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Mathematics

CONTENTS

General Mathematical Resources 
Puzzles, Problems-of-the-week, etc. 
Factoids and Oddities 
Worksheets, Example sheets 
Abstract Algebra, Topology, Set Theory 
Calculus 

Eric Weisstein's Mathworld  (previously known as the Concise Encyclopedia of Mathematics) has (as of Aug 1, 2005) 12,325 entries (more than one myriad), hundreds of thousands of cross-references, thousands of figures, hundreds of animated graphics, and about a thousand live Java applets.
http://www.thesaurus.maths.org is a comprehensive math resource, with many java applets to help you visualize mathematical concepts.

Cut The Knot!

An interactive column using Java applets by Alex Bogomolny, part of the Cut-the-knot website.
Math Pages
MathPages.com
Number Theory
Combinatorics
Geometry
Algebra
Calculus & Diff Eqs
Probability & Statistics
Set Theory & Foundations
Reflections on Relativity
History
Physics
Music
Animated Illustrations
Combined List of Articles
Quotations

KöMaL

A mathematical journal for high school students
Ask Dr. Math, http://mathforum.org/dr.math/
(Mostly K-12 math and college algebra in a Q&A format.)
Dr. Gerard Michon, of Numericana Numericana

Final Answers on Numericana
by Dr. Michon.

Many basic and advanced scientific questions answered within days.
Ask Gerard any question.  Some answers are posted here.

Currently (on 1/26/2008), that's over 820 articles.

 

Link Farms


KABOL: Knot a Braid of Links
"Your rough guide to math on the web", a link farm.

KaBoL is a "cool math site of the week" service to the mathematics community provided within Camel by the Canadian Mathematical Society.


MAA - www.maa.org - The Mathematical Association of America 
Click "Publications", and then look for the section called Web / Electronic.  There you'll find these MAA Online Columns.

The Mathematical Tourist, by Ivars Peterson
Devlin's Angle, by Keith Devlin
Card Colm
,
by Colm Mulcahy
Launchings
, by David Bressoud
Math Games
,
by Ed Pegg, Jr.
How Euler Did It
,
by Ed Sandifer
Math Cha
t, by Frank Morgan
Cut the Knot
,
by Alex Bogomolny
MathTrek, By Ivars Peterson

according to http://www.stetson.edu/~efriedma/mathmagic/  . . . . . .

Great Math Sites: | Geometry Junkyard | Integer Sequences | Mathematician Biographies |
| Numbers With Names | Inverse Calculator | Geometric Dissections |
Recreational Math Sites: | Mike Keith | Harvey Heinz | World of Numbers | Fibonacci |
| GIMPS | Primes | Polyforms | More Polyforms | Soup Kitchen |

Solvers

Helpful Internet Computing Websites

quickmath.com uses Mathematica to solve, simplify, and graph,
and so does   -- Here are some tips for using Wolfram's Integrator from David Loeffler:

With a bit of ingenuity you can use Wolfram's integrator for definite integrals too. If you embed a definite integral inside a vacuous indefinite integral, it will evaluate the definite integral first.  For example if you enter Integrate[Exp[-y^2], {y,0,Infinity}] into the box, it will try and evaluate
Latex image
and return x times the value of the integral in the middle, which is just 1/2 Öp.  You can put any expression you like, not necessarily an integral, inside: feed it Sum[1/(n^2 + a^2),{n,0,Infinity}], for example. Just as long as what you're giving it doesn't involve x, you're fine.

Prime Factorization Machine does just what it says.
Dario Alpern's page, Factorization using the Elliptic Curve Method does it faster!
Inverse Symbolic Calculator turns a number into the formula that generated that number! 
  Plouffe's Inverter also turns a number into the formula that generated that number!
Fibonacci Calculator gives exact values of Fibonacci Numbers, Lucas Numbers, and "Rabbit" numbers. (linked from here)

Letter Puzzle Solvers

The Cryptarithmetic Puzzle Solver solves problems like LIP+LIP=KISS and THREE+THREE+F0UR=ELEVEN

The Alphametic Puzzle Solver also solves such problems

Links to Links -- a master table of mathematical links

NRICH.maths.org/  (part of the Millennium Mathematics Project)-- click "Links" to get hundreds of categorized links

  Math Forum Internet News is a newsletter with links to all sorts of math resources

Radio programs

Five Numbers (Zero, Pi, Phi, i, and infinity) -- click the link at the bottom of this page to hear the program (originally broadcast in March, 2002, on BBC Radio4) in Real Audio format.

