (1998).
		Although these circles were for many years thought to provide the solutions to Malfatti's problem, they were subsequently shown never to provide the solution.
	mathworld.wolfram.com /MalfattiCircles.html (410 words)

	Triangle (Site not responding. Last check: )
		The [[Circumcenter is the centre of a circle passing through the three vertices of the triangle.]] A perpendicular bisector of a Triangle is a straight line passing through the midpoint of a side and being perpendicular to it, i.e.
		[[Nine point circle demonstrates a symmetry where six Points lie on the same circle.]] The midpoints of the three sides and the feet of the three altitudes all lie on a single circle, the triangle's nine point circle.
		The center of the Nine point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter.
	triangle.iqnaut.net (1965 words)

	more circles
		The Bankoff circle B is the circle through the cusp of the arbelos and the tangent points of the first Pappus circle.
		Given a triangle, put three circles in it, so that each circle is tangent to the other two and to two sides of the triangle.
		The circle skating rink curve is formed by four circle arcs, one four each side, so that the curve is tangent to two concentric circles (of different size).
	www.2dcurves.com /conicsection/conicsectioncm.html (1139 words)

	[No title]
		Malfatti and many other mathematicians thought that the solution of this problem is given by the three circles each of which is tangent to the other two and also to two sides of the triangle.
		Malfatti computed the radii of these circles, and they are now known as Malfatti's circles.
		The third circle is inscribed either in the same angle or in the middle angle of the triangle, depending on which of them has bigger area.
	www.math.uconn.edu /~newsltr/archives/December.10.2001.html (485 words)

	Philosophical implications of Malfatti's problem
		Malfatti's solution was not simply wrong some of the time, but it turned out that Malfatti's solution was wrong every time -- there is absolutely no triangle in which Malfatti's accepted solution is correct.
		Malfatti's calculations correctly found the circles with the largest area where each circle touches one other circle and touches two sides of the triangle.
		Malfatti originally restricted his interest only to circles inscribed within a right triangle, however, the correct solution for right triangles was discovered in the same paper (Zalgaller and Los, 1990) that found the solution for any triangle.
	virgil.gr /54 (572 words)

	Malfatti biography
		Gianfrancesco Malfatti studied under Vincenzo Riccati, F M Zanotti, and G Manfredi at the College of San Francesco Saverio in Bologna.
		Then, in 1754, Malfatti went to Ferrara where he taught mathematics and physics in a school that he started up there.
		Malfatti wrote an important work on equations of the fifth degree.
	www-history.mcs.st-and.ac.uk /history/Biographies/Malfatti.html (469 words)

	Colloquium - 13 November 2001 - Department of Mathematics - University of Montana
		Malfatti and many other mathematicians have thought that the solution of this problem is given by the three circles each of which is tangent to the other two and also to two sides of the triangle.
		Malfatti has computed the radii of these circles and they are now known as Malfatti's circles.
		In the first part of this lecture we shall discuss the Malfatti problem for two circles in a triangle or in a square.
	www.umt.edu /math/Colloq/fall01/111301.html (272 words)

	Dynamic Geometry Gallery
		The circle of Adams, concentric to the incircle of a triangle.
		A triangle possessing a circle with respect to which every side is the polar of the opposite vertex.
		Resembles to the tritangent circles of a triangle...
	server.math.uoc.gr /~pamfilos/eGallery/Gallery.html (4742 words)

	Math in the Media 0704
		"Malfatti's problem aims to extract three circular vertical cylinders from a triangular vertical prism made of marble, with the least material loss." [In fact, there are two non-equivalent problems, initially confused by Malfatti.
		In an equilateral triangle, in fact, the incircle and two smaller inscribed circles give a larger area than the three mutually tangent circles.
		Malfatti solved problem (2), which, as is clear from the image on the Zaman website, is the problem Mustafa Tongeman actually addressed.
	www.math.sunysb.edu /~tony/whatsnew/jul04/07-2004-media.html (735 words)

	Malfatti's Problem, Hart's Proof from Interactive Mathematics Miscellany and Puzzles
		To draw within a given triangle three circles each of which is tangent to the other two and to two sides of the triangle.
		Conversely, if a very small circle be drawn tangent to two sides of the triangle, the two circles each touching this little circle and two other sides will surely intersect.
		But if the little circle swells up, always touching the two sides until it becomes the incircle, the other two circles shrinking in the process, are eventually separated it.
	www.cut-the-knot.org /Curriculum/Geometry/MalfattiZoom.shtml (604 words)

	Malfatti (print-only)
		In 1802 he gave the first solution to the problem of describing in a triangle three circles that are mutually tangent, each of which touches two sides of the triangle, the so-called Malfatti problem.
		Jacob Bernoulli had solved this for an isosceles triangle while, after Malfatti, the problem was also solved by Steiner and Clebsch, the latter solving it using elliptic functions.
		His papers dealt with many subjects from probability to mechanics and he participated in the debate around Ruffini's attempt to prove the impossibility of solving (in the meaning of that period) equations of higher degree than four.
	www-groups.dcs.st-and.ac.uk /~history/Printonly/Malfatti.html (373 words)

	The Math Forum - Math Library - Conic Sections/Circles
		Inversion across a circle was introduced by Appolonius of Perga, whose definition of inversion was synthetic, as was all geometry at that time.
		A cardioid curve (roughly resembling a kidney bean) is the locus of points traced by a point on a moving circle that rolls without slipping on the outside of a circle of equal radius (explore the illustrative applets).
		This lab uses The Geometer's Sketchpad to explore the geometry of circles, culminating in the discovery of a famous result of the nineteenth century called Monge's Theorem and outlining a proof of the theorem using dilations.
	mathforum.org /library/topics/conic_g/?keyid=25884899&start_at=51&num_to_see=50 (2121 words)

