MARTINDALE'S CALCULATORS ON-LINE CENTER MATHEMATICS: E-H (Calculators, Applets, Spreadsheets, and where Applicable includes: Courses, Manuals, Handbooks, Simulations, Animations, Videos, etc.)

US/Pacific: Saturday, July 5, 2008 Sydney, Australia: Sunday, July 6, 2008 File Download Time Calculator Author, E-Mail, Privacy Policy & Disclaimer Currently the Calculators On-Line Center contains over "23,535" Calculators & Spreadsheets, over "3,000" Courses, Lectures, Manuals, Handbooks, & "1,000's" of Movies, Videos, Simulations & Animations

Complex Math Calculators by Specialty: E-H Eigenvalues & Eigenvectors ~ EggMath Encryption, Cryptography & Quantum Cryptography Ergodic Theory, Bers Slices, Riemann Surfaces, Teichmüller Theory, TeichmüllerSpace Fault Tolerant Computing ~ Fibonacci Numbers ~ Fourier ~ Fractals Geometry Advanced Geometry (Differential Geometry, Geometry & Quantum Field Theory, etc.) Computational Geometry Graph Theory ~ Graphing & Plotting Calculators Hypercube & N-Dimensional ~ Hysteresis Mathematics Calculators Home Page Calculators On-Line Center Home Page

Eigenvalues & Eigenvectors EIGENVALUES AND EIGENVECTORS COURSES & TEACHING MODULES EIGENVALUE DEMONSTRATIONS & MINI-LECTURES ON EIGENVALUES (FLASH) - G. Strang, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Eigenvalue Demonstrations & Mini-lectures on Eigenvalues (Text, Images, Videos/Movies & Audio/Sound). VERY VERY EXTENSIVE. Examples of Mini-lectures on Eigenvalues include: "...Eigenvectors and Trace Video Lecture; Powers Video Lecture; Diagonalization Video Lecture; Differential Equations Video Lecture; Symmetry Video Lecture; Positive Definite Video Lecture; etc..." For more information see the Linear Algebra Course 18-06; Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare EIGENVALUES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS EIGENVECTORS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS EIGENEXPLORER - J.R. Senning, Department of Mathematics & Computer Science, Gordon College, Wenham, MA EigenExplorer "...is a Java applet designed to explore the the relationships between a matrix A, a vector x, and the matrix-vector product Ax..." For more information see Linear Algebra Visualization Assistant; Jonathan R. Senning's Home Page or the Department of Mathematics & Computer Science EIGENVALUES AND EIGENVECTORS - AKiTi.ca, David Binner, Vancouver, British Columbia, Canada VERY VERY EXTENSIVE. Eigenvalues and Eigenvectors Calculators include: "...Eigenvalues of a 2 by 2 Matrix Calculator; Eigenvalues of a 3 by 3 Matrix Calculator; Eigenvalues of a 4 by 4 Matrix Calculator; Eigenvalues of a 5 by 5 Matrix Calculator; Eigenvalues of a 6 by 6 Matrix Calculator; etc..." For more information see Math Functions: Miscellaneous Mathematical Utilities or AKiTi EIGENVALUES AND EIGENVECTORS APPLETS - Nicholas Exner, Computational Science and Engineering Graduate Option Program, University of Illinois, Urbana-Champaign VERY EXTENSIVE. Eigenvalues and Eigenvectors "...illustrate properties of eigenvalues and eigenvectors of matrices, and demonstrate the behavior of algorithms for computing them..." Eignevalue Applets include: "...Power Iteration and Inverse Iteration; QR Iteration with Shifts; Jacobi's Method; Gershgorin's Theorem..." For more information see Interactive Educational Modules in Computational Science or the Computational Science and Engineering Graduate Option Program INTRODUCTION TO EIGENVALUES AND EIGENVECTORS (JAVA APPLET) - Department of Mathematics, Duke University Introduction to Eigenvalues and Eigenvectors Calculator "...can be used to explore a linear transformation written in the form y = Ax, where A is a two-by-two matrix..." For more information see Lite Applets; The Design of Classroom Lessons in Mathematics from Web-based Materials or the Department of Mathematics EIGENVALUES AND EIGENVECTORS OF MATRICES IN TWO DIMENSIONS EIGENVALUES AND EIGENVECTORS OF MATRICES IN TWO DIMENSIONS (JAVA APPLETS) - B. Casselman, Department of Mathematics, University of British Columbia, Vancouver, Canada VERY EXTENSIVE. For more information see Topics in Geometry - Mathematics 309; Bill Casselman's Home Page or the Department of Mathematics EIGENVALUES OF A MATRIX THE OVALS OF CASSINI AND GERSHGORIN'S CIRCLES - R.S. Verga & A. Krautstengl, Department of Mathematics & Computer Science, Kent State University The Ovals of Cassini and Gershgorin's Circles "...This page presents an interactive introduction to some ideas about the location of the eigenvalues of a matrix..." For more information see Gershgorin-Type Problems; 1999 Abstracts or Electronic Transactions on Numerical Analysis (ETNA) EggMath MATHEMATICS CALCULATORS & APPLETS RELATING TO EGGS EGG MATH (JAVA APPLETS) - S. Bradlow, J. Sullivan, S. Levy & B. Klamik, Chickscope, Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana-Champaign VERY EXTENSIVE. Egg Math is "...a collection of web modules (including many interactive applets) covering different topics in mathematics related to eggs..." For more information see Chickscope or the Beckman Institute for Advanced Science and Technology Examples of EggMath Calculators & Simulations include The Shape of an Egg The White/Yolk Theorem Embryo Calculus

Encryption - Cryptography - Quantum Cryptography

Basic Encryption & Cryptography Cryptography Dictionaries & Glossaires Cryptography Courses, Lectures, Online Textbooks Quantum Cryptography Courses & Publications Cryptography Calculators & Applets - All Inclusive (Affine Cipher, ElGamal Cipher, Least Common Multiple, Prime Factorization, Viginère Enciphering, etc.) DES & ECP Cryptography Electronic Paper & Pencil Cryptography Enigma Encryption Machine ~ Monoalphabetic Encryption System Rectangular Transposition Encryption Reed-Solomon Encryption ~ RSA Encryption Shift Ciphers ~ Vingenere Encryption

