Geometry.Net - Theorems_And_Conjectures: Geometry Theorem

Wilson Stothers' Inversive Geometry And CabriJava Pages
The object of these pages is to introduce inversive geometry. and its transformations,we begin by looking at a classical greek theorem (Apollonius's theorem).
http://www.maths.gla.ac.uk/~wws/cabripages/inversive/inversive0.html
HYPERBOLIC GEOMETRY
the hybrid distances theorem Suppose that A and B are points in the disk, and O is Sincewe know more about the euclidean geometry of the disk, this is useful.
http://www.maths.gla.ac.uk/~wws/cabripages/hyperbolic/hybrid.html
PinkMonkey.com Geometry Study Guide - 6.2 The Theorem Of Pythagoras
6.2 The theorem of Pythagoras. Figure 6.3. D ABC is a right triangle. Index. 6.1The Right Triangle 6.2 The theorem of Pythagoras 6.3 Special Right Triangles.
http://www.pinkmonkey.com/studyguides/subjects/geometry/chap6/g0606201.asp

Extractions: 6.2 The Theorem of Pythagoras Figure 6.3 D ABC is a right triangle. l (AB) = c l (BC) = a l (CA) = b CD is perpendicular to AB such that D ABC ~ D CBD or l (BC) l (AB) l (CD) a = c x = cx D ABC ~ D ACD or l (AC) l (AB) l (AD) b = c Therefore, from (1) and (2) a + b = cx + cy = c ( x + y ) = c c = c a + b = c The square of the hypotenuse is equal to the sum of the squares of the legs. Converse of Pythagoras Theorem : In a triangle if the square of the longest side is equal to the sum of the squares of the remaining two sides then the longest side is the hypotenuse and the angle opposite to it, is a right angle. Figure 6.4
PinkMonkey.com Geometry Study Guide - 5.4 Basic Proportionality Theorem
5.4 Basic Proportionality theorem. If a line is drawn parallel toone side of a triangle and it intersects the other two sides at
http://www.pinkmonkey.com/studyguides/subjects/geometry/chap5/g0505401.asp

Extractions: Figure 5.4 l paralled to seg.QR. l intersects seg.PQ and seg.PR at S and T respectively. D PTS and D QTS D QTS ) = A ( D SRT ) as they have a common base seg.ST and their heights are same as they are between parallel lines. l which is parallel to seg.QR divides seg.PQ and seg.PR in the same ratio. next page
Background On Geometry
Before embarking on trigonometry, there are a couple of things you need to knowwell about geometry, namely the Pythagorean theorem and similar triangles.
http://aleph0.clarku.edu/~djoyce/java/trig/geometry.html

Extractions: Before embarking on trigonometry, there are a couple of things you need to know well about geometry, namely the Pythagorean theorem and similar triangles. Both of these are used over and over in trigonometry. Let's agree again to the standard convention for labeling the parts of a right triangle. Let the right angle be labeled C and the hypotenuse c. Let A and B denote the other two angles, and a and b the sides opposite them, respectively. C and the hypotenuse c, while A and B denote the other two angles, and a and b the sides opposite them, respectively, often called the legs of a right triangle. The Pythagorean theorem states that the square of the hypotenuse is the sum of the squares of the other two sides, that is, c a b This theorem is useful to determine one of the three sides of a right triangle if you know the other two. For instance, if two legs are a = 5, and b = 12, then you can determine the hypotenuse c by squaring the lengths of the two legs (25 and 144), adding the two squares together (169), then taking the square root to get the value of c
The Geometry Of The Sphere
This material was the text for part of the Advanced Mathematics course in the High School Teachers Category Science Math geometry In plane geometry we study points, lines, triangles, polygons, etc. First we willprove Girard's theorem, which gives a formula for the sum of the angles in a
http://math.rice.edu/~pcmi/sphere/

Extractions: Rice University The material on these pages was the text for part of the Advanced Mathematics course in the High School Teachers Program at the IAS/Park City Mathematics Institute at the Institute for Advanced Study during July of 1996. Teachers are requested to make their own contributions to this page. These can be in the form of comments or lesson plans that they have used based on this material. Please send email to the author at polking@rice.edu to inquire. Pages can be kept at Rice or on your own server, with a link to this page. Putting mathematics onto a web page still presents a significant challenge. Much of the effort in making the following pages as nice as they are is due to Dennis Donovan Boyd Hemphill added two nice appendices. Susan Boone helped construct the Table of Contents. All of them are teachers and members of the Rice University Site of the IAS/Park City Mathematics Institute. Table of Contents A Proof of Euler's formula Appendices Incidence relations in the plane and in space Degrees and radians , by Boyd E. Hemphill
Geometry Of The Sphere 4.
a remarkable departure from what we would expect from our knowledge of plane geometry.Exercise Find the formula for the result of Girard's theorem when the
http://math.rice.edu/~pcmi/sphere/gos4.html

