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Topic: Triangle geometry


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In the News (Thu 23 May 19)

  
  Triangle (Geometry) - LoveToKnow 1911
TRIANGLE, in geometry, a figure enclosed by three lines; if the lines be straight the figure is called a plane triangle; but if the figure be enclosed by lines on the surface of a sphere it is a spherical triangle.
The three sides and angles constitute the six elements of a triangle; it is customary to denote the angular points by capital letters and refer to the angles by these symbols; the sides are usually denoted by the lower case letter corresponding to that of the opposite angular point.
We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.
www.1911encyclopedia.org /Triangle_%28Geometry%29   (847 words)

  
  Triangle (geometry) - MSN Encarta
A capital letter is customarily used to designate a vertex of a triangle, the angle at that vertex, or the measure of the angle in angular units; the corresponding lower case letter designates the side opposite the angle or its length in linear units.
Therefore, the three angles of a scalene triangle are of different sizes; the base angles of an isosceles triangle are equal; and the three angles of an equilateral triangle are equal (an equilateral triangle is also equiangular).
For example, the sum of the angles of a spherical triangle is between 180° and 540° and varies with the size and shape of the triangle.
encarta.msn.com /encyclopedia_761563143/Triangle_(geometry).html   (827 words)

  
 NationMaster - Encyclopedia: Enneagon   (Site not responding. Last check: 2007-11-05)
In geometry, an enneagon or nonagon is a nine-sided polygon.
A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments.
Erchingers heptadecagon In geometry, a heptadecagon (or 17-gon) is a seventeen-sided polygon.
www.nationmaster.com /encyclopedia/Enneagon   (599 words)

  
  TRIANGLE - LoveToKnow Article on TRIANGLE   (Site not responding. Last check: 2007-11-05)
geometry, a figure enclosed by three lines; if the lines be straight the figure is called a plane triangle; hut if the figure be enclosed by lines on the surface of a sphere it is a spherical triangle.
The three sides and angles constitute the six elements of a triangle; it is customary to denote the angular points by capital letters and refer to the angles by these symbols; the sides are usually denoted by the lower case letter corresponding to that of the opposite angular point.
We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.
80.1911encyclopedia.org /T/TR/TRIANGLE.htm   (970 words)

  
 Triangle - Wikipedia, the free encyclopedia
A triangle is one of the basic shapes of geometry: a two-dimensional figure with three vertices and three sides which are straight line segments.
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.
The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base.
en.wikipedia.org /wiki/Triangle   (2072 words)

  
 NationMaster - Encyclopedia: Square (geometry)   (Site not responding. Last check: 2007-11-05)
In mathematics, plane geometry may mean: geometry of the Euclidean plane; or sometimes geometry of a projective plane, most commonly the real projective plane but possibly the complex projective plane, Fano plane or others; or geometry of the hyperbolic plane or two-dimensional spherical geometry.
In spherical geometry, a square is a polygon whose edges are great circle arcs of equal distance, which meet at equal angles.
Spherical geometry is the geometry of the two-dimensional surface of a sphere.
www.nationmaster.com /encyclopedia/Square-%28geometry%29   (1410 words)

  
 PlanetMath: non-Euclidean geometry
A non-Euclidean geometry is a geometry in which at least one of the axioms from Euclidean geometry fails.
It is relatively easy to see that, in this geometry, given a line and a point not on the line, there are infinitely many lines passing through the point that are parallel to the given line.
One final example of a non-Euclidean geometry is semi-Euclidean geometry, in which the axiom of Archimedes fails.
www.planetmath.org /encyclopedia/BeltramiKleinModel.html   (420 words)

  
 triangleIndex
Geometry tutorials (pdf's) When I was learning triangle geometry about 10 years ago, I wrote articles for myself and for friends.
As geometry goes this is pretty advanced, using barycentric coordinates and general knowledge of triangle geometry, especially projective triangle geometry.
Abstract Algebra and Triangle Geometry We are in the third great period of discovery in triangle geometry.
paideiaschool.org /TeacherPages/Steve_Sigur/geometryIndex.htm   (1247 words)

  
 Figures and polygons
The sum of the angles of a triangle is 180 degrees.
One of the angles of the triangle measures 90 degrees.
A right triangle has the special property that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
www.mathleague.com /help/geometry/polygons.htm   (620 words)

