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# Topic: Median (geometry)

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 Encyclopedia :: encyclopedia : Geometry   (Site not responding. Last check: 2007-09-17) The earliest recorded beginnings of geometry may be traced to Ancient Egypt (see geometry in Egypt) and Ancient Babylon (see Babylonian mathematics) around 3000 B.C. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. The first and most important was the creation of analytic geometry, or geometry with coordinates and equations, by Rene Descartes (1596-1650) and Pierre de Fermat (1601-1665). In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. www.hallencyclopedia.com /topic/Geometry.html   (2103 words)

 PlanetMath: median The median of a triangle is a line joining a vertex with the midpoint of the opposite side. If the length of the three sides of the triangle are known, the length of the medians can be found by means of Apollonius theorem. This is version 9 of median, born on 2001-10-06, modified 2006-11-03. planetmath.org /encyclopedia/Median.html   (97 words)

 Arrow’s Theorem   (Site not responding. Last check: 2007-09-17) If the median line perpendicular to the line through x and y is on the x side of the perpendicular bisector, it follows that more than half the ideal points are on the x side of the bisector, so x beats y. The median line M is the perpendicular bisector of the reflection line of x through m. If every median line passes through x, then for any y distinct from x, the median line perpendicular to the line through x and y is closer to x than to y (for indeed it passes through x), so x beats y. userpages.umbc.edu /~nmiller/RESEARCH/Geometry_of_Voting.html   (5123 words)

 SparkNotes: Review of Geometry II: Theorem Review The length of the median to the hypotenuse is 1/2 the length of the hypotenuse. The median of a trapezoid is parallel to its bases and the average of their lengths. The proportion of the lengths of the medians of similar triangles is the same as that between the corresponding sides of those triangles. www.sparknotes.com /math/geometry2/review/theoremlist.html   (1187 words)

 median - Search Results - MSN Encarta Median (mathematics), the value of the middle member of a set of numbers when they are arranged in order. Median (geometry), line connecting a point—called a vertex—of a triangle and the midpoint of the opposite side. Highways with fully controlled access generally have two or more lanes for each direction of travel and often include medians (dividers in the middle... encarta.msn.com /median.html   (196 words)

 median. The Columbia Encyclopedia, Sixth Edition. 2001-05 In the group 4, 5, 6, 9, 13, 14, 19, the median is 9, three numbers being larger and three smaller. When there is an even number of numerals in the group, the median is usually defined as the number halfway between the middle pair. The median of a trapezoid is the line segment connecting the midpoints of the nonparalled opposite sides. www.bartleby.com /65/me/median.html   (171 words)

 Geometry Using the TI-83 Plus/TI-84 Plus Institute by Texas Instruments - US and CANADA Transformational geometry is one of the most important branches of geometry studied in Middle and High School. Altitudes, medians, and angle bisectors are common structures used to study triangle geometry. This investigation is an extension of the activity "Altitude, Median, and Angle Bisector of a Triangle." The same lines will be constructed in quadrilaterals to explore patterns and properties that seem to be true in four-sided figures rather than triangles. education.ti.com /educationportal/sites/US/nonProductMulti/pd_geometry83and84.html?bid=2   (2487 words)

 Geometry Software Programs Full Year Course Geometry help and geometry formulas are available from a clickable menu of choices. Geometry help is available for each geometry problem with a click on the HINT buttons. Geometry formulas and geometry proofs are explained and practiced with interactive geometry help. www.mathmedia.com /higschoolgeo.html   (747 words)

 All about medians Since for two medians the points thus defined coincide, the same, by symmetry, is true for the remaining median. In Affine Geometry, all triangles are the same in the sense that between any two triangles there exists an affine transformation that maps vertices of one triangle sequentially on the vertices of another. In an isosceles triangle, side medians meet on the axes of symmetry of the triangle which, among other things, serves as the third median. www.cut-the-knot.org /triangle/medians.shtml   (1288 words)

 Median (geometry) - Search Results - MSN Encarta Median (geometry) - Search Results - MSN Encarta Geometry, like most other sciences, advanced little from the fall of the Roman Empire in the 5th century ad to the end of the Middle Ages in the 15th... Geometry : History of Geometry : Geometry During the Middle Ages encarta.msn.com /Median_(geometry).html   (165 words)

