
	Where results make sense

Topic: Gergonne point

Related Topics

boiling point

neutral point of view

West Point

floating point

point of view

Lagrangian point

fixed point

West Point, New York

Point to Point Protocol

critical point

fixed point mathematics

In the News (Fri 27 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Gergonne biography
		Gergonne spent a month at the Châlons artillery school in 1794 and after this he was commissioned as a lieutenant.
		Gergonne looked at how to estimate the values of the response function, and of its derivatives, at a point when there are random errors in the observed values.
		Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816.
	turnbull.dcs.st-and.ac.uk /~history/Biographies/Gergonne.html (1148 words)

	Symmedian - Wikipedia, the free encyclopedia
		The symmedians intersect in the Lemoine point L. The symmedian point of a triangle with sides a, b and c has homogeneous trilinear coordinates [a : b : c].
		The symmedian point of a right triangle is therefore the midpoint of the altitude on the hypotenuse.
		The symmedian point is the isogonal conjugate of the triangle's centroid.
	en.wikipedia.org /wiki/Symmedian (220 words)

	PlanetMath: Lemoine point
		The Lemoine point of a triangle, is the intersection point of its three symmedians.
		, the Lemoine point of its Gergonne triangle is the Gergonne point of
		This is version 5 of Lemoine point, born on 2002-01-08, modified 2002-05-17.
	www.planetmath.org /encyclopedia/LemoinePoint.html (124 words)

	The Gergonne Point
		The Gergonne Point, so named after the French mathematician Joseph Gergonne, is the point of concurrency which results from connecting the vertices of a triangle to the opposite points of tangency of the triangle's incircle.
		Now that it has been shown that the point B is between the other two points on each segment and that the point is on all three segments at the same time, then it must be a point of concurrency for all three segments.
		Another approach to showing the existence of the Gergonne Point is to use GSP to create axes and a grid in order to examine the three linear equations that could be formed from making segments that join the vertices of each triangle to the points of concurrency of the incenter to each side.
	jwilson.coe.uga.edu /EMT668/EMT668.Folders.F97/Cowart/essay3/gergpoint.html (839 words)

	Geometry.Net - Scientists: Gergonne Joseph
		Gergonne introduced the word polar and the principal of duality in projective geometry grew out of his work.
		The theorem goes as follows: the segments from the vertices of a triangle to the points of tangency of the incircle with the opposite sides of the triangle are concurrent.
		Recall that the incenter is the point of concurrency of the angle bisectors (red) of a triangle.
	www4.geometry.net /detail/scientists/gergonne_joseph.html (2239 words)

	Symmedian Info - Bored Net - Boredom (Site not responding. Last check: 2007-11-01)
		The symmedians intersect in the Lemoine point L. The symmedian point of a triangle with sides a, b and c has homogeneous trilinear coordinates [a : b : c].
		The symmedian point L can also be constructed differently: the three lines joining the midpoint of a side to the midpoint of the altitude on that side intersect in L.
		The Gergonne point of a triangle is the same as the symmedian point of the triangle's contact triangle.
	www.borednet.com /e/n/encyclopedia/s/sy/symmedian.html (189 words)

	Incircle and excircles of a triangle - the free encyclopedia (Site not responding. Last check: 2007-11-01)
		From these formulas we see in particular thatthe excircles are always larger than the incircle, and that the largest excircle is the one attached to the longest side.
		The triangle's nine point circle is tangent to the threeexcircles as well as to the incircle.
		The Gergonne point of a triangle is equal to the symmedian pointof its contact triangle.
	www.the-free-web-encyclopedia.com /default.asp?t=Excircle (331 words)

	Essay Ideas for EMT 669, UGa (Site not responding. Last check: 2007-11-01)
		The inversion of a point P in a circle of radius AB, center at A, is a mapping of C to a point C' such that AC.AC' = AB.AB.
		Use the segment of length d from this point to the near vertex of the triangle to define a length and direction for constructing a parallelogram on the third side.
		The point of concurrency is the Gergonne Point.
	jwilson.coe.uga.edu /EMT669/Essay.Ideas/Essay.ideas.html (440 words)

	standard
		The Gergonne and Nagel points are on the Feuerbach hyperbola since their isogonal conjugates are the centers of similitudes of the circumcircle and the incircle.
		Now, if a point M lies on a hyperbola W, D is a line going through M, U,U' are the common points of D and the asymptots of W, the second common point of D and W is the reflection of M wrt the midpoint of UU'.
		The isodynamic points X(15), X(16) are the intersection of the Parry circle (2,110,111) and the Brocard axis OK. The two points are inverses with respect to the circumcircle, and X(15) is the interior one.
	forumgeom.fau.edu /POLYA/ProblemCenter/POLYA022.html (1836 words)