	The Geometry Junkyard: All Topics
		Circle fractal based on repeated placement of two equal tangent circles within each circle of the figure.
		Two nested circles define a continuous family of triangles having endpoints on the outer circle and edge midpoints on the inner circle.
		Miquel's pentagram theorem on circles associated with a pentagon.
	www.ics.uci.edu /~eppstein/junkyard/all.html (9712 words)

	Circle (Site not responding. Last check: )
		A circle is the degenerate case of an
		Polar Coordinates, the equation of the circle has a particularly simple form.
		In Cartesian Coordinates, the equation of a circle of
	www.math.sdu.edu.cn /mathency/math/c/c305.htm (379 words)

	List of circle topics - Wikipedia, the free encyclopedia
		This list of circle topics is not intended for metaphorical circles, but rather for topics related to the geometric shape.
		Thus, for example, a link to inner circle does not belong here.
		This page was last modified 22:01, 26 June 2006.
	en.wikipedia.org /wiki/List_of_circle_topics (73 words)

	The Geometry Junkyard: Sphere Packing
		Apollonian Gasket, a fractal circle packing formed by packing smaller circles into each triangular gap formed by three larger circles.
		Packing circles in the hyperbolic plane, Java animation by Kevin Pilgrim illustrating the effects of changing radii in the hyperbolic plane.
		C code for finding dense packings of circles in circles, circles in squares, and spheres in spheres.
	www.ics.uci.edu /~eppstein/junkyard/spherepack.html (790 words)

	Malfatti
		Given the trianlge ABC construct 3 circles a', b', c', each tangent to the other two and tangent to two sides of the triangle.
		Start with D, the incenter of the triangle and draw the incenters E, F, G of the triangles DBC, DAC, DAB respectively.
		The other inner tangents of these circles pass all by a point T and define three quadrangles on which inscribed the requested circles with centers L, P and R. Produced with EucliDraw©
	www.math.uoc.gr /~pamfilos/eGallery/problems/Malfatti.html (78 words)

	YFF-MALFATTI POINT
		The Malfatti problem, dating from Ajima in the late 1700's and Malfatti in the early 1800's, is to construct three circles inside a triangle, each tangent to the other two and also tangent to two of the sidelines of the triangle.
		In 1997, Peter Yff considered the classical Ajima-Malfatti configuration and realized that if the requirement that the circles lie inside the triangle is dropped, then there is a second configuration that solves the problem.
		In the figure, the reference triangle is labeled ABC, and the points of pairwise tangency of the circles are labeled A', B', C'.
	faculty.evansville.edu /ck6/tcenters/recent/yffmalf.html (145 words)

	GIAN FRANCESCO MALFATTI
		The famous Malfatti problem, to construct in a triangle three circles, each tangent to the other two and to two sides of the triangle, was first solved analytically by Malfatti in 1802.
		Because of their close connection to the Malfatti problem, certain recently discovered triangle centers are now known as the Ajima-Malfatti points and the Yff-Malfatti point.
		After completing his studies in Bologna, Malfatti founded a school of mathematics and physics at Ferrara in 1754.
	faculty.evansville.edu /ck6/bstud/malfatti.html (110 words)

	Geometry from Interactive Mathematics Miscellany and Puzzles
		A Circle Related to Incenter and Circumcenter [Java]
		Constructing a triangle from its angle bisectors is in general impossible
		Two Circles on a Side of a Triangle [Java]
	www.cut-the-knot.org /geometry.shtml (916 words)

	FG200303index (Site not responding. Last check: )
		Milorad Stevanović, Triangle centers associated with the Malfatti circles,
		Abstract: Various formulae for the radii of the Malfatti circles of a triangle are presented.
		We also express the radii of excircles in terms of the radii of the Malfatti circles, and give the coordinates of some interesting triangle centers associated with the Malfatti circles.
	forumgeom.fau.edu /FG2003volume3/FG200308index.html (54 words)

	Historia Matematica Mailing List Archive: Re: [HM] Malfatti's p
		> the incircle is one of the 3 circles involved.
		The authors give the solution of the Malfatti problem to place three non-
		$K\sb 1$ be a circle inscribed into a triangle $ABC$, $K\sb 2$ be a circle
	sunsite.utk.edu /math_archives/.http/hypermail/historia/mar00/0131.html (502 words)

	c8 (Site not responding. Last check: )
		Draw the incircles ca, cb, cc of IBC, IAC, IAB.
		2) Two of these circles have two internal common tangents: as exemple, cb and cc have IA and a new line a.
		3) The circle tangent to AC and BC and also to a and b is a Malfatti circle.
	www.xtec.es /~qcastell/ttw/ttweng/construccions/c8.html (58 words)

	The Math Forum - Math Library - Triangles/Polygons
		Leçons en français are also available in French: Théorie des nombres; Circonférence et aire des circles; et Périmètre et aire des polygones.
		A Java applet for the area of a circle of radius 1.
		Definitions and illustrations: Area; Area of a square; Area of a rectangle; Area of a parallelogram; Area of a trapezoid; Area of a triangle; Area of a circle; Perimeter; Circumference of a circle.
	www.mathforum.org /library/topics/triangle_g (2328 words)

	Geometry: Circles and their properties In Depth
		Algebra -> Algebra -> Circles -> Geometry: Circles and their properties In Depth (Log On)
		View all solved problems on Circles -- maybe yours has been solved already!
		Submit your problem: I checked all 412 available answers on Circles and could not find answer:
	www.algebra.com /algebra/homework/Circles/InDepth.html (67 words)

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