Encryption - Cryptography - Quantum Cryptography BASIC ENCRYPTION CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS BASIC CRYPTOGRAPHY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS MODULAR ARITHMETIC - S. Addington, Department of Mathematics, California State University, San Bernardino (CSUSB) For more information see Susan Addington's Home Page Some examples Basic Encryption Calculators include A Clock (Modular) Arithmetic Calculator Encode and decode secret messages CRYPTOGRAPHY GLOSSARIES & DICTIONARIES CRYPTO AG'S CRYPTO & ENCRYPTION GLOSSARY - Crypto AG, Switzerland Multimedia Crypto & Encryption Glossary (Text & Images). For more information see Crypto AG RITTER'S CRYPTO GLOSSARY AND DICTIONARY OF TECHNICAL CRYPTOGRAPHY - T. Ritter Multimedia Crypto Glossary and Dictionary of Technical Cryptography (Text & Images). For more information see Ciphers By Ritter: Cryptography and Technology CRYPTOGRAPHY COURSES, LECTURES, TEXTBOOKS & TEACHING MODULES CRYPTOGRAPHY - Z. Grunschlag, Department of Computer Science, Columbia University Multimedia Cryptography Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Cryptography Lectures include: "...Classical Ciphers; Cryptanalysis of Classical Ciphers; Probability Theory and Randomized Algorithms; Perfect Secrecy; Block Ciphers; Message Authentication Codes and the Discrete Log Hash Function; Computational Number Theory; Probabilistic Encryption and Computational Security; Pseudorandom Generators; etc..." For more information see the Introduction to Cryptography (COMS W4261); Courses; Zeph Grunschlag's Home Page or the Department of Computer Science An example of Cryptography Software: Webcrypt: Cryptographically Enabled Web Browser CRYPTOGRAPHY - D. Wagner, Computer Science Division, University of California, Berkeley Multimedia Cryptography Course (Text & Images). VERY VERY VERY...EXTENSIVE. Cryptography "...Cryptography has been around for over two thousand years; one date commonly cited for the earliest cryptosystems is 500 BC. The Romans provide some good examples of early efforts to send secret messages, some of which were not cryptosystems as we conceive of them today. For example, they would shave a slave's head, write the message to be transmitted on the exposed skin, wait for the hair to grow back, and send the slave off to deliver the message..." Examples of Cryptography Lectures include: "...Basic motivating scenarios for cryptography; Shannon secrecy; Symmetric-key encryption algorithms; Trapdoor one-way permutations; Square roots modulo n are as hard as factoring; The Goldreich-Levin theorem; Pitfalls of the random oracle model; Zero knowledge proofs; etc..." For more information see the Teaching; David Wagner or the Computer Science Division CRYPTOGRAPHY: THE FOUNDATIONS OF CRYPTOGRAPHY - O. Goldreich, Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Israel Multimedia Foundations of Cryptography Textbook (Text & Images). VERY VERY VERY...EXTENSIVE. The Foundations of Cryptography "...are the paradigms, approaches and techniques used to conceptualize, define and provide solutions to natural Cryptographic problems..." Examples of Foundations of Cryptography Volume 2 Chapters include: "...Encryption Schemes; Digital Signatures and Message Authentication; General Cryptographic Protocols; etc..." For more information see the Oded Goldreich's Home Page or the Faculty of Mathematics and Computer Science INTRODUCTION TO MODERN CRYPTOGRAPHY - M. Bellare & P. Rogaway, Department of Computer Science and Engineering, University of California, San Diego (USCD) Multimedia Cryptography Course (Text & Images). VERY VERY VERY...EXTENSIVE. Modern Cryptography "...is a remarkable discipline. It is a cornerstone of computer and communications security, with end products that are imminently practical. Yet its study touches on branches of mathematics that may have been considered esoteric, and it brings together fields like number theory, computational-complexity theory, and probabiltity theory..." Cryptography Lectures include: "...Block ciphers; Pseudorandom functions; Symmetric encryption; Hash functions; Message authentication; Number-theoretic primitives; etc..." For more information see the Cryptography Course Home Page; Courses; Mihir Bellare's Home Page or the Department of Computer Science and Engineering MODERN CRYPTOLOGY - B. Cherowitzo, Department of Mathematics, University of Colorado, Denver, Colorado Multimedia Modern Cryptology Course (Text & Images). VERY VERY EXTENSIVE. Examples of Modern Cryptology Course Lectures include "...Redundancy and Information Theory; Data Encryption Standard (DES) & Advanced Encryption Standard (AES); The extended Euclidean Algorithm; The Solovay-Strassen Primality Test; The Chinese Remainder Theorem; Coding Theory; etc..." For more information see Modern Cryptology: Math 5410 Home Page; Teaching Activity; Bill Cherowitzo's Home Page or the Department of Mathematics CRYPTOGRAPHIC PRIMITIVES - Paul Garrett, School of Mathematics, University of Minnesota Multimedia Cryptographic Primitives Article (Text & Images). Cryptographic Primitives emphasizes "...algorithms related mostly to RSA, primality testing, and factoring attacks, as opposed to discrete logs and/or elliptic curves, and give only simple naive forms of protocol-ideas rather than refined forms..." For more information see Paul Garrett's Home Page or the School of Mathematics QUANTUM CRYPTOGRAPHY COURSES & PUBLICATIONS FOR QUANTUM COMPUTERS, QUITS, TELPORTATION, ETC. COURSES, DATABASES & CALCULATORS SEE QUANTUM COMPUTERS, QUITS, TELPORTATION QUANTUM CRYPTOGRAPHY - arXiv.org, Cornell University Library Multimedia Quantum Cryptography Publications (Text & Images). VERY VERY VERY...EXTENSIVE. For more information see arXiv.org QUANTUM CRYPTOGRAPHY (PDF) - Hoi-Kwong Lo & Yi Zhao, Center for Quantum Information and Quantum Control, Department of Physic sand Department of Electrical & Computer Engineering, Universityof Toronto, Toronto, Canada; arxiv.org/pdf/0803.2507, April 1, 2008 Multimedia Quantum Cryptography (Text & Images). VERY VERY VERY...EXTENSIVE. Quantum Cryptography "...is the synthesis of quantum mechanics with the art of code-making (cryptography)..." "...quantum cryptography is a branch of quantum information processing, which includes quantum computing, quantum measurements, and quantum teleportation. Among all branches, quantum cryptography is the branch that is closest to real-life applications. Therefore, it can be a concrete avenue for the demonstrations of concepts in quantum information processing..." Examples of Quantum Cryptography Chapters include "...Quantum Key Distribution: Motivation and Introduction; Security Proofs; Experimental Fundamentals; Experimental Implementation of BB84 Protocol; Other Quantum Key Distribution Protocols; Quantum Hacking; etc..." For more information see arXiv: Quantum Cryptography; arXiv.org or the Center for Quantum Information and Quantum Control QUANTUM CRYPTOGRAPHY ROADMAP (PDF) - R. Hughes & T. Heinrichs, Quantum Information Science and Technology Roadmapping Project, Los Alamos National Laboragory Multimedia Quantum Cryptography Lectures (Text & Images). VERY VERY EXTENSIVE. Examples of Quantum Cryptography Lectures include "...Weak Laser Pulses over Fiber Implementations for QKD and Quantum Cryptography; Single-Photon Light Source Implementations for QKD and Quantum Cryptography; Entangled-Photon Pair Implementations for QKD and Quantum Cryptography; Continuous Variable Implementations for QKD and Quantum Cryptography; etc..." For more information see Quantum Information Science and Technology Roadmapping Project or the Los Alamos National Laboragory QUANTUM INFORMATION NETWORKS - Quantum Information Networks, Advanced Network Technologies Division (ANTD), Information Technology Laboratory (ITL), National Institute of Standards and Technology (NIST) Multimedia Quantum Networks Publications (Text & Images). Quantum networks "...enable secure distribution of quantum crypto keys among multiple users in a commercial network infrastructure..." For more information see Advanced Network Technologies Division (ANTD) Information Technology Laboratory (ITL) or the National Institute of Standards and Technology (NIST)