 Amazon.com: Geometry: Books: David A. Brannan,Matthew F. Esplen,Jeremy J. Gray   (Site not responding. Last check: 2007-09-17) During the last third of the book (the chapters on hyperbolic and spherical geometry), some basic familiarity with trigonometric functions and hyperbolic functions is assumed (cosh, sinh, tanh, and their inverses). In the eighth chapter all of these geometries are demonstrated to be special cases of the Kleinian vieuw of geometry: that is, every geometry can be seen as consisting of the invariants of a specific group of transformations of the 2 dimensional plane into itself. And, by passing to the more abstract Projective geometry, you can express the abstract idea of 'conic' by giving just one quadratic curve, be it a parabola, ellipse or hyperbola, by the pair (Qu, P), whereby P is the group of all projective transformations. www.amazon.com /Geometry-David-Brannan/dp/0521597870   (2910 words)

 Medians of Triangle - interactive applet The properties of the medians of a triangle are explored using an interactive geometry applet. The median of a triangle is a line that passes through a vertex and the midpoint of the opposite side of the triangle. Below, an applet is used to explore the definition and properties of the medians of a triangle. www.analyzemath.com /Geometry/MediansTriangle/MediansTriangle.html   (247 words)

 TN Department of Education:K-12 Geometry uses problem situations, physical models, and appropriate technology to investigate and justify geometric concepts and relationships. The concepts and topics emphasized in the course include measurement, geometric patterns, coordinate geometry, two- and three-dimensional figures, transformational geometry, congruence, similarity, inductive and deductive reasoning, logic, and proof. Throw randomly and count the throws that hit the board to determine which board yields the highest probability of a dart’s landing in a circle. www.state.tn.us /education/ci/standards/mathhighschool/mathgeometry.shtml   (2029 words)

 Flickr: Photos from jef safi According to the median vacuum semiotics idiom stocklist, this is a selfme doing a selfello... According to the median vacuum semiotics idiom stocklist, is this selfme a selfghost or a... According to the median vacuum semiotics idiom stocklist, this is a selfeet... www.flickr.com /photos/36764355@N00   (120 words)

 Geometry Definitions A central angle is an angle with its vertex at the center of a circle. In a triangle, the three medians, three perpendicular bisectors, three angle bisectors, and three altitudes are each concurrent. A median is a segment connecting any vertex of a triangle to the midpoint of the opposite side. www.learner.org /channel/courses/learningmath/geometry/keyterms.html   (2247 words)

 GEOMETRY   (Site not responding. Last check: 2007-09-17) But, at the same time, it does seem that ideal points will typically be distributed in such a fashion that each median line would cut more or less through the center of the distribution, so that there would be a fairly small region (though not a single point) through which all median lines pass. The location of the yolk may be thought of as indicating the generalized center (in the sense of the median) of the distribution of ideal points. In three dimensions median "lines" become median planes, the yolk is a sphere, and at least four median planes are tangent to the yolk. userpages.umbc.edu /~nmiller/RESEARCH/GEOMETRY.htm   (8805 words)

 median - Definitions from Dictionary.com For example, in the sequence 4, 8, 10, 56, the median is 9 (the average of 8 and 10). If there are an even amount of numbers in the series, the median is found by taking the mean of the two numbers in the middle of the distribution. In certain cases, the median can be a good way to determine an approximate average, especially when dealing with a set of numbers that could otherwise be skewed by outliers, such as the number 25 in the first set. dictionary.reference.com /browse/median   (955 words)

 Geometry Expressions -- Medians of a general triangle -- Interactive Symbolic Geometry Geometry Expressions -- Medians of a general triangle -- Interactive Symbolic Geometry The incenter of a triangle is the intersection of its medians. We see that the incenter is located 2/3 of the way down the median. www.geometryexpressions.com /Geometry_Atlas/GeometryAtlas.php?path=Intersections_and_Centers/&file=Medians.htm   (54 words)

 median - OneLook Dictionary Search Phrases that include median: median plane, median strip, median eminence, median antebrachial vein, median point, more... Words similar to median: average, medial, medianly, more... This is a OneLook Word of the Day, which means it might be in the news. www.onelook.com /?w=median&loc=wotd   (427 words)