Help for Math students

SAT preparation and more
Mathactive.com -- test preparation, tutoring, and distance learning for mathematics
NRICH.maths.org/
-- click "ask NRICH" to access the web board
mcraefamily.com/MathHelp/ is Graeme's math website
algebra.com is yet another homework-solving mathboard
purplemath.com is a resource for algebra students
mnemo.nu  a brand new (as of 9/27/2002) discussion board website from some foreign country
www.mathematics.0catch.com/ asks for a donation in return for help with math or physics homework
www.cms.livjm.ac.uk/cmsjkung/index11.htm is an experimental Java-based math tutor.
www.hotmath.org provides free solutions for actual math homework problems in many popular algebra, geometry, and calculus textbooks
physicsforums.com has a number of free forums, including one on mathematics.

Anne Bell's Recommendations

www.cia.gov/cia/ciakids/codegame/index.html -- Break the secret code
http://mathforum.org/alejandre/magic.star -- Like a magic square, except it's a star
www.aplusmath.com/games/index.html -- Flashcards, worksheets, java programs
www.nottingham.ac.uk/education/number -- Fun facts about the number of today's date
www.cookwithlyle.co.uk -- A shockwave-enhanced resource for kids
www.bbc.co.uk/education/schools/digger -- English, Math, and Science for kids up to age 11
www.cadburylearningzone.co.uk/maths/index_content.htm  -- math for kids
www.funbrain.com/ofm/index.html -- escape the haunted house by solving math puzzles
www.learningplanet.com/sam/ff/index.asp -- shockwave-enhanced Fraction Frenzy
www.mathscats.com/explore/multiplicationtable.html -- not found on 6/16/2002
www.funbrain.com/linejump/index.html -- arithmetic facts using a number line 

Graphing and solving utilities

Links to several dozen problem-solving methods including 3D Plotting Tool, Bar Graph, Brownian Motion Simulator, Bull's-Eye Shot, Calculator, Computing a Summation, Curve Fit, Definite Integrals, Diffusion Simulator, Elastic collision, Elastic collision (2:1 ratio), Factoring a Polynomial, Gas under a piston, Grade Manager, Implicit Differentiation, Integration, Kepler's laws, Laboratory Report Writer, Limits, Limits & Derivative Tools, Multiplication Table, Osmosis Simulator, Pie Graph, Polynomial Addition, Polynomial Multiplication, Projectile motion, Regression Analysis, Solar system, Solids of Revolution, Solving a System of Equations, Solving a Polynomial Equation, Tangent Lines, and Weight & Measure

Java-based visualization aids

http://www.thesaurus.maths.org/dictionary/map/word/2098 -- The first Napoleon Point

http://math2.math.nthu.edu.tw/jcchuan/java-sketchpad/jsp.html -- A smorgasbord of java applets for visualizing all sorts of geometric factoids

 

 

Elliptic Curves Franz Lemmermeyer's "Mother of all Elliptic Curves Resources" site.  (Also, see here).

 

Geometry

 

 Geometry Theorems & Problems

 Inca Geometry

Archimedes' Book of Lemmas:Try to solve the Archimedes' problems of geometry (High school Level)

Butterfly Theorem Proof. Puzzle.

Butterfly Theorem Introduction.

Carnot's Theorem

Ceva's Theorem Concurrency

Circles

Clifford's Circle Chain Theorems

Equilic Quadrilateral Five theorems.

Equal Incircles Theorem. Interactive presentation.

Eyeball Theorem

Gergonne Point Theorem

Johnson Theorem

Heron's Formula. Key facts and a purely geometric step-by-step proof

Kurschak's Tile and Theorem

Kurschak's Tile and Theorem. No frames.

Langley Theorem. Adventitious angles.

Menelaus' Theorem. Triangle and transversal line.