CRYPTOGRAPHY CALCULATORS & APPLETS: ALL INCLUSIVE ENCRYPTION CALCULATORS & APPLETS: ALL INCLUSIVE ONLINE SAGE CALCULATOR & SAGE NOTEBOOK CALCULATOR - William Stein, Department of Mathematics, University of Mathematics VERY VERY VERY...EXTENSIVE. SAGE Calculator (Software for Algebra and Geometry Exploration) & SAGE Notebook Calculator are a "...studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra..." For more information see William Stein's Home Page or the Department of Mathematics CRYPTO TOOLS - D.J. Wright, Department of Mathematics, Oklahoma State University VERY VERY EXTENSIVE. For more information see Introduction to Cryptology; David J. Wright's Home or the Department of Mathematics Some examples from over "25" Cryptography Calculators include Encrypt and Decrypt Text by RSA Calculator Frequency Counts: Count Letter Frequencies in Text Calculator Affine Cipher Calculator Monoalphabetically Encode Text Calculator Encode and Decode Text by Viginère Method Calculator Crack a Viginère Cipher - Kasiski's Method Calculator CRYPTOGRAPHY (MATH 390) - T. Linton, Department of Mathematics & Computer Science, Central College, Pella, Iowa VERY VERY EXTENSIVE. Cryptography "...refers to writing, using various methods to keep the message a secret, as well as more modern applications (like web security, user authentication, etc.) of these methods. Cryptanalysis is the science of attacking secret messages or decrypting ciphers. The term cryptology encompasses both directions (making the codes and breaking the codes)..." For more information see Tom Linton's Home Page or the Department of Mathematics & Computer Science Some examples from over "12" Cryptography Calculators include Modular Multiplier Calculator Cryptogram Calculator Index of Coincidence Calculator Kasiski and Splitter Calculator CRYPTOGRAPHY AND NUMBER THEORY - F. Richman, Department of Mathematics, Florida Atlantic University VERY VERY EXTENSIVE. For more information see Fred Richman's Home Page Some examples from over "11" Cryptography Calculators include Shift Ciphers Calculator Viginère Enciphering Calculator Monographic Frequencies Calculator Primality Testing with Fermat's Little Theorem Calculator CRYPTOGRAPHY DEMOS - P. Hriljac, Embry-Riddle Aeronautical University VERY EXTENSIVE. For more information see Project; ERAU Prescott Campus or Embry-Riddle Aeronautical University Some examples from over "6" Cryptography Applets include Diffusion in SDES Simulation Applet Subkey Generation in SDES Simulation Applets CRYPTOGRAPHY LABORATORY (CECS 590) - Author: D. Williams & Hosted by the Computer Engineering & Computer Science Department, Speed Scientific School (College of Engineering and Applied Sciences), University of Louisville VERY VERY VERY...EXTENSIVE. Cryptography Calculators include: Least Common Multiple (LCM) Calculator; Greatest Common Divisor (GCD) Calculator; Prime Factorization Calculator; Multiplicative Inverse Calculator; Modular Arithmetic Calculator; Euclidean Algorithm Calculator; Prime Number Theorem Calculator; Discrete Logarithms Calculator; Affine Cipher Calculator; ElGamal Cipher Calculator; Hill Cipher Calculator; Railsplitter Cipher Calculator; RSA Cipher Calculator; Shift Cipher Calculator; Vigenere Cipher Calculator; One Time Pad Cipher Calculator; DES Cipher Calculator; Affine Analysis Calculator; Frequency Analysis Calculator; Cycle Decomposition Calculator; Primitive Roots Calculator; Fast Exponentiation Calculator; Roots mod P Calculator; Charmichael Lambda Function Calculator; Euler Criterion Calculator; Fermat Pseudoprimes Calculator; etc. For more information see Ahmed Desoky's Home Page or the Computer Engineering & Computer Science Department

DES & ECP CRYPTOGRAPHY CALCULATORS & APPLETS DES JAVA IMPLEMENTATION - Authors: E. Nurvitadhi & E. Khair; Ç.K. Koç, Information Security Lab, School of Electircal Engineering and Computer Science, Oregon State University VERY EXTENSIVE. DES Java Implementation "...In this project, we implemented the single DES with ECB mode as a Java applet..." "...The algorithm is based on the text book for this class, Introduction to Cryptography with Coding Theory, 1/e..." For more information see Class Projects - 2002; Data Security & Cryptography - ECE 575; Çetin Kaya Koç's Home Page or the Information Security Lab ELECTRONIC PAPER & PENCIL CRYPTOGRAPHY CALCULATORS & APPLETS CIPHERCLERK'S APPLET - W.M. Plotz, Austria VERY EXTENSIVE. CipherClerk's Applet "...is implementing a collection of historic ciphers. Most ciphers are 'paper & pencil' types, e.g. to use them you wouldn't need more than a sheet of paper and something to write...." For more information see Wilhelm M. Plotz's Home Page Examples of other Cipher Applets include Virtual U.S. Army Cipher Device, Model M-94 Major Bazeries Cipher Device ENIGMA ENCRYPTION MACHINE CALCULATORS & APPLETS THE ENIGMA MACHINE (JAVA APPLET) - R. Schwager VERY EXTENSIVE. The Enigma Machine Applet "...has several variable settings that affect the operation of the machine. The user must select three rotors from a set of rotors to be used in the machine. A rotor contains one-to-one mappings of all the letters. Some Enigma machines had more than 3 rotors which just added to the number of possible encryption combinations..." ENIGMA APPLET - A. Carlson VERY EXTENSIVE. The Enigma Applet "...simulates a WWII German Enigma encryption machine. You can use your computer keyboard to type, or use your mouse to click on the machine's keys..." For more information see About Enigma and Its Decryption MONOALPHABETIC ENCRYPTION SYSTEM CALCULATORS & APPLETS BREAKING A MONOALPHABETIC ENCRYPTION SYSTEM USING A KNOWN PLAINTEXT ATTACK (JAVA APPLET) - D.P. Little & A. M. Garsia, Department of Mathematics, Eberly College of Science, Pennsylvania State University VERY EXTENSIVE. Breaking a Monoalphabetic Encryption System using a Known Plaintext Attack "...A program that encrypts/decrypts/breaks Monoalphabetic Substitution encoded messages..." For more information see Cryptography; Java Index; David Little's Home Page or the Department of Mathematics RECTANGULAR TRANSPOSITION ENCRYPTION CALCULATORS & APPLETS BREAKING THE RECTANGULAR TRANSPOSITION ENCRYPTION SYSTEM (JAVA APPLET) - D.P. Little, M. Zabrocki & A.M. Garsia, Department of Mathematics, Eberly College of Science, Pennsylvania State University VERY EXTENSIVE. Breaking the Rectangular Transposition Encryption System "...A program that encrypts/decrypts/breaks Rectangular Transposition encoded messages..." For more information see Cryptography; Java Index; David Little's Home Page or the Department of Mathematics REED-SOLOMON ENCRYPTION CALCULATORS & APPLETS REED-SOLOMON DECODER APPLET - Computer Science, Division of Engineering and Applied Science, CALTECH VERY EXTENSIVE. For more information see Kai Chen's Home Page FINITE FIELD CALCULATOR AND REED-SOLOMON SIMULATOR (JAVA APPLET) - E. Soljanin, Mathematics of Communications, Mathematical Sciences Research Center, Lucent Technologies VERY EXTENSIVE. Finite Field Calculator "...allows arithmetic over extension fields of GF(2)..." Reed-Solomon Encoder/Decoder Calculator "...A codeword is generated based on a random information word. A random set of t errors is generated and added to the codeword..." For more information see Emina Soljanin's Home Page or the Mathematics of Communications Home Page RSA ENCRYPTION CALCULATORS & APPLETS FINDING THE RSA PUBLIC KEY (JAVA APPLET) - Andreas de Vries, Math It, Fachbereich Technische Betriebswirtschaft, Germany In English & German/Deutsch. VERY EXTENSIVE. Finding the RSA Public Key Simulation "...determines the RSA public key (e, n) depending on the given secret key (d, p, q)..." For more information see Math It Mathematical Applets or Math It RSA DEMO APPLET - R. Holowczak, Computer Information System, Zicklin School of Business, Baruch College, CUNY VERY EXTENSIVE. RSA Applet "...demonstrates the basics of RSA Public Key cryptography..." For more information see Electronic Commerce CIS 9444; Richard Holowczak's Home Page or Computer Information System SHIFT CIPHERS CALCULATORS & APPLETS SHIFT CIPHERS - J.J. Holt (University of Virginia) & J.W. Jones (Arizona State University) and hosted by the Department of Mathematical Sciences, Michigan Technological University; a W. H. Freeman and Company Production Shift Ciphters Calculator "...When implementing the shift cipher, each letter of the message is shifted a fixed distance down the alphabet..." For more information see Applications of Congruences; Number Theory or the Department of Mathematical Sciences VINGENERE ENCRYPTION CALCULATORS & APPLETS BREAKING THE VINGENERE ENCRYPTION SYSTEM (JAVA APPLET) - D.P. Little, M. Zabrocki & A.M. Garsia, Department of Mathematics, Eberly College of Science, Pennsylvania State University VERY EXTENSIVE. For more information see Cryptography; Java Index; David Little's Home Page or the Department of Mathematics VIGENERE CIPHER APPLET - Authors: C. Munsee & C. Lee; Ç.K. Koç, Information Security Lab, School of Electircal Engineering and Computer Science, Oregon State University VERY EXTENSIVE. The Vigenere Cipher Calculator "...is capable of encrypting and decrypting a message using the Vigenere algorithm as well as breaking or finding the key for a message encrypted using that algorithm..." For more information see Class Projects - 2002; Data Security & Cryptography - ECE 575; Çetin Kaya Koç's Home Page or the Information Security Lab