Extractions: Consider the black triangle T on the sphere to the left. We will be deriving a formula for the area of T . The key to understanding the derivation is the configuration of the three great circles on the sphere, as shown on this figure. There is no difficulty understanding what you see there. What might cause problems is what the configuration looks like on the other side of the sphere. However this figure is a java applet and you can rotate it by clicking and dragging the mouse starting anywhere on the figure. We will label the vertices of T by R G , and B , and the corresponding angles of T by r g , and b . The letters stand for red, green, and blue, and, for example, the vertex R is the vertex of T where T is opposite a red triangle. The angles at R in the black triangle T and in the red triangle are opposite angles and therefore are equal. Their value will be denoted by r . In fact R is the vertex of two congruent lunes, one of which consists of the red triangle and a gray triangle, and the other of which contains the black triangle and another red triangle. We will refer to these two lunes as the red lunes. We will denote by L r the red lune which does not contain T , and by L r the red lune which does contain T . In exactly the same way we see that G is the vertex of two congruent, green lunes -
6.2 The Geometry Of The Classical Theorem
6.2 The geometry of the Classical theorem. Let us examine the geometry related tothe theorem and begin with a simple, but illustrative example. Example 6.1.
http://www.immt.pwr.wroc.pl/kniga/node27.html

Extractions: Theorem The dimensional geometry derives from the specific group of movements. The suitable symmetry group named the gauge group was denoted by and described in detail in the previous chapter. Once the geometry is established it may replace all algebraic considerations. According to dimensional geometry any dimensional function (in the classical sense) becomes equivalent to a geometrical construction. Linear object are defined in close analogy to Euclidean geometry. For example let x x be the two points from W , then the line x x passing through both points is defined as the set of all points x given by x x t x 1 - t for t R where R denotes the set of all real numbers. In a similar manner the plane passing through three points x x x is the set of all points y , where y x t x u x 1 - t - u for t u R Now we may apply the above geometrical tools to analyze the form of dimensional functions. Let us examine the geometry related to the Theorem and begin with a simple, but illustrative example.
Mathematics Archives - Topics In Mathematics - Geometry
Mathworld geometry ADD. KEYWORDS Definitions, List of theorem; Museo Universitariodi Storia Naturale e della Strumentazione Scientifica - Mathematical
http://archives.math.utk.edu/topics/geometry.html

Extractions: ADD. KEYWORDS: Two Dimensional Tilings, Three Dimensional Tilings, Face-Transitive Tilings, Periodic Delone Tilings, Orbifold Graphs, Classification of 3-Dimensional Tilings, Tiling Space by Platonic Solids, Enumeration of Polyhedral Crystal Structures The Computation of Certain Numbers Using a Ruler and Compass
LycosZone Directory > Homework > Math > Geometry And Trigonometry > Pythagorean
Proof of the Pythagorean theorem Below is an animated proof of the Pythagoreantheorem. .. or you can Check out other geometry and Trigonometry Web Pages
http://www.lycoszone.com/dir/Homework/Math/Geometry and Trigonometry/Pythagorean

Extractions: Search For: Lycos Zone Home Family Zone Teachers Zone What kind of Pythagorean Theorem Websites are you looking for? Animated Proof of the Pythagorean Theorem "Below is an animated proof of the Pythagorean Theorem. Starting with a right triangle and squares on each side, the middle size square is cut into congruent quadrilaterals. Then the quadrilaterals are hinged and rotated and shifted to the big square. Fina"
Ez5-3 Pythagorean Theorem & Its Converse (Prentice Hall Geometry)
Pythagorean, Converse, About Pythagorus. Prentice Hall geometry Section53. This section introduces the Pythagorean theorem and its converse.
http://www.e-zgeometry.com/classph/sec5/5.3/5.3.htm