  
 Geometry Session 2, Part B: Linkage-Strip Constructions
The triangle inequality is the mathematical statement of the old adage, "The shortest distance between two points is a straight line." If you don't travel along the straight line, you travel two sides of a triangle, and that trip takes longer.
Triangles are the only rigid polygon, which makes them quite useful for construction.
If the three sides of one triangle have the same lengths as the three sides of another triangle, then the two triangles are congruent.
www.learner.org /channel/courses/learningmath/geometry/session2/part_b/properties.html   (235 words)

  
 triangle Index
Geometry tutorials (pdf's) When I was learning triangle geometry about 10 years ago, I wrote articles for myself and for friends.
As geometry goes this is pretty advanced, using barycentric coordinates and general knowledge of triangle geometry, especially projective triangle geometry.
Abstract Algebra and Triangle Geometry We are in the third great period of discovery in triangle geometry.
www.paideiaschool.org /Teacherpages/Steve_Sigur/geometryIndex.htm   (2193 words)

  
 Some Triangle Geometry: Introduction
And nineteenth century triangle geometry did seem an old fashioned pursuit, suitable perhaps for enthusiastic amateurs but not an adequate preparation for the mathematics that was increasingly being applied in new and prestigious fields So why this present modest attempt to revive some mathematics that has been decently buried for some time?
Geometry matters - for various reasons, but also because points lines and circles are symbols of what I lie on, pass through or touch.
Triangle geometry provides an interesting area for geometrical exploration and at the same time a way of coming to grips with important issues about proof.
www.partnership.mmu.ac.uk /cme/Geometry/TriangleGeometry/Intro.html   (986 words)

  
 Hugues Hoppe's home page
The geometry clipmap introduced in Losasso and Hoppe 2004 is a new level-of-detail structure for rendering terrains.
Geometry images have the potential to simplify the rendering pipeline, since they eliminate the "gather" operations associated with vertex indices and texture coordinates.
Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data.
research.microsoft.com /~hoppe   (9135 words)

  
 triangle (geometry)
In geometry, a three-sided plane figure, the sum of whose interior angles is 180°.
Triangles can be classified by the relative lengths of their sides.
An equilateral triangle has three equal sides (and three equal angles of 60°); it has three lines of symmetry.
www.tiscali.co.uk /reference/encyclopaedia/hutchinson/m0006747.html   (249 words)

  
 Geometry Tutorials, Problems and Interactive Applets
The properties of the medians of a triangle are explored using an interactive geometry applet.
The properties of perpendicular bisectors in triangles and circumcircles are explored interactively using a geometry java applet.
A table of formulas for geometry, related to area and perimeter of triangles, rectangles, cercles, sectors, and volume of sphere, cone, cylinder are presented.
www.analyzemath.com /geometry.html   (660 words)

  
 triangle (geometry)
In geometry, a three-sided plane figure, the sum of whose interior angles is 180°.
Triangles can be classified by the relative lengths of their sides.
An equilateral triangle has three equal sides (and three equal angles of 60°); it has three lines of symmetry.
www.tiscaliten.com /reference/encyclopaedia/hutchinson/m0006747.html   (212 words)

  
 Cool math .com - Geometry Lessons - Interior Angles of Polygons
The sum of the measures of the interior angles of a triangle is 180 degrees.
The interior angles of an equilateral triangle are all 60 degrees.
Notice that not all of the angles of the triangles are involved with the interior angles of the polygons.
www.coolmath.com /interior.htm   (469 words)

  
 Math Forum Discussions
>'isogonal conjugate' A"B"C" of this triangle (
>> the world of triangle geometry, this is an important and deep structure.
From the point of view of triangle geometry, we are faced with an
www.mathforum.org /kb/thread.jspa?threadID=349133&messageID=1070111   (1037 words)

  
 Math Forum - Ask Dr. Math Archives: Middle School Geometry - Triangles/Polygons
Exploring the areas of a triangle with side lengths 6 and 7.
No triangle can be formed using any three of 8 sticks, each of integer length.
The Math Forum is a research and educational enterprise of the Drexel School of Education.
www.mathforum.com /library/drmath/sets/mid_triangles.html   (637 words)

  
 Some Triangle Geometry: Introduction   (Site not responding. Last check: 2007-11-05)
Classical Greek geometry started with congruent triangles that were supposed to be able to be picked up and made to coincide.
Geometry matters - for various reasons, but also because points lines and circles are symbols of what I lie on, pass through or touch.
Triangle geometry provides an interesting area for geometrical exploration and at the same time a way of coming to grips with important issues about proof.
s13a.math.aca.mmu.ac.uk /Geometry/TriangleGeometry/Intro.html   (986 words)