Ergodic Theory, Bers Slices, Riemann Surfaces, Teichmüller Theory, Teichmüller Space ERGODIC THEORY, RIEMANN SURFACES, TEICHMTÜLLER THEORY & TEICHMTÜLLER SPACE COURSES & SEMINARS ERGODIC THEORY - C.T. McMullen, Department of Mathematics, Faculty of Arts & Sciences, Havard University Multimedia Ergodic Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Advanced Ergodic Theory Chapters include: "...Ergodic Theory; Dynamics on Hyperbolic Surfaces; Orbit Counting, Equidistribution and Arithmetic; Spectral Theory; Mixing of Unitary Representations of SLn R; Amenability; The Laplacian; Kazhdan's Property T; Ergodic theory at infinity of hyperbolic manifolds; Lattices: Dimension 1, Dimension 2; Lattices, Norms and totally Real Fields; etc..." For more information see Math 275; C.T. McMullen's Home Page or the Department of Mathematics RIEMANN SURFACES, DYNAMICS, GEOMETRY & TEICHMTÜLLER THEORY - C.T. McMullen, Department of Mathematics, Faculty of Arts & Sciences, Havard University Multimedia Riemann Surfaces, Dynamics, Geometry & Teichmüller Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Riemann Surfaces, Dynamics, Geometry & Teichmüller Theory Course "...will concern the interaction between: hyperbolic geometry in dimensions 2 and 3; the dynamics of iterated rational maps; and the theory of Riemann surfaces and their deformations..." Riemann Surfaces, Dynamics, Geometry & Teichmüller Theory Chapters include: "...Geometric Function Theory; Teichmüller Theory; Dynamics of Rational Maps; Hyperbolic 3-Manifolds; Holomorphic Motions and Structural Stability; Iteration on Teichmüller Space; Geometrization of 3-Manifolds; etc..." For more information see Math 275; C.T. McMullen's Home Page or the Department of Mathematics TEICHMTÜLLER SPACE (CLASSICAL & QUANTUM) SEMINAR/WORKSHOP - Organised by Shigeyuki Morita, Athanase Papadopoulos & Robert C. Penner, Oberwolfach, Germany, 2006 Multimedia Teichmüller Space (Classical & Quantum) Seminar/Workshop (Text & Images). VERY VERY VERY...EXTENSIVE. For more information see David Dumas' Home Page or the Department of Mathematics CALCULATORS, APPLETS & SOFTWARE BEAR: BERS SLICES OF PUNCTURED TORI - D. Dumas, Department of Mathematics, Brown University VERY VERY VERY...EXTENSIVE. BEAR: BERS Slices of Punctured Tori Calculator "...is a mathematical research tool for calculating and testing discreteness of holonomy representations of complex projective structures on punctured tori. It can be used to draw pictures of Bers slices and explore the geometry of quasifuchsian space in the SL2(C) representation..." For more information see David Dumas' Home Page or the Department of Mathematics RANDOM CHORDS APPLET - D. Dumas, Department of Mathematics, Brown University VERY EXTENSIVE. Random Chords Applet "...demonstrates a result from the paper Distribution of intersection lengths of a random geodesic with a geodesic lamination by..." For more information see David Dumas' Home Page or the Department of Mathematics Fault Tolerant Computing FAULT TOLERANT COMPUTING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FAULT TOLERANT COMPUTING SIMULATOR (JAVA APPLETS) - I. Koren, Department of Electrical and Computer Engineering, College of Engineering, University of Massachusetts VERY VERY VERY...EXTENSIVE. Fault Tolerant Computing Subject Chapters include: "...Error Detection and Correction Codes; Fault Detection in Encryption Algorithms; Reliability Evaluation; Networks; etc..." For more information see Israel Koren's Home Page or the Department of Electrical and Computer Engineering Some examples from over "27" Fault Tolerant Computing Calculators & Applets include The Cyclic Code Simulator: Cyclic Encoder/Decoder Systematic and Standard Cyclic Codes Arithmetic Encoder/Decoder Applet Advanced Encryption Algorithm - Detection: Fault Detection in AES Encoder and Decoder Applet 4-state Markov Chain Solver Calculator Calculation of Terminal Reliability for Two Nodes in a Network Applet Checkpointing Calculators Checkpointing Calculators include Uniprocessor Checkpointing for Multiple Instructions Calculator; Domino Effect Animation for Distributed Checkpointing Calculator. Fibonacci Numbers FIBONACCI COURSES & TEACHING MODULES WITH CALCULATORS & SIMULATIONS FIBONACCI NUMBERS AND THE GOLDEN SECTION - R. Knott, and hosted by the Department of Mathematics of Surrey University, U.K. Multimedia Fibonacci Numbers Lectures & Teaching Modules (Text, Images, Calculators, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Examples of Fibonacci Numbers Lectures & Teaching Modules include Fibonacci Numbers and Nature; The Mathematical Magic of the Fibonacci numbers "...looks at the patterns in the Fibonacci numbers themselves: the Fibonacci numbers in Pascal's Triangle; using the Fibonacci series to generate all right-angled triangles with integers sides based on Pythagoras Theorem..." Two-dimensional Geometry and the Golden section or Fantastic Flat Facts about Phi; etc. For more information see Fibonacci Numbers and the Golden Section or Ron Knott's Home Page FIBONACCI CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FIBONACCI AND LUCUAS NUMBERS CALCULATORS & APPLETS FIBONACCI AND LUCUAS NUMBER CALCULATOR - R. Knott, and hosted by the Department of Mathematics of Surrey University, U.K. VERY VERY EXTENSIVE. "...For Fibonacci(i) and Lucas(i) you have a choice of Precision: exact or approximate. Exact: the calculator will find Fibonacci(i) and Lucas(i) for i into the thousands..." Approximate: Immediate result. The length of the answer decreases as i gets larger..." For more information see Fibonacci Numbers and the Golden Section or Ron Knott's Home Page FIBONACCI NUMBER SYSTEM CALCULATORS & APPLETS A FIBONACCI NUMBER SYSTEM - K.M. Levasseur, Department of Mathematical Sciences, University of Massachusetts Lowell VERY EXTENSIVE. Fibonacci Number System Calculator INPUT Values include: "...Enter a positive integer..." For more information see UMass Lowell WebMathematicaScripts; Kenneth M. Levasseur's Home Page; Department of Mathematical Sciences or HostSRV FIBONACCI SEQUENCES CALCULATORS & APPLETS FIBONACCI SEQUENCES WITH MULTIPRECISION JAVA - F. Richman, Department of Mathematics, Florida Atlantic University VERY EXTENSIVE. Fibonacci Sequences Calculator "...You can set the initial values, the number of terms in the sequence, and the number of decimal places in the ratios..." For more information see JavaScripts or Fred Richman's Home Page FIBONACCI SERIES CALCULATORS & APPLETS GENERALISING THE FIBONACCI SERIES - R. Knott, and hosted by the Department of Mathematics of Surrey University, U.K. VERY VERY EXTENSIVE. For more information see Fibonacci Numbers and the Golden Section or Ron Knott's Home Page Some examples of Fibonacci Calculators include General Fibonacci Series Calculator General Fibonacci Series Calculator "...is a simple calculator to show you some terms of a General Fibonacci Series..." Wythoff Array Calculator Stolarsky Array Calculator