	GERGONNE POINT (Site not responding. Last check: 2007-11-01)
		F = point where the incircle meets side AB.
		The lines AD, BE, CF meet in a point, labeled X in the figure.
		It is called the Gergonne point of triangle ABC.
	faculty.evansville.edu /ck6/tcenters/class/gergonne.html (58 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-01)
		The most notable points in a triangle collinear with the incenter and the Gergonne point are the De Longchamps point, the isoperimetric point, and the equal detour point.
		The De Longchamps point is the reflection of the orthocenter (the intersection of the altitudes) through the circumcenter (the intersection of the perpendicular bisectors).
		The equal detour point is the point X that equalizes the detour when you travel from a vertex to another vertex via X (for example, the detour from A to B equals AX+XB-AB).
	www.mathforum.com /library/drmath/view/55117.html (270 words)

	isogons
		The Gergone point is the intersection of the segments from a vertex to the tangent point of the incircle with the opposite side.
		It is frequently called the Second Lemoine circle, and sometimes the Cosine circle because the length of the chords formed by two points of intersection nearest a vertex (EF for example) is proportional to the cosines of the angles (angle B for EF) at the adjacent vertices..
		As the LHuilier-Lemoine-Grebe point is the point of concurrence of the three symmedians of a triangle, the geometer Robert Tucker (as in Tucker circles) introduced yet another name for the point: symmedian point.
	www.pballew.net /isogon.html (1694 words)

	Historical Notes
		Joseph-Diez Gergonne (1771-1859): geometer who studied the point of concurrence of lines joining the vertices of a triangle to the points of contact of the inscribed circle.
		Christian von Nagel (1803-82): constructed a point in the same way as the Gergonne point but using the point of contact of an escribed circle; the point is now sometimes named after him.
		Jacob Steiner (1746-1827): Swiss mathematician who contributed to various branches of pure geometry; a point associated with the triangle is named after him, and so is the envelope of the pedal line of a point as it moves round the circumcircle.
	www.partnership.mmu.ac.uk /cme/Geometry/TriangleGeometry/HistoricalNotes.html (701 words)

	mar04web
		The Greeks studied four notable points of the triangle the centroid, incenter, circumcenter, and orthocenter.
		The incenter, the point equidistant to each of the sides of the triangle, is at the intersection of the angle bisectors.
		The circumcenter is the point equidistant to the vertices of the triangle.
	noether.uoregon.edu /~mathpeers/newsletter/mar04 (342 words)

	Incircles and Excircles in a Triangle
		From the just derived formulas it follows that the points of tangency of the incircle and an excircle with a side of a triangle are symmetric with respect to the midpoint of the side.
		The cevians joinging the two points to the opposite vertex are also said to be isotomic.
		For the incircle, the point is Gergonne'; for the points of excircle tangency, the point is Nagel's.
	www.cut-the-knot.org /triangle/InExCircles.shtml (254 words)

	[No title]
		Hence, the Schröder point Sc is the inverse of the centroid of XYZ in the incircle of ABC.
		And while the Schröder point Sc is the inverse of X(55), the internal center of similtude of circumcircle and incircle, in the circumcircle of ABC, the Bevan-Schröder point Sb is the inverse of X(56), the external center of similtude of circumcircle and incircle, in the circumcircle of ABC.
		is the foot of the A-altitude, and the point H is the antipode of A on the circumcircle of triangle AYZ.
	de.geocities.com /darij_grinberg/Schroeder/Schroeder.html (6708 words)

	PlanetMath: Gergonne point
		concurrent, and the common point is called the Gergonne point of the triangle.
		See Also: Ceva's theorem, triangle, Lemoine point, Gergonne triangle, incircle, incenter, symmedian, trigonometric version of Ceva's theorem
		This is version 3 of Gergonne point, born on 2002-01-08, modified 2002-05-17.
	www.planetmath.org /encyclopedia/GergonnePoint.html (50 words)

	points on Steiner ellipse and circumcircle (Site not responding. Last check: 2007-11-01)
		The isotomic conjugate of a point at infinity is on the Steiner ellipse.
		The isogonal conjugate of a point at infinity is on the circumcircle.
		Each point on an object can be regarded as orginating from a point in the triangle plane.
	www.paideiaschool.org /TeacherPages/Steve_Sigur/resources/ptsonSEandCC.html (214 words)

	Lecture Notes 4 - Math 3210 (Site not responding. Last check: 2007-11-01)
		If three points, one on each side of a triangle are collinear, then the product of the ratios of the division of the sides by the points is -1.
		Look at point determined by two of the points and a side of triangle...show it is the third point.
		Thm 4.19 : If three points are chosen, one on each side of a triangle then the three circles determined by a vertex and the two points on the adjacent sides meet at a point called the Miquel point.
	www-math.cudenver.edu /~wcherowi/courses/m3210/hg3lc4.html (481 words)

	Gergonne point (Site not responding. Last check: 2007-11-01)
		The name of the symbol '''.' used to separate a whole number from a decimal fraction: 10.5 (ten point five) ten and a half.
		Despite some changes in the Point, this annual event is indeed taking place.
		At the November PRNC meeting, Ted Cuzzillo and Steve Spencer are just two of the members clearly yearning for their own Richmond Bridge model kit for Christmas.
	www.serebella.com /encyclopedia/article-Gergonne_point.html (584 words)

