to.. ELA Web Portal

ELA MATHEMATICS DIRECTORY

Sponsor.. Statistics add-in for Microsoft Excel

⇑ Absolute Value | Accuracy | §Acronyms /Dictionaries/Glossaries§ | Adult Education ⇑
Algebra | Analysis | Analytic Geometry | Angle Trisection | Animations
§ARCHITECTURE§ Arithmetic | Arts | §ART & SCIENCE§ | Articles | §ARTIFICIAL INTELLIGENCE§
Associations | Astronomy | §ASTRONOMY§ | Audio Files
Biography | §BIOLOGY§ | Blogs | Books | §Boundary Element Method§ | §BUSINESS§
Calculators (Graphing) | §Calculators§ | Calculus | Calculus of Variations | §Chaos§
Collaboration | Competitions | Complex Analysis | §Complexity§ | §COMPUTERS§ | Computational Geometry | Computer Algebra | Computing
Conic Sections | Constants | Coordinate Geometry | Curves
Demonstrations | §Dictionaries & Glossaries§ | Differential Equations | Differential Geometry | Discreet | Diversions
e | §ECONOMICS§ | Education | §EDUCATION§ | §ELECTRICITY§ | §ENGINEERING§ | Error Analysis | Exponentials | Exponents
Factoring Polynomials | FIND | §Finite Element Analysis§
FOCUS | FORUMS | Foundations | Fourier Analysis | Fractals | Fractions | Fun | Function
Games | §Game Theory§ | GED | Genetic & Evolutionary Alogorithms | §GENETICS§
Geogebra | Geometry | Golden Ratio | Graphics | Graphing Calulators | Graphing Calulators Online | Graph Theory | Group Theory
Handbooks | Heuristics | High School | §History of Math & Science§
Images | Induction | Infinitesimals | Infinity | Instruments | Interactive Mathematics Program (IMP)
§JAVA§ | Journals | K-8 | Kids | Knots
Language | Lesson Plans | Liberal Arts | §LINGUISTICS§ | Linear Algebra/Programming | Linear Regression | Logarithms | §Logic§
Mandelbrot Set | Manipulatives | §MAPS§ | Masters | Mathematicians | §Math History§
Matrices | Metaphysics | Modular Arithmetic | Multiplication Tables | Museums | Music
§NANOSCIENCE§ | Natural Math | NEWS | Non-Euclidean Geometry | §Nonlinear§ | Nonstandard Analysis
Notation | Number Theory | Numerical Analysis | Numerology | Nurbs
Open Education | §Operations Research§ | Optimization
Paradox | Partial Differential Equations | Periodicals | §PHILOSOPHY of Mathematics§ | §PHYSICS§
Plane Curves | Platonism | Polyhedra | Polymath Project | Polynomials | Power Law | PreCalculus | Precision | Primes
Probability & Statistics | Problem Solving | Progressions | Projective Geometry | §Problem Solving§ | PROOF |
Puzzles, Problems & Games | Pythagorean Theorem
§Qualitative Research§ | Quotations | Random Numbers | Recreational | Religion | Roman Numerals
§SCIENCE§ | Scientific Notation | Sequences & Series | Set Theory | Significant Figures | Simulations
Software | §SOFTWARE§ | Solutions | Splines | Statistics | Symbols | Symmetry
§TEACHERS & EDUCATION§ | Tables | Tensors | Topology | Trigonometry | TV | TUTORIALS
Uncertainty | Vectors | Videos | Visual Demonstrations | §Web Math Notation/Markup§ | Whitehead | §XML§
(Click above to jump to Listings on this page or to an § ALTERNATE ELA DIRECTORY§)

 
^ MATH

Let x = length of side of the square base of the pyramid and h its height.
At any height y, length of the square section
= x * (y/h)
so Area = [ x * (y/h) ]^2

Volume of a thin slice of pyramid at a height y and having thickness dy
= [ x * (y/h) ]^2 dy

Integrating from y = 0 to y = h,

Total volume
= (x/h)^2 ? y^2 dy [y=0 to y=h]
= (1/3) (x/h)^2 [ y^3 ] [y=0 to y=h]
= (1/3) (x/h)^2 * h^3
= (1/3) * h * x^2
i.e., one-third the height times area of the base.