Miquel's Pentagram Theorem Proof

Miquel's Pentagram Dynamic Geometry

Monge & d'Alembert Three Circles Theorem I Dynamic Geometry

Monge & d'Alembert Three Circles Theorem II Dynamic Geometry

Morley's Theorem

Nagel Point Theorem Proof

Napoleon's Theorem

Newton's Theorem

Parallelogram&Squares

Pentagons and Pentagrams. Menelaus and Collinearity.

Platonic Solids Interactive animation

Poncelet's Theorem

Proposed Problems about congruence of line segments, angles, and triangles.
Key Theorems or Facts to know

Sangaku Problem 1

Sangaku Problem 2

Sangaku Problem 3

Semiperimeter and Incircle

Semiperimeter and Excircles

Semiperimeter, Incircle and Excircles

Seven Circles Theorem

Simson Line

Simson Line: Angle

Steiner's Theorem

100° Isosceles

Triangles

Triangle with the bisectors of the exterior angles. Collinearity.

Triangle and Squares. Fifteen theorems, visual illustrations.

Triangle&Squares 0 Two squares

Triangle&Squares 1 Two squares

Triangle&Squares 2 Two squares

Triangle&Squares 3 Three squares

Triangle with Squares 4 Finsler-Hadwiger Theorem

Triangle with Squares 5: Median and Altitude

Triangle with Squares 6: Four squares

Triangle Centers

Van Aubel's Theorem

Adjacent Angles

Varignon & Wittenbauer

 

 Triangle Centers

Centroid

Orthocenter

Circumcenter

Incenter

Excenter

Apollonius Point

Nine-Point

Gergonne Point See also: Gergonne Point Theorem Proof

Nagel Point See also Nagel Point Theorem Proof

Fermat Point

Napoleon Point

Bevan Point The circumcenter of the excentral triangle. Illustration with animation.

Symmedian (Lemoine) Point

Mittenpunkt Point

Steiner Point

Bevan Point Puzzle

Triangle Centers Word Find Puzzle

 

 Inspiration for Problem Solving

Achieve Your Dreams. Inspirational Poem.

I've Learned Inspirational Poem.

The Road Not Taken Robert Frost's poem about choices and decision making.

If Rudyard Kipling' Poem. Nobel Prize 1907.

If (Spanish version)

If - Math Humor, High School version.

Desiderata Ehrmann's Poem for a way of life.

Desiderata (Spanish) Poema de Ehrmann para una forma de vida.

Raft of the Medusa Free interpretation of Gericault's famous painting with Fractals.

Balsa de la Medusa (Spanish version) Interpretación libre de la famosa pintura de Gericault.

Raft of the Medusa (Traditional Chinese version)

On Children a poem by Kahlil Gibran.

Archimedes & Rhombicuboctahedron  Archimedes "The Geometer"

Experiencing Geometry Poem

Top Ten Reasons to Enjoy Geometry

Euler and his beautiful and extraordinary formula

The Landscape of Geometry Terms

The Landscape of Geometry Terms. No frames.

Machu Picchu and Geometric Art

The Lord of Sipan and Geometric Art

Angkor Wat and Geometric Art

Giza Pyramids and Geometric Art

Vatican City and Geometric Art

Morley's Theorem

Hyperbolic Tessellation and Geometric Art.

Star Wars and Geometric Art.

The Chronicles of Narnia and Geometric Art

The Lord of the Rings and Geometric Art

Geometry Wars and Geometric Art

Torino Games and Geometric Art

Simson Line

Sierpinski Triangle and Machu Picchu with fractals.

Nazca Lines Animation. Mystery on the Desert.

Nazca Lines: The Monkey. Geometric Art.

Kurschak's Tile and Theorem. No frames

Home Introduction

46th Annual Georgia Mathematics Conference 2005

Geometric Art. Table of Content

The School of Athens. Interactive Map.

 

The Landscape of Terms

The Landscape of Academic Disciplines

The Landscape of Books of All Time

The Landscape of the Da Vinci Code

The Landscape of E-Learning

The Landscape of Expert System

The Landscape of Geometry terms

The Landscape of Harry Potter terms. Glossary