Fourier

Fourier Analysis Courses & Lectures Fourier Transform & Fast Fourier Transform Discrete Fourier Transform ~ Fourier-Laplace Fourier Transform Experimentation: Image Processing Fourier Series ~ Fourier Synthesis

Fourier FOURIER ANALYSIS COURSES, LECTURES, TEXBOOKS, MANUALS, ETC. FOURIER AND COMPLEX ANALYSIS - R.L. Herman, Department of Mathematics and Statistics, College of Arts & Sciences, University of North Carolina, Wilmington, North Carolina Multimedia Fourier and Complex Analysis Course (Text & Images). VERY VERY VERY...EXTENSIVE. Fourier and Complex Analysis "...This is an introduction to topics in Fourier analysis and complex analysis. It is a course aimed at students majoring in mathematics and science who are at least at their junior level of mathematical maturity. Students are introduced to Fourier series, Fourier transforms, and a basic complex analysis..." Examples of "Fourier and Complex Analysis" Lectures include: "...Sequences and Series; Binomial Expansion; Function Series; Power Series; Fourier Series; Fourier Transforms; Signals Introduction; Discrete Fourier Transform; etc. For more information see Applied Analyical Methods; Russell L. Herman's Home Page or the Department of Mathematics and Statistics FOURIER ANALYSIS 1 - Christoph Thiele, Department of Mathematics, University of California, Los Angeles (UCLA) Multimedia Fourier Analysis 1 Lecture, PDF, 48 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Fourier Analysis 1" Lectures include "...Schwartz Functions; The Space S(Rn) as Frechet Space; The Fourier Transform; Tempered Distributions; Intermediate Banach Spaces, Regularity; The Poisson Summation Formula; Paley Wiener Theroems; Distributions versus Tempered Distributions; etc..." For more information see Lectures; Christoph Thiele's Home Page or the Department of Mathematics FOURIER ANALYSIS 2 - Christoph Thiele, Department of Mathematics, University of California, Los Angeles (UCLA) Multimedia Fourier Analysis 2 Lecture, PDF, 51 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Fourier Analysis 2" Lectures include "...The Haar Basis; The Calderon Zygmund Decomposition; The Littlewood Paley Square Function; Khintchine's Inequality; The Space BMO as Function Space; Maximal Truncated Singular Integrals; Paraproducts and a Discrete T1 Theorem; The Cotlar-Stein Lemma; etc..." For more information see Lectures; Christoph Thiele's Home Page or the Department of Mathematics FOURIER ANALYSIS: THEORY & APPLICATIONS - Richard Melrose, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Fourier Analysis: Theory and Applications Course (Text & Images). VERY VERY VERY...EXTENSIVE. Fourier Analysis: Theory and Applications "...Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals..." Examples of Fourier Analysis: Theory and Applications" Lectures include: "...Chebyshev's Inequality; Law of Large Numbers; The Integral; Fatou's Lemma; Bessel's Inequality: Convergence of Fourier Series; Riesz Representation Theorem; Fourier Transform; Hilbert-Schmidt Operators; etc..." For more information see Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare HARMONIC ANALYSIS - W. Schlag, Department of Mathematics, University of Chicago Multimedia Harmonic Analysis Textbook - PDF, 93 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Harmonic Analysis Textbook Chapters include "...Fourier Series: Convergence and Summability; Harmonic Functions on the Disk and Poisson Kernel; L1 bounded analytic functions and the F. & M. Riesz theorem; The Conjugate Harmonic Function; Calderon-Zygmund Theory of Singular Integrals; Almost Orthogonality; Schauder Estimates; LP -multipliers, Mikhlin theorem and Littlewood-Paley theory; Restriction of the Fourier transform, Stein-Tomas theorem, Strichartz estimates; The endpoint for the Stein-Tomas theorem and Strichartz estimates; Some pointwise questions for Fourier series: the case of L1 (T); etc..." For more information see the Wilhelm Schlag's Home Page or the Department of Mathematics FOURIER TRANSFORM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FOURIER CALCULATORS & APPLETS FOURIER TRANSFORMS CALCULATORS & APPLETS FFT ALGORITHM CALCULATORS & APPLETS FFT CALCULATORS & APPLETS FAST FOURIER TRANSFORM (FFT) FOR POLYNOMIAL MULTIPLICATION (JAVA APPLET) - Author: J. Beaver & Hosted by K. Pruhs, Department of Computer Science, University of Pittsburgh VERY VERY EXTENSIVE. Fast Fourier Transform for Polynomial Multiplication Calculator "...includes a description of the algorithm, a description of the Roots of Unity, a step feature which allows the user to see what is going on in the algorithm, and a multimedia section..." For more information see Applets; Applet Demonstration; CS 1501; Kirk Pruhs's Home Page or the Department of Computer Science FAST FOURIER TRANSFORM CALCULATOR - J. Clymer, Cincinnati, Ohio VERY EXTENSIVE. Fast Fourier Transform (FFT) Calculator "...performs Fourier Transforms, and DHTML to produce graphs of functions..." For more information see Jeffery Clymer's Home Page FAST FOURIER TRANSFORM (FFT) LABORATORY (JAVA APPLET) - D. Hale, Stanford Exploration Project (SEP), Stanford University For more information see Dave Hale's Home Page or the Stanford Exploration Project (SEP) FOURIER (JAVA APPLET) - R. E. Williamson & S. Schwarz, Dartmouth University VERY EXTENSIVE. Fourier Calculator "...Computes