DIRECTORIES-Math
dmoz Open Directory | Google | Math Forum | Mathtools.net | Wikipedia | WWW Virtual Library | Yahoo.com

Advanced Geometric Configurations Advanced Geometry Applets (Some Source)

Annenberg Media Learner.org, Teacher Resources
• Learning Math: Geometry (K-8) geometric reasoning as a method of problem solving
• Workshops and Courses

Archimedes' quadrature of the parabola, Thomas L. Heath, from Bill Casselman, U British Columbia

AskEric.org (K-12) - Alphabetical Topics, Search, Site Map
• Ask an Expert - parents/teachers ask general education questions
• Geometry Lesson Plans

AST Library World Coordinate Systems in Astronomy: U St Andrews
Basic 3D Math Mark J. Feldman

Bill Casselman @ U British Columbia Math
• Euclid's Elements of Geometry
    º Oliver Byrne's edition: Introduction (with Introductions including Byrne, Heath & Joyce) Books 1, 2, 3, 4, 5, 6

Blogspot.com
• the Euclidean Triangle

Cabri.com ( $ ) 3D educational geometry software

C.a.R. (free source, GNU Lic.) Compass and Ruler construction software by Prof. Dr. R. Grothmann, Links
• Applications
• C.a.R. User-Wiki
    º Howto Pages
    º User FAQ
• Tutorial
• Video Demos

Clark Kimberling's Encyclopedia Of Triangle Centers - etc, U Evansville

Codeplex.com: LiveGeometry educational software to experiment & create interactive ruler & compass constructions
Colby Community College, Mathematics Dept, Geometry Terminology

Cut-the-knot.org Geometry articles, theorems, problems, applets, games
• About a Line and a Triangle
• Ceva's Theorem with Corollary 4 (Gergonne point)
• A Problem In an Isosceles Right Triangle: What is this about? A Mathematical Droodle
• A Property of Equiangular Polygons: What Is It About? A Mathematical Droodle
• Pythagorean Theorem
• All Triangles Are Isosceles How Is It Possible?
• Angles in Triangle Add to 180 degrees
• Triangle Classification
• Triangles, Squares and Areas from Temple Geometry`

David Eppstein's
• Geometry in Action
• Geometry Junk Yard
• Recreational Math, non-geometrical Publications
• Software

Eric Weisstein's World of Mathematics:   WOLFRAM Research
• Geometry - PlaneGeometry

Euclid's Elements ( alt ) an Introduction (& full text) by David E. Joyce, Clark U
• The Geometry Applet - using the Applet
• Links
• Side-Side-Side Congruence Thm Book I, Proposition 8
• Quick Trip through the Elements
• Subject Index, Table of Contents

• Euclid's Elements, Thomas L. Heath
• Euclid's Elements (Greek), J. L. Heiberg
both of the above from the Perseus Digital Library

Euclid's Elements of Geometry - Oliver Byrne's edition & Links, from Bill Casselman, U British Columbia

Euclid's Elements from U British Columbia SunSite, Digital Math Archive
• Oliver Byrne's edition of Euclid page by page scanned images
• Erhard Ratdolt - first publisher of Euclid


Forum Geometricorum (pdf's) journal on classical Euclidean geometry & related areas, Author & Title Index (2001-2006)
• Volume 1 (2001)
    º Heron Triangles: A Gergonne-Cevian-and-Median Perspective, K.R.S. Sastry
• Volume 2 (2002)
• Volume 3 (2003)
• Volume 4 (2004)
• Volume 5 (2005)
• Volume 6 (2006)
• Volume 7 (2007)
• Volume 8 (2008)
• Volume 9 (2009)

Galaxy Search (Ads!) - Geometry at Mathematics: Science
Geocadabra software

Geogebra.org free, multi-platform learning & teaching software joining arithmetic, geometry, algebra & calculus with graphics, algebra & spreadsheets
• Help
    º Quick Start
• Help & Documentation
• Forum, Forum FAQ
• GeoGebra Institute of Ohio the first local GeoGebra Institute in North America
• International GeoGebra Institute (IGI)
• Introduction to GeoGebra online book
• Wiki Wiki Help
• Workshops

Geometry in Action & The Geometry Junkyard by David Eppstein, U California, Irvine
Geometry Calculators Links: ifigure.com

The Geometry Center from U Illinois, Urbana-Champaign
• Gallery of Interactive Geometry