  
 Geometry: Triangles 165 | Shop Essentials   (Site not responding. Last check: 2007-11-05)
In a triangle, a line drawn perpendicular to the base, from the base to the opposite vertex, that represents the height of the triangle.
In an isosceles triangle, the one side that is not equal to the other sides.
In an isosceles triangle, one of the two angles formed by the base and a leg.
www.toolingu.com /tu/Shop_Essentials/Geometry_Triangles/Geometry_Triangles.html   (424 words)

  
 ez4-2 Measuring Angles in a Triangle (Glencoe Geometry)   (Site not responding. Last check: 2007-11-05)
The sum of the measures of the angles of a triangle is 180.
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
is formed by one side of a triangle and the extension of another side.
www.e-zgeometry.com /class/class4/4.2/4.2.htm   (269 words)

  
 perplexus.info :: Geometry : Equilateral Triangle
Suppose ABC is an equilateral triangle and P is a point inside the triangle, such that PA = 3 cms., PB = 4 cms., and PC = 5 cms.
Consider a triangle formed by the point and the nearest two points on the equilateral triangle.
If one side of the original triangle (the remaining side of the new triangle) is length s, then we can find angle a, adjacent to the length-3 side by the law of cosines: 4^2 = 3^2 + s^2 -2*3*s*cos(a).
perplexus.info /show.php?pid=723&cid=10586   (325 words)

  
 E-Example 4.2.1: Investigating the Concepts of Triangle and Properties of Polygons   (Site not responding. Last check: 2007-11-05)
Students can compare the triangles on their geoboards and discuss whether or not each shape is actually a triangle.
Some students may feel that a triangle with a vertex oriented toward the bottom of the geoboard is not really a triangle.
Geoboard shapes can be described with a simple system of coordinate geometry; thus two shapes on a geoboard are also congruent if their constructions can be described in the same way.
standards.nctm.org /document/eexamples/chap4/4.2/index.htm   (632 words)

  
 PinkMonkey.com Geometry Study Guide - 5.6 Similar Triangles
Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
It is however not essential to prove all 3 angles of one triangle congruent to the other, or for that matter all three sides proportional to the other.
S A S Test: If two sides of one triangle are proportionate to the two corresponding sides of the second triangle and the angles between the two sides of each triangle are equal the two triangles are similar.
www.pinkmonkey.com /studyguides/subjects/geometry/chap5/g0505601.asp   (283 words)

  
 Lightmaps on tristripped geometry? - GameDev.Net Discussion Forums
Problem is that in all light tutorials I have seen each triangle is mapped to new UV coordinates on the light map texture.
This means that the list of indexes in the geometry in made to reuse vertices between adjacent triangles in the mesh.
Lastly, you need to make sure triangle edges that are actually connected in the mesh, but have been split due to the uv-mapping, have smooth lightmapping between them (otherwise there will be a visible seem along the triangle edge).
www.gamedev.net /community/forums/ViewReply.asp?id=801604   (1120 words)

  
 Darij Grinberg
The Mitten point of a triangle, defined as the perspector of the medial and excentral triangles, is shown to be the radical center of a variable circle triad.
It is shown that triangle XYZ is oppositely similar to triangle ABC, that the lines AX, BY, CZ pass through the Nagel point of triangle ABC, and that one of the segments OX, OY, OZ is equal to the sum of two others.
The note is on a new proof that the midpoints of the sides, the feet of the altitudes and the midpoints between the vertices and the orthocenter of a triangle lie on one circle.
de.geocities.com /darij_grinberg   (3184 words)

  
 Geometry Solution   (Site not responding. Last check: 2007-11-05)
Geometry Solutions is a sophisticated calculator that calculates the perimeter, lateral and surface areas, and volume of plane and solid geometric figures.
For example, when you type in the angle, side, or the hypotenuse of a right angle, Geometry Solutions will calculate the perimeter and area based on the information you entered.
Geometry Solutions and geometric formulas when used together will strengthen your knowledge and abilities in geometry.
www.gomath.com /geometrycal.html   (159 words)

  
 Hyperbolic Geometry
(the Poincaré unit disc model) by (2, i, i) triangles, that is, with angles (90, 0, 0).
Every triangle has two vertices on the disc boundary (at infinity).
The diagram was built up from an initial triangle with a vertex at the centre, by reflection (inversion in a disc line) about one of its sides.
mcs.open.ac.uk /tcl2/nonE/nonE.html   (353 words)

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