Fourier coefficients of a function,and plots the function and the Fourier approximation of degree at most 20..." For more information see Interactive Math Programs or the Department of Mathematics FOURIER TRANSFORMS (FT) OF A GIVEN POINTSET (JAVA APPLET) - S. Weber VERY EXTENSIVE. Fourier Transform on Periodic Point Sets Calculator "...calculates Fourier transforms (FT) of a given pointset. The pointset is generated by the plane space groups (see Project 22). You may transform all points..." For more information see Java Applets; Steffen Weber's Home Page or JCrystal FOURIER TRANSFORMS (FT) OF QUASIPERDIODIC POINT SETS (JAVA APPLET) - S. Weber VERY EXTENSIVE. For more information see Java Applets; Steffen Weber's Home Page or JCrystal DISCRETE FOURIER TRANSFORM CALCULATORS & APPLETS DISCRETE FOURIER TRANSFORM: FFT OF "BIT PATTERN" APPLET & FFT OF ARBITRARY FUNCTION APLET - Bert G. Wachsmuth, Department of Mathematics and Computer Science, Seton Hall University VERY VERY EXTENSIVE. Fast Fourier Transform of "Bit Pattern" Calculator "...illustrates what happens when trying to send bits representing a character (coded as the 8-bit ASCI code) though a wire that includes a "low-pass" filter, i.e. frequencies above a certain point are filtered out..." Fast Fourier Transform of Arbitrary Function Calculator "...lets you enter an arbitrary function and decompose it into its Fourier coefficients..." For more information see Java Applets; Bert G. Wachsmuth's Home Page or Department of Mathematics and Computer Science FOURIER-LAPLACE CALCULATORS & APPLETS FOURIER-LAPLACE CALCULATOR - Xiao Gang, Laboratoire J.-A. Dieudonné, Université de Nice, Nice, France VERY EXTENSIVE. Fourier Laplace Calculator "...computes the Fourier transform or Laplace transform of a function, and their inverse transforms..." For more information see WIMS FOURIER TRANSFORM EXPERIMENTATION CALCULATORS & APPLETS - IMAGE PROCESSING INTERACTIVE FOURIER TRANSFORM EXPERIMENTATION - IMAGE PROCESSING (JAVA APPLET) - R. Fisher, S. Perkins, A. Walker and E. Wolfart, School of Informatics, University of Edinburgh, Edinburgh, Scotland, U.K. VERY VERY EXTENSIVE. For more information see Interactive Experimentation; HIPR2: Hypertext Image Processing Reference; Robert Fisher's Home Page or the School of Informatics FOURIER SERIES CALCULATORS & APPLETS FOURIER SERIES (JAVA APPLET) - F. Embacher & P. Oberhuemer, Universität Wien, Austria Fourier Series Calculator: "...the user may choose the first 21 coefficients of a Fourier series by means of scroll bars and to look at the graph of the resulting function..." For more information see Applets or Maths Online FOURIER SERIES APPROXIMATION (JAVA APPLET) - Project Director: W.J. Rugh, Department of Electrical and Computer Engineering, Johns Hopkins University Fourier Series Calculator allows you to "...explore the Fourier series approximation, select a labeled signal, use the mouse to sketch one period of a signal, or use the mouse to modify a selected signal. Specify the number of harmonics, N, and..." For more information see the Signals, Systems & Controls or the Department of Electrical and Computer Engineering FOURIER SERIES CALCULATION FOR TYPICAL DIGITAL WAVEFORMS - EE Circle VERY EXTENSIVE. Fourier Series Calculator for Typical Digital Clock Waveforms "...Computes complex Fourier series coefficients (harmonics) of rectangular, triangular or trapezoidal shaped waveform & Plots both the time-domain waveform and the magnitude of the coefficients..." For more information see EE Applets or EE Circle FOURIER SERIES SIMULATION (JAVA APPLET) - P. Falstad VERY EXTENSIVE. Fourier Series Calculator "...is a method of expressing an arbitrary periodic function as a sum of cosine terms. In other words, Fourier series can be used to express a function in terms of the frequencies..." For more information see Math, Physics & Engineering Applets or Paul Falstad's Home Page FOURIER SYNTHESIS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FOURIER SYNTHESIS (JAVA APPLET) - Yves Moreau & J. Porque, Centre d'Electronique et de Micro-Optoélectronique de Montpellier, CNRS & the Universite des Sciences Montpellier, Montpellier, France VERY VERY EXTENSIVE. Available in English & French/Français. Fourier Synthesis Calculator "...choose a saturated cosine, a square signal, a rectified cosine or triangle signal (choose curve on top line). Vary the frequency, the amplitude and phase and play it...Then click on add comp to let the computer generate the first component (cosine) of the fourier expansion..." For more information see Group photonique (Photonics Group) or the Centre d'Electronique et de Micro-Optoélectronique de Montpellier FOURIER SYNTHESIS (JAVA APPLET) - M. Thole, Institut für Netzwerktheorie und Schaltungstechnik, Braunschweig, Bundesrepublik Deutschland (Germany) VERY EXTENSIVE. Fourier Synthesis Calculator "...A periodic signal can be described by a Fourier decomposition as a Fourier series, i. e. as a sum of sinusoidal and cosinusoidal oscillations..." For more information see Schaukasten FOURIERSYNTHESE (JAVA APPLET) - M. Thole, Institut für Netzwerktheorie und Schaltungstechnik, Braunschweig, Bundesrepublik Deutschland (Germany) VERY EXTENSIVE. Fourier Synthesis Calculator "...Ein periodisches Signal kann durch eine Fourierzerlegung mathematisch..." For more information see Schaukasten