The Geometry Center (mirror from U Illinois, Urbana Champaigne)
• Course Materials - Technology in Geometry Course Materials
• Distance Learning
• Documents - Geometry and the Imagination
• Interactive Applications - HTML, Java
• Reference Archive - Formulas and Facts, 2D Coordinate Geometry:
• Triangles, Quadrilaterals, Regular Polygons, Circles, Conics, Alternative, Gen Quadratic..
• Software download
• Topological Zoo

The Geometry Center: U Minnesota (or try the Google cache)
• Gallery of Interactive Geometry

The Geometry Forum Angle Trisection

Geometry.net online learning center, Math
• Book Author: Index (General Math)
• Categorical Geometry links

Geometry Online from RICE U, Mathematics

Geometry of the Sphere, John C. Polking, Rice U
• Basic Information
• Area, Area of a Triangle (Girard's Theorem), Consequences (maps)
• Euler's Formula

Geometry Step by Step from the Land of the Incas
Geomview Download 3D geometry viewing program: the Geometry Center

Google Books
• Euclid's Elements by Sir Thomas Little Heath (1908): Introduction, Books 1 & 2, Books 3 - 9, Books 10-13 & Appendix

Intergeo Project (I2geo.net) accessible interoperable interactive geometry for mathematics teaching in Europe, About

Interactive Mathematics Miscellany and Puzzles - Geometry, Glossary, many theorems & Java demo's, eg..
• Angle Bisectors in a Quadrilateral form cyclic (can be inscribed in circle) quad => sum (opp <'s) = 180º
• Area of Parallelogram
• Pythagorean Theorem (39) Proofs - "Extra-geometric&quot;, Generalizations, implies Pll Postulate, Mechanical
• Remarkable Line in Cyclic Quadrilateral
• Shapes of constant width
• Sine, Cosine, and Ptolemy's Theorem
• Squaring a circle

Jeff Weeks' Topology and Geometry Software (Geometrygames.org) Fun & Games, ages 10 & up
• Computer Graphics in Curved Spaces (OpenGL, Direct3D)
• Exploring the Shape of Space geometry and cosmology for grades 6-10
• Games: KaleidoTile, Kali, Torus & Klein Bottle games
• SnapPea Research Software for Mathematicians (Linux, Macintosh, Windows)

Jim Loy's Mathematics Page Geometry
• Angle-Side-Side Theorem
• The Pythagorean Theorem
• Trisection of an Angle

Jim Wilson, U Georgia
• Mark Cowart
    º Concurrency And The Gergonne Point (including Ceva's Theorem)
    º Theorem of The Broken Chord

Ludi geometrici construct & post ruler & compass solutions to listed problems using C.a.R tools; includes online help, About
• Problems Archive

MacTutor History of Mathematics archive, Search
• Bolyai, Janos 1802 - 1860
• Desargues, Girard
• Descartes, Rene
• Euclid of Alexandria ~325 BC - ~265 BC
• Galois, Evariste 1811 - 1832
• Gauss, Johann Carl Friedrich 1777 - 1855
• Geometry and Topology Index
    º Euclid's definitions
    º Mathematics and art - perspective
    º Non-Euclidean geometry
• Lobachevsky, Nikolai Ivanovich 1792 - 1856
• Pascal, Blaise
• Pythagoras of Samos ~569 BC - ~475 BC
• The real numbers: Pythagoras to Stevin
• Riemann, Georg Friedrich Bernhard 1826 - 1866

MATH-abundance Tutorials & Links, Johan Claeys
• Lines in a plane - Orthogonality; Distances

Math2.org by David Manura, formerly Dave's Math Tables ( Site Download )
• Geometry - Areas, Volumes, Surface Areas, Circles

MathCasts.org Math247 screencasts, where Creativity Counts!
• Geometry with Geogebra
    º sin(θ) and the Unit Circle - for θ between 0° and 360°

The Math Forum
• Ask Dr. Math - Geometric Formulas
• Geometry Formulas and Facts - Two-Dimensional Geometry
• Geometry Reference Archives - Graphics Archive
• Geometry.College discussion group
• Geometry Software, Forum
• Geometry Turned On: Dynamic Software in Learning, Teaching, and Research - Download
• K-12 geometry
• College-Level geometry
• Advanced geometry

The Math Open Reference with interactive animations
• Bisecting an Angle
• Constructing a 30 degree angle
• Constructing a 45 degree angle
• Constructing a 60 degree angle
• Introduction to Euclidean Constructions