	Feuerbach hyperbolas
		It is known that the perspector of a regular circumhyperbola is on the Polar axis and its center is on the nine point circle.
		By my theory of infinite points, points on conics belong to families that can be associated with triangle centers.
		It is known that a Mineur conic is tangent to a pivotal cubic at the conjugate of the pivot point.
	www.paideiaschool.org /TeacherPages/Steve_Sigur/resources/feuerbach%20web/feuerbach.html (1277 words)

	Gallery
		Here is a view of the figure used in a solution of the Fagnano Problem: Given the accute-angled triangle ABC, find the position of the inscribed triangle DEF, that has the least possible perimeter.
		Here is a view of Morley's Theorem: Construct the trisectors of the angles of a triangle ABC and consider the three intersection points D, E, F of these trisectors, as shown.
		The rotation's center is the intersection point of the two mirors.
	www.euclidraw.com /Eng_fls/Gallery.html (629 words)

	Ceva's Theorem
		Indeed, assume that K is the point of intersection of BE and CF and draw the line AK until its intersection with BC at a point D'.
		The points D, E, F may lie as well on extensions of the corresponding sides of the triangle, while the point of intersection K of the three cevians may lie outside the triangle.
		Another exceptional case is when one (or two) of the points D, E, or F is (are) at infinity which means that one of the Cevians is parallel to the side it's supposed to cross.
	www.cut-the-knot.org /Generalization/ceva.shtml (1600 words)

	JGG 08003 (Site not responding. Last check: 2007-11-01)
		--> With the traditional definition of the Gergonne center of a triangle in mind, it is natural to consider, for a given tetrahedron, the intersection of the cevians that join the vertices to the points where the insphere touches the faces.
		Another approach is to note that the cevians through any point inside a triangle divide the sides into 6 segments, and that the Gergonne center is characterized by the requirement that every two segments sharing a vertex are equal.
		Similarly, the cevians through any point inside a tetrahedron divide the faces into 12 subtriangles, and one may define the Gergonne center as the point for which every two subtriangles that share an edge are equal in area.
	www.heldermann.de /JGG/JGG08/JGG081/jgg08003.htm (211 words)

	[No title]
		, are the inradii of the triangles ADB, and BDC respectively, the points E, F, and G are points of tangency.
		It's a curve that, connects two given points such that it takes the same amount of time for a particle to slide from any point on the curve to the lower point, under ideal physical law.
		Isoptic of a given curve C and a given angle α is the locus of a point P such that P is the intersection of tangents of C that meets in angle α.
	gh-math.blogfa.com (1885 words)

	Gergonne (Site not responding. Last check: 2007-11-01)
		It was in 1830 the Gergonne became rector of the University of Montpellier.
		Gergonne introduced the word polar and the principal of duality in
		He noticed the fact that certain forms of geometry yielded theorems which appeared in related pairs, and the led him to a more detailed analysis of why this was so.
	202.38.126.65 /mirror/www-history.mcs.st-and.ac.uk/history/Mathematicians/Gergonne.html (1115 words)

	Nineteenth Century Geometry
		As a result of this, the neighborhood relations among points in projective space and on projective planes differ drastically from those familiar from standard geometry, and are highly counterintuitive.
		No real-valued function of point pairs, defined on all projective space, can be an invariant of the projective group, but there is a function of collinear point quadruples, called the cross-ratio, which is such an invariant.
		The distance between two points in space can be ascertained with a rod, or a tape, or by optical means, and the result depends essentially on the physical behavior of the instruments used.
	plato.stanford.edu /entries/geometry-19th (4771 words)

	Dynamic Geometry Module: Lesson 5 (Site not responding. Last check: 2007-11-01)
		The medians of a triangle all intersect in a point (the centroid of the triangle).
		The same is true of the angle bisectors (the incenter), the altitudes (the orthocenter) and the perpendicular bisectors of the sides (the circumcenter).
		Let X be the point where the ex-circle opposite A touches BC; Y the point where the ex-circle opposite B touches AC; Z the point where the ex-circle opposite C touches AB.
	mtl.math.uiuc.edu /modules/dynamic/lessons/lesson5.html (516 words)

	A Theorem of J.D. Gergonne (Site not responding. Last check: 2007-11-01)
		) The segments from the vertices of a triangle to the points of tangency of the incircle with the opposite sides of the triangle are concurrent.
		Since the two tangents from a point to a circle are congruent, AE=AF, CE=CD, BD=BF, and
		Thus, the three segments are concurrent by the converse of
	pegasus.cc.ucf.edu /~xli/gerg.htm (52 words)

	Unusual Properties of Triangles
		In a paper of 1873 he studied the point of intersection of the symmedians of a triangle.
		If we take the point where the angle bisectors of an acute triangle meet (are concurrent) as the center point of a new circle and draw that circle so that it just touches one side of the triangle we find that it will just touch all three sides of the triangle.
		For example, the distance from the vertex A to point a is the same as the distance from the vertex A to point c.
	www.world-destiny.org /or/unusualproperties.htm (1089 words)

Try your search on: Qwika (all wikis)