Fractals ANATOMY OF MANDELBROT AND JULIA SETS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS "ANATOMY" OF THE MANDELBROT AND JULIA SETS (JAVA APPLETS) - E. Demidov, Department of Semiconductor Physics, Institute for Physics of Microstructures (IPM), Russian Academy of Sciences (RAS), Russia VERY VERY VERY....EXTENSIVE. Available in English & Russian. "...A virtual investigation with interactive pictures..." For more information see E-notes; Evgeny Demidov's Home Page or the Institute for Physics of Microstructures Some examples from over "40" Mandelbrot & Julia Sets Applets include Attractors: Tangent bifurcations Renormalization: "Inverse" quadratic-like maps Crises: Complex Crises Intermittency: Transition to chaos through intermittency Period doubling cascade: Reverse period doubling cascades Chaotic dynamics: Distance Estimator algorithm FRACTAL CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FRACTALS (JAVA APPLETS) - G. Booth VERY VERY VERY...EXTENSIVE. Fractals Applets are a "...series of simulators is for teaching Fractal Geometry..." For more information see CourseWare Simulations or Ginger Booth's Home Page Some examples from over "11" Fractal Calculators & Applets Fractal Music Composer Fractal Music Composer is "...a powerful music editor. Students build their own musical phrases out of notes from their choice of multiple keys and musical scales..." Box Dimension Box Dimension "...explores the idea of fractal dimension by counting boxes along geographical edges..." Fractal Iterative Dynamics Fractal Iterative Dynamics "...explores iterated function dynamics via 6 different analytic plots..." Fractal Statisics Fractal Statisics "...does R/S analysis and comparison to a normal distribution, on a time series, with or without difference processing on the input data..." PATTERNS IN NATURE (JAVA APPLET) - P. Trunfio & G. McGath, Center for Polymer Studies, Department of Physics, Boston University VERY EXTENSIVE. Patterns in Nature consists of "...a number of hands-on activities, laboratory experiments, and interactive visualization programs for which encourage students to explore how fundamentally random microscopic events can give rise to fractal macroscopic patterns..." For more information see Center for Polymer Studies or the Department of Physics Examples of Fractal Applets include Diffusion Limited Aggregation Applet (Aggregation: Growing Fractal Structures) Fractal Coastlines Applet The Anthill and Molecular Motion Applet DISCRETE FRACTALS CALCULATORS & APPLETS DISCRETE FRACTALS (JAVA APPLET) - V.B. Balayoghan, Department of Computer Science, University of Texas, Austin, Texas Dicrete Fractals include: "...An Interference Pattern of Binary Digits Applet (builds a fractal-like image using the patterns present in the binary representation of natural numbers, etc.); and A Discrete Fractal Based on Pascal's Triangle Applet..." For more information see A Motley Assemblage of Stuff - Java Applets; V.B. Balayoghan's Home Page or the Department of Computer Science FRACTAL MODELING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FRACTAL GALLERIES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FRACTALS: 3D STRANGE ATTRACTORS AND SIMILAR OBJECTS - T. Stilson, Center for Computer Research in Music and Acoustics, Stanford University VERY VERY EXTENSIVE. For more information see Tim Stilson's Welcome Page or the Center for Computer Research in Music and Acoustics JULIA SETS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS MANDELBROT SETS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS JULIA AND MANDELBROT SET GENERATION - D.E. Joyce, Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts VERY EXTENSIVE. For more information see Dave's Geometric Pix Gallery; David E. Joyce's Home Page or the Department of Mathematics and Computer Science Examples of Related Applets include Quilted Millefiori with parameters Kaleidoscope Newton Basin Generation MANDELBROT APPLET - P. Alfeld, Department of Mathematics, University of Utah VERY EXTENSIVE. For more information see Java Page or Peter Alfeld 's Home Page MANDELBROT EXPLORER - Panagiotis Christias, Department of Electrical and Computer Engineering, National Technical University of Athens (NTUA), Greece VERY EXTENSIVE. For more information see the National Technical University of Athens (NTUA) MANDELBROT AND JULIA SET EXPLORER - D.E. Joyce, Department of Mathematics and Computer Science, Clark University VERY EXTENSIVE. For more information see David E. Joyce's Home Page or the Department of Mathematics and Computer Science

Geometry

Basic Geometry & Trigonmetry Middle School - High School Geometry Courses & Teaching Modules with Calculators & Applets Euclid's Elements ~ Eculidean & Non-Eculidean Geometry Pythagorean & Pythagorean Triples Geometry Calculators & Applets All Inclusive Geometry Calculators & Applets by Various Categories Advanced Geometry (Differential Geometry, Geometry & Quantum Field Theory, etc.) Computational Geometry

Geometry MIDDLE SCHOOL - HIGH SCHOOL GEOMETRY & TRIGONMETRY TEACHING MODULES, CALCULATORS & APPLETS GEOMETRIC FORMULAS - Web page design, diagrams, and applets by S. Seastone, Ask Dr. Math, The Math Forum, Swarthmore College Multimedia Geometry Teaching Modules with Applets (Text & Images). VERY VERY VERY...EXTENSIVE. Geometric Teaching Modules & Formulas for Perimeter, Area, Volume, etc. includes Two-dimensional Figures "...also called a plane or planar figure, is a set of line segments or sides and curve segments or arcs, all lying in a single plane. The sides and arcs are called the edges of the figure. The edges are one-dimensional, but they lie in the plane, which is two-dimensional..." Three-dimensional Figures "...sometimes called a solid figure, is a set of plane regions and surface regions, all lying in three-dimensional space. These surface regions are called the faces of the figure. Each of them is two-dimensional. The arcs of curves that are the edges of the faces of the figure are called the edges of the figure..." Geometric Teaching Modules, Formulas & Applets include "...Triangles; Quadrilaterals; Regular Polygons; Circles; etc..." For more information see Formulas; Ask Dr. Math FAQ or The Math Forum GEOMETRY (JAVA APPLETS) - Asian Technology Conference in Mathematics (ATCM) VERY VERY VERY...EXTENSIVE. Geometry Applet Subject Categories include: "...Angles and Pararell Applets; Congruent Figures and Triangles Applets; Quadrilaterals and Conservation Applets; Similar Figures Applets; Circle Applets; Pythagorean Theorem Applets; etc..." For more information see Manipula Math With Java or Math Education and Technology Examples of Categories which include more than '90' Geometry Applets Angle and Parallel Lines Applets Congruent Figures and Triangles Applets Circle Applets GEOMETRY APPLETS - National Library of Virtual Manipulatives, Utah State University VERY EXTENSIVE. Available in English, French & Spanish. For more information see the National Library of Virtual Manipulatives TRIANGLE CALCULATORS (JAVA APPLETS) - Saltire Software, Beaverton, Oregon Triangle Calculators "...allow you to calculate a triangle based on the specified parameters..." For more information see Geometry Gallery or Saltire Software Some examples of Triangle Calculators include Triangle Given 3 Sides Calculator Triangle Given 2 Angles and the Included Side Calculator Derived Qantities Calculator TRIGONMETRY CALCULATORS & APPLETS (METRIC) - Wonga Beach Q.L.D. Australia VERY VERY EXTENSIVE. Trigonmetry Calculators include: "...Triangles Calculator; Circles Calculator; Angles Calculator..." Circles Calculator "...gives Horizontal Tank Volume Litres & Sphere Litres..." You can also "...input Horizontal Tank (cylinder) Length; Input Type of Liquid "...some examples from over 50 Liquids/Chemials: Acetone, Alcolol, Benzene, Caster Oil,Crude Oil, Gasoline, Heptane, Propane, Water, etc..." Output Values include Total Litres that the Horizontal Cylinder Tank will hold and the Weight. For more information see Blocklayer TRIGONMETRY CALCULATORS & APPLETS - Asian Technology Conference in Mathematics (ATCM) VERY VERY VERY...EXTENSIVE. Examples form over "24" Trigonmetry Calculators & Applets include: "...Sine Function Box; Tangent Function Box; Cosine Function Box; Graph of y=sin ax; The Law of Cosines; Law of Sines; etc..." For more information see Manipula Math With Java or Math Education and Technology GEOMETRY COURSES & TEACHING MODULES WITH CALCULATORS, APPLETS, ANIMATIONS SIMULATIONS GEOMETRY - Alexander Bogomolny Multimedia Teaching Modules with Calculators & Applets (Text & Images). VERY VERY VERY...EXTENSIVE. Geometry "...Geometry is a branch of mathematics that is concerned with the properties of configurations of geometric objects - points, (straight) lines, and circles being the most basic of these..." For more information see Interactive Mathematics Activities or Interactive Mathematics Miscellany and Puzzles Some examples from over "700" Geometry Calculators & Applets with Teaching Modules include Archimedes' Book of Lemmas Napoleon's Theorem The Butterfly Theorem Arbelos - the Shoemaker's Knife EUCLID'S ELEMENTS CALCULATORS, APPLETS, ANIMATIONS SIMULATIONS EUCLID'S ELEMENTS (JAVA APPLETS) - D.E. Joyce, Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts Euclids Elements Course (Text, Images, Applets & Simulations). VERY VERY VERY...EXTENSIVE. Euclid's Elements "...form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages..." For more information see the History of Mathematics; David E. Joyce's Personal Home Page; David Joyce's Home Page or the Department of Mathematics and Computer Science Some examples from the 13 Books with "100's" of Applets include Book I: The Fundamentals of Geometry: Theories of Triangles, Parallels, and Area Book VII: Foundations of Ratios and Proportions EUCLID'S ELEMENTS: TRANSLATION OF JOYCE'S "EUCLID'S ELEMENTS" INTO SPANISH & CATALAN (JAVA APPLETS) - JDL euclides.org & Development Network Services Presence with permission from D.E. Joyce, Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts Euclids Elements Course (Text, Images, Applets & Simulations). VERY VERY VERY...EXTENSIVE. For more information see the Joyce's Euclid's Elements EUCLID'S ELEMENTS OF GEOMETRY (JAVA APPLETS) - B. Casselman, Department of Mathematics, University of British Columbia, Vancouver, Canada Multimedia Euclid's Elements of Geometry Teaching Modules & Applets (Text & Images). VERY VERY VERY...EXTENSIVE. Euclid's Elements of Geometry includes "...The integrated text (Byrne, Joyce, and Heath) at UBC: Book I thru Book XIII; A local collection of proofs of Pythagoras' Theorem in Java; On Erhard Ratdolt, publisher of the 1482 edition of Euclid (the very first, based on the somewhat faulty medieval edition produced by Campanus); etc..." For more information see Bill Casselman's Home Page or the Department of Mathematics ECULIDEAN & NON-ECULIDEAN GEOMETRY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS GEOMETRY APPLETS & VRML - Department of Mathematics, National Tsing Hua University, Hsin-Chu, Taiwan In Chinese & English. VERY VERY VERY...EXTENSIVE. Includes over "600" Geometry Calculators & Applets. For more information see Department of Mathematics or the National Tsing Hua University PYTHAGOREAN CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PYTHAGOREAN TRIPLETS CALCULATORS & APPLETS GENERATING PYTHAGOREAN TRIPLES (JAVA APPLET) - N. Exner, Office for Mathematics, Science & Technology Education, University of Illinois, Urbana-Champaign Pythagorean Triples Calculator "...generates non-trivial Pythagorean Triples of increasing value.�It can be used to locate Pythagorean Triples of significant size..." For more information see MSTE Online Resources or the Office for Mathematics, Science & Technology Education PYTHAGOREAN EXPLORER (JAVA APPLET) - The Shodor Education Foundation, Inc. For more information see Interactive Activities or The Shodor Education Foundation, Inc. PYTHAGOREAN TRIPLETS CALCULATOR - H.B. Meyer, Faust-Gymnasium, Staufen, Bundesrepublik Deutschland (Germany) VERY EXTENSIVE. Available in English & German/Deutsch. Pythagorean Triplet Calculator "...consists of three natural numbers x, y and z with x2 + y2 = z2. PT's with greatest common divisor 1 ("TPT's") are of particular interest..." For more information see Hans-Bernhard Meyer's Home Page GEOMETRY CALCULATORS & APPLETS: ALL INCLUSIVE GEOMETRY USING CABRI JAVA APPLETS - Department of Mathematics, National Tsing Hua University, Hsin-Chu, Taiwan In English & Chinese. VERY VERY VERY...EXTENSIVE. Includes over "400" Geometry Applets in the Following Subject Categories "...Circle Applets; Parabola Applets; Epicycloids-Hypocycloids-Trochoids Applets; Constructions with the Compasses Alone Applets; Poncelet's Porisms Applets; Pole and Polar Applets; Coaxal Systems Applets; Steiner's Porisms Applets; Other Curves Applets; Conic Applets; Linkage Applets; Dissection Applets; Line Applets; Constructions Using Ruler Only Applets; Regular Pentagon Applets; Seven Circles Theorem Applets;, etc..." For more information see Cabrijava; Department of Mathematics or the National Tsing Hua University GEOMETRY CALCULATORS & APPLETS BY VARIOUS CATEGORIES CHEING-PLEIJEL APPLET - B. Cheng VERY EXTENSIVE. Available in English & Chinese. Cheing-Pliejel "...By definition, the Cheng-Pleijel point O is the point where the sum of the areas of the triangles O'AB, O'BC, O'CD, O'DA, are at a minimum for a given value of H. In particular, the cone formed by the apex O' and the base quadrangle ABCD is a minimal surface, or more precisely, a minimal surface with boundary constraint..." Cheing-Pliejel Applet allows you to "...experiment with different positions of A,B, C,D, and H, and observe how the position of O varies..." For more information see Ben Cheng's Home Page GEOMETRY DEMONSTRATIONS USING CINDERELLA (JAVA) - Cinderella, Jürgen Richter-Gebert & Ulrich Kortenkamp, Germany VERY VERY EXTENSIVE. "...The Interactive Geometry Software Cinderella..." For more information see Cinderella, The Interactive Geometry Software Some examples from over "30" Geometry Applets include Light going through a Lens Applet A Conchoid in Elliptic Geometry Applet GEOMETRY APPLETS - R. Blond, Edmonton, Alberta, Canada Some examples from over "10" Geometry Applets include Circle Geometry Applet (Inscribed & Central Angles) Circle Geometry Applet (Tangents & Radii) Slope Comparison Applet HYPERDIMENSION APPLETS - I. Yoshiaki, Japan VERY EXTENSIVE. Include over "20" HyperDimension Applets including "... HyperWorm Applet; HyperPlane Applet; HyperCube Applet; 4DHyperbola Applet; 4DTorus Applet; 5DCube Applet; etc..." For more information see Ishihama Yoshiaki's Home Page PYTHAGORA'S HEAVEN - J. Morey, Departments of Mathematics, University of British Columbia, Canada Pythagora's "...shows a geometrical proof of Pythagoras' Theorem..." For more information see Interactive Math or the Department of Mathematics THE NINE POINT CIRCLE - R.F. Rossa, Department of Computer Science & Mathematics, Arkansas State University For more information see Mathematics Topics: Calculators & Tutorials or the Department of Computer Science and Mathematics

Advanced