MathResources.com
• Gergonne Point

Mr. Dreyer's Geometry Classes at Lexington High School
• Fibonacci/Golden Ratio Lab
• Coordinate geometry and transformations
• Coordinate transformations in a nutshell (pdf)
• Transformations

NonEuclid Hyperbolic Geometry Article & free Java Compass & Ruler Applet, Relativity
by Joel Castellanos, U New Mexico, Joe Dan Austin & Ervan Darnell of Rice U
• Area
• Axioms and Theorems
• Disk and Upper Half-Plane Models
• Pseudosphere
• Parallel Lines
• The Shape of Space & Einstein's General Theory of Relativity
• What is Non-Euclidean Geometry?
• X-Y Coordinate System
plus..
• Conceptual Mechanics of Expression in Non-Euclidean Fields artwork by Clifford Singer

Paul Yiu's Geometry
• Dynamic Triangle Geometry: Families of Lines with Equal Intercepts
• Geometric Constructions
• A Short Tour of Triangle Geometry Around the Nine-point Circle
• A Tour of Triangle Geometry

Penn State U, Dept Mathematics - Elementary Geometry Tutorial, Glossary

ScienceU.com - Geometry (Coord):
• Facts & Figures - Formulas, Platonic & Archimedian Solids
• Formulas - Lines, Dist, Angle, Col, Conc, Triangles, Quadrilaterals, Reg Polygons, Circles, Conics..
• Software Download - Math, Links & Search

Sir Roger Penrose Penrose Tiles, Penrose Staircase, Tribar

Thinkquest Library
• Go Forth and Multiply
    º Geometry
• Interactive Mathematics Online
    º Introduction to Geometry

U Toronto, Math Dept: Mathnet Question Corner and Discussion Area

the Triangle Web by Quim Castellsaguer
• Gergonne Point

Wikibooks: Geometry for elementary school
• Side-Side-Side congruence theorem

Wikipedia (Mathematicians)
• Desargues, Gerard (1591-1661)
• Descartes, Rene (1596-1650)
• Euclid (300 BC)
    º Euclidean geometry
    º Euclid's Elements
• Euler, Leonhard (1707-1783)
• Gauss, Carl Friedrich (1777-1855)
• Heron of Alexandria
    º Heron's formula

Wikipedia
    º Category:Analytic geometry
    º Category:Geometers
    º Category:Geometric algorithms
    º Category:Geometry
    º History of geometry
    º History of trigonometry
    º List of interactive geometry software
• Algebraic geometry
• Analytic geometry
• Cartesian coordinate system
• Cavalieri's principle
• Chord (geometry)
• Circle
• Compass and straightedge constructions
• Computational geometry
• Conic section
• Curvature
• Curve
• Descriptive geometry
• Differential geometry
• Euclidean geometry
• Geometrography
• Geometry
• History of geometry
• History of trigonometry
• Line (geometry)
    º Secant line
    º Tangent
    º Tangent lines to circles
• Line segment
    º Chord (geometry)
    º Diameter
    º Radius
• Mathematical proof
• Non-Euclidean geometry
• Parallel postulate
• Polygon
• Polyhedron
• Projective geometry
• Pythagorean theorem
• Secant line line intersecting two points on the curve, from the Latin secare, to cut
• Solid geometry
• Spherical geometry
• Synthetic geometry
• Thales' theorem
• Trigonometric functions
• Trigonometry

Wikiversity
• School:Mathematics
    º Introductory Algebra and Geometry: Topic:Euclidean geometry
• Topic:Computational geometry
• Topic:High school mathematics

Wolfram Mathworld
• Altitude
• Angle Bisector
• Bevan Circle
• Circumcenter
• Circumcircle
• Contact Triangle
• Euler Line, Euler Points
• Excentral Triangle
• Excircles
• Extouch Triangle
• Feuerbach Point
• Gergonne Point
• Incenter
• Incentral Triangle
• Incircle
• Medial Triangle
• Nagel Point
• Nine-Point Center
• Nine-Point Circle
• Orthic Triangle
• Orthocenter
• Perpendicular Bisector
• Triangle Median, Triangle Centroid

WWW Interactive Mathematics Server
• Ruler and Compass online construction tool

Yahoo Groups
• Hyacinthos Triangle Geometry discussions

YouTube
• DrJamesTanton
    º Lateral Area of a Cone
    º Volume of a Cone
    º Volume of a Sphere
    º Surface Area of a Sphere


^ MATH