 Geometry/History Lesson Plan Have students discover certain features of the centroid; Locus of points of a median, properties of the segments that form the median, areas of the smaller sections(triangles) formed by the medians. Therefore the point of concurrency of the medians divides the triangle into equal areas creating a balance point or center of gravity called the centroid. Geometry Sketchpad (Key Curriculum Press) (Appendix B) Self - contained packet with instructions, and guidelines to discovering the special features of the medians and centroid of a triangle. courses.wcupa.edu /jkerriga/Lessons/T.Lauriahistgeom.html   (1126 words)

 The Medians of a Triangle The median with endpoint C remains in its original position, thus completing a new triangle. However, the length of the medians (the perimeter of the median triangle) appears to fluctuate as the triangle becomes obtuse. It looks as though the length of the medians is decreasing (in comparison to the perimeter of the original triangle). web.pdx.edu /~shuirman/The_Medians_of_a_Triangle.html   (579 words)

 High School Level — Geometry He makes geometry feel like a long, cool drink as he guides you through the mysteries of lines, planes, angles, inductive and deductive reasoning, parallel lines and planes, triangles, polygons, and more. The language of geometry is beautifully expressed in words, symbols, formulas, postulates, and theorems. He was explaining to his class the calculation of the volumes of pyramids and cones and the ways in which these were similar. www.teach12.com /ttc/assets/coursedescriptions/105.asp   (976 words)

 Educational Geometry Videos These are educational geometry videos at the introductory level. This video goes over basic geometry principles in an entertaining way, explaining it on an introductory level that is easy to understand. A fantastically comprehensive series of 30 video lessons at the high school level geometry by Jim Noggle, a nationally renowned mathematics teacher. geometryalgorithms.com /videos_educational.shtml   (205 words)

 Interactivate: Activities Students can create boxplots which DO use the median in calculating the interquartile ranges for either builtin or user-specified data as well as experiment with outliers. Students enter data and view the mean, median, variance and standard deviation of the data set. Students can change the median standard deviation of the graphed normal distribution to create a skewed distribution, allowing them to observe properties like what it means for the mean, median, and mode to be different. www.shodor.org /interactivate/activities   (3277 words)

 Properties of the Median   (Site not responding. Last check: 2007-09-17) The three medians of a triangle all pass through one point. The third segment has the same length as the sum of the lengths of the three medians of the triangle. The sum of the lengths of the three medians of a triangle is more than 3/4 p and less than p, where p is the perimeter of the triangle. illuminations.nctm.org /tools/IGD_lines/MedianProperties.html   (422 words)

 Appendix:  Discrete Algebra The median is a measure of central tendency. The lower quartile is the median of the numbers below the median of a set of data. The upper quartile is the median of the numbers above the median. library.thinkquest.org /16284/a_discrete_2.htm   (355 words)

 Right Triangle Median, Altitude, Bisector The median CM and altitude CH of triangle ABC are reflections about the bisector of angle C iff ABC is a right triangle. The bisector of angle ACB also bisects angle MCH because the purple angle inscribed in the circle is half that of the central angle, M, because they are both subtended by the same arc. Triangle Trisection -- If a point, P, on the median of triangle ABC is the isogonal conjugate of point Q, on the altitude of ABC, then ABC is a right triangle. mcraefamily.com /MathHelp/GeometryTriangleRightMedianAndAltitudeAreReflectionsAboutBisector.htm   (386 words)

 Median The statistical median is middle number of a group of numbers that have been arranged in order by size. If there is an even number of terms, the median is the mean of the two middle numbers: If there is an odd number of terms, the median is the center term. www.aaamath.com /sta518-stat-median2.html   (107 words)

 PCB Libraries, Inc Three land pattern geometry variations are supplied for each of the device families; maximum land protrusion (Density Level A), median land protrusion (Density Level B) and minimum land protrusion (Density Level C). The geometry furnished for these devices, as well as inward and “J”-formed lead contact device families, may provide a wider process window for reflow solder processes as well. The median land patterns furnished for all device families will provide a robust solder attachment condition for reflow solder processes and should provide a condition suitable for wave or reflow soldering of leadless chip and leaded gull-wing type devices. www.pcblibraries.com /store/detail.aspx?ID=32   (1924 words)

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