Extractions: Section # Previous Section Chapter # Next Section Pythagorean ... Converse About Pythagorus Prentice Hall Geometry Section This section introduces the Pythagorean Theorem and its converse. This theorem is used numerous times over the year. The Pythagorean Theorem: Theorem The Pythagorean Theorem In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. The Pythagorean Formula If c is the measure of the hypotenuse and a and b are the measuresof the legs then For example if a = 3 and b = 4 to find the length of the hypotenuse c we would calculate 3 = c , 9 + 16 = c , 25 = c and c = 5. Much more on this formula later...... Theorem -5 The Converse of the Pythagorean Theorem If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle. Pythagorean Triples A Pythagorean Triple is a group of three whole numbers that satisfies the equation , where c is the greatest number. One common Pythagorean triple is 3,4 and 5.
Bigchalk: HomeworkCentral: Pythagorean Theorem & Distance Formula (Geometry)
HomeworkCentral Linking Policy. Lesson Plan Archives Mathematics High School geometry Pythagorean theorem Distance Formula.
http://www.bigchalk.com/cgi-bin/WebObjects/WOPortal.woa/Homework/Teacher/Resourc
Fermat's Theorem Using Projective Geometry
Solution to Fermat's theorem by CF Russell using projective geometry calculating circle Znuz is Znees vol. 4. Back to Contents.
http://www.cfrussell.homestead.com/files/fermat.htm
Riverdeep | Tangible Math | Geometry Inventor | Pythagorean Theorem
activity listed underneath. Product, Tangible Math, Unit, GeometryInventor. Activity, Pythagorean theorem, Overview, In this activity
http://www.riverdeep.net/math/tangible_math/tm_activity_pages/geometry_inventor/
Interact Tutorial: Geometry Applications: Pythagorean Theorem
Chapter 5 Positive and Negative Decimal Numbers Section 5.8 GeometryApplications Pythagorean theorem. Practice with our InterAct
http://www.mathnotes.com/book6/book6_05/book6_0508.html

Extractions: Section 5.8: Geometry Applications: Pythagorean Theorem Practice with our InterAct Math tutorial exercises on the Web! To use the Interact Math tutorials over the Web, you will need to download and install the InterAct Math Plug-in for Windows. Click the Download Interact Math button for complete instructions. You will only need to install the plug-in once.
Interact Tutorial: Geometry Applications: Pythagorean Theorem
Chapter 5 Positive and Negative Decimal Numbers Section 5.8 GeometryApplications Pythagorean theorem. InterAct Tutorials will
http://www.mathnotes.com/Prealg/Pre5interact/prealg5_8.html
Projective Geometry
one can move on in synthetic projective geometry by studying the properties of perspectivitiesand the Fundamental theorem of Projective geometry which states
http://halogen.note.amherst.edu/~wing/project/content.php?page=6
John Millar Kast Grant Projective Geometry - Bezout's Theorem
Mathematics. Projective geometry Bezout's theorem. The Kast fund gaveme the opportunity to study at West Chester University this summer.
http://www.ga.k12.pa.us/faculty/pro_development/KastGrants/Kast00/Millar/summary

Extractions: Upper School Mathematics Projective Geometry - Bezout's Theorem The Kast fund gave me the opportunity to study at West Chester University this summer. I signed up for work that was billed as an exploration of a number of geometries, including Euclidean, projective, hyperbolic, spherical, symplectic, affine, and differential. What follows is a brief description of the highlights of the work. Let F=0 and G=0 be complex curves of degree m and n such that F and G have no common factors of positive degree. Then F=0 and G=0 intersect exactly mn times, counting multiplicities, in the complex projective plane. Without going into excruciating detail, here are some of the highlights. The projective plane is the set of points determined by ordered triples of numbers (a, b, c) where a, b, and c are not all zero and where the triples (ta, tb, tc) represent the same point as t varies over all nonzero real numbers. Thus in the projective plane (12, 6, 3), (6, 3, 3/2) and (4, 2, 1) all represent the same point. Such ordered triples are called homogeneous coordinates. Similarly, for c nonzero, (a, b, c) and (a/c, b/c, 1) represent the same point and thus define the 1 to 1 mapping between the c nonzero portion of the projective plane and the Euclidean plane determined by Z = 1. Finally the 1 to 1 mapping between (a/c, b/c, 1) and the Euclidean point (a/c, b/c) demonstrates that each point in the Euclidean plane has its 1 to 1 image waiting in the projective plane.
Geometry Connects A New Theorem
Return Column Navigator A New theorem This investigation verifiesa discovery made by a Georgia High School Student the proof
http://www.math.vt.edu/people/hagen/Registration/Studenttheorem.html

Extractions: While looking at the different points of the triangle , he knew the Perpendicular bisectors of the sides of the triangles intersected at the same point. He also knew about the relationship of the slopes of perpendicular lines and decided to look at the reciprocal of the slope without the negative. The blue lines below represent the lines with same slope as the perpendicular bisectors (red lines), but opposite sign. Move the triangle around to see that these lines do intersect. This point of intersection lies on a well known circle connected to triangles. Click the link above to find out why.
Bounded Geometry And L2-index Theorem (4 Papers)
Thomas Schick Bounded geometry and L2index theorem. The analysis ofmanifolds with boundary and of bounded geometry, and the development
http://www.uni-math.gwdg.de/schick/publ/bg_L2ind.html

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