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Topic: Orthocentric system


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  Kids.Net.Au - Encyclopedia > Orthocentric system
In geometry, an orthocentric system is a set of four points in the plane where one point is the orthocenter of the triangle formed by the other three.
If four points form an orthocentric system, then each of the four points is the orthocenter of the other three -- thus there are four possible triangles.
The centers of the incircle and excircles of a triangle form an orthocentric system.
www.kids.net.au /encyclopedia-wiki/or/Orthocentric_system   (103 words)

  
 The Complete Quadrilateral
The mathematical object that goes by the name of complete quadrilateral is neither complete nor quadrilateral, at least not in the sense in which the word "quadrilateral" appears in, say, Brahmagupta's theorem about cyclic quadrilaterals.
A complete quadrilateral is a configuration of four straight lines in general position and six points at which the lines intersect.
Morley, Orthocentric Properties of the Plane n-Line, Trans Amer Math Soc, 4 (1903) 1-12.
www.maa.org /editorial/knot/CompleteQuadrilateral.html   (1548 words)

  
  Nine point circle - Wikipedia, the free encyclopedia
If an orthocentric system of four points is given, then the four triangles formed by any combination of three distinct points of that system all have the same nine point circle.
The centers of the incircle and excircles of a corresponding triangle form an orthocentric system.
The feet of the altitudes of the triangle formed by that orthocentric system are the vertices of the original triangle.
en.wikipedia.org /wiki/Nine_point_circle   (611 words)

  
 Orthocentric system Definition / Orthocentric system Research   (Site not responding. Last check: )
In geometry, an orthocentric system is a set of four points in the plane where one point is the orthocenterIn geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i.e.
orthocentric system is a set of four points in the plane where one point is the orthocenter of the triangle formed by the other three.
orthocentric system is the circumcircle of the original triangle.
www.elresearch.com /Orthocentric_system   (310 words)

  
 Triangle - Wikipedia, the free encyclopedia
The three vertices together with the orthocenter are said to form an orthocentric system.
The centers of the in- and excircles form an orthocentric system.
A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas.
en.wikipedia.org /wiki/Triangle   (2072 words)

  
 Feminine hygiene device - Patent 4848572
The orthocentric portion 26 is the most prominent of the three portions and corresponds to the apex of a chamber which encloses the pad 38.
Thus, the orthocentric portion 26 is the bulkiest and thickest portion of the sanitary napkin 12, located precisely in the orthocenter of the napkin between the other two portions 28 and 30, with which the orthocentric portion defines an indivisible and uniform body.
The orthocentric portion 26, the most prominent part of the sanitary napkin 12, must be adjusted to the area around the vaginal orifice, with the narrow portion 30 oriented towards the back.
www.freepatentsonline.com /4848572.html   (4463 words)

  
 Orthocentric System -- from MathWorld
In an orthocentric system, each point is the orthocenter of the triangle of the other three, as illustrated above (Coxeter and Greitzer 1967, p.
The incenter and excenters of a triangle are an orthocentric system.
The centers of the circumcircles of the points in an orthocentric system form another orthocentric system congruent to the first, and are the reflection of the original points in their common nine-point...
nsdl.org /resource/2200/20061002145513046T   (496 words)

  
 Various points related to triangles   (Site not responding. Last check: )
Such points are said to form an orthocentric system.
Any three points from an orthocentric system all have the same nine-point circle associated with them.
The incenter of the triangle is the point at which the three bisectors of the interior angles of the triangle meet.
www.mathlab.sunysb.edu /~scott/mat360.spr04/cindy/various.html   (359 words)

  
 Triangle
The three altitudes intersect in a single point, called the orthocenter of the triangle.
The orthocenter lies inside the triangle if and only if the triangle is not obtuse.\nThe three vertices together with the orthocenter are said to form an orthocentric system.
An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half.
encyclopedia.codeboy.net /wikipedia/t/tr/triangle.html   (1784 words)

  
 Nine Point Circle
The four points A, B, C and H taken three at a time form four triangles - ABC, ABH, BCH, CAH - with the property that the remaining point serves as the orthocenter of the corresponding triangle.
The incenter of a triangle together with its three excenters form the configuration of four points that fits the foregoing discussion.
In particular, the excenters and the incenter of a triangle form an orthocentric system.
www.cut-the-knot.org /Curriculum/Geometry/SixPointCircle.shtml   (477 words)

  
 Orthocentric system -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: )
In (The pure mathematics of points and lines and curves and surfaces) geometry, an orthocentric system is a set of four points in the plane where one point is the (Click link for more info and facts about orthocenter) orthocenter of the (A three-sided polygon) triangle formed by the other three.
These four possible triangles will all have the same (Click link for more info and facts about nine point circle) nine point circle.
The centers of the (Click link for more info and facts about incircle) incircle and (Click link for more info and facts about excircle) excircles of a triangle form an orthocentric system.
www.absoluteastronomy.com /encyclopedia/o/or/orthocentric_system.htm   (134 words)

  
 Orthocentric System From Rectangle
Orthocentric System From Rectangle: What Is This About?
Let X, Y, Z, and W be the projections of P onto the lines AB, BC, CD, and DA, respectively.
Prove that the points X, Y, Z, W form an orthocentric system.
www.cut-the-knot.org /Curriculum/Geometry/OrthoSystemInRect.shtml   (227 words)

  
 Nine point circle   (Site not responding. Last check: )
If an orthocentric system of four points is given any of them define a triangle and these triangles all have the same nine point
The point circle created for that orthocentric system the circumcircle of the original triangle.
I decided to give the D-Link wireless system a try because of its price and their claim to double standard 802.11b bandwidth (22Mbps instead of 11).
www.freeglossary.com /Feuerbach_point   (682 words)

  
 Math Forum - Ask Dr. Math   (Site not responding. Last check: )
Pick three points out of the four points A, B, C, and H. The fourth point is the orthocenter of the first three.
For this reason the four points are called an orthocentric system.
One of the famous orthocentric systems is formed by the incenter and the three excenters.
mathforum.org /dr.math/problems/carbonetti.11.12.99.html   (258 words)

  
 On The Square   (Site not responding. Last check: )
So, it appears that there are always solutions unless the four points form an orthocentric system.
The four-point square construction is always possible if the four points do not form an orthocentric system.
The construction is impossible only if the four points form an orthocentric system.
www.whistleralley.com /square/square.htm   (1447 words)

  
 CDC 6600 bei eLexi - das Onlinelexikon   (Site not responding. Last check: )
The basis for the 6600 is what we would today refer to as a RISC system, one in which the processor is tuned to do instructions which are comparatively simple.
The philosophy of many other machines was toward using instructions which were complicated — for example, which would fetch an operand from memory and add it to a value in a register.
These machines, called peripheral processors, or PPUs, were full computers in their own right, but tuned to performing I/O tasks and running the operating system.
www.elexi.de /en/c/cd/cdc_6600.html   (601 words)

  
 Orthocenter
"Note_: As a matter of historical interest our readers may be reminded that the term ``Orthocentre'' was invented by two mathematicians, Besant and Ferrers, in 1865, while out for a walk along the Trumpington Road, a road leading out of Cambridge toward London.
A tetrahedron with this property is called an orthocentric tetrahedron.
It is known that if three altitudes of a tetrahedron are concurrent, the fourth will also pass through the same point.
www.pballew.net /orthocen.html   (1819 words)

  
 Amazon.com: "orthocentric system": Key Phrase page
See all pages with references to "orthocentric system".
40 An orthocentric system consists of four points,...
Since the incenter and the excenters form an orthocentric system, each being the orthocenter of the triangle formed by the others [2], it is known [7] that any conic passing...
www.amazon.com /phrase/orthocentric-system   (366 words)

  
 Sketchpad Investigations of the Orthocenter
The points A, B, C, and D are called an orthocentric system.
This new system appears to be congruent to the first one.
After constructing the orthocentric system, you constructed the circumcenter of each triangle.
whistleralley.com /orthocenter/orthocenter.htm   (813 words)

  
 Orthocentric System   (Site not responding. Last check: )
Circumcircles of an orthocentric system form another orthocentric system congruent to the first.
Circumcircles of points in an orthocentric system taken three at a time (illustrated above) have equal
The four triangles of an orthocentric system have a common
www.math.sdu.edu.cn /mathency/math/o/o122.htm   (118 words)

  
 wiki/Feuerbach point Definition / wiki/Feuerbach point Research   (Site not responding. Last check: )
J, K, L - the points on each altitude midway between the vertex and the orthocentre (labelled S) The nine point circle is tangent externally to the three excirclesIn geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.
The center of the incircle is called the triangle's incenter.
If an orthocentric systemIn geometry, an orthocentric system is a set of four points in the plane where one point is the orthocenter of the triangle formed by the other three.
www.elresearch.com /wiki/Feuerbach_point   (812 words)

  
 [No title]
An orthocentric system is given by the picture below and here on GSP.
It’s simply the four sets of triangles given by one triangle A, B, C and its orthocenter, H. According to this picture there are four such different combinations, and all of their circumcircles have an equal radius.
So our assumption that all the circumcircles in our orthocentric system are the same is true.
jwilson.coe.uga.edu /EMT668/EMAT6680.2003.fall/Drew/Assign8/Assignment8.htm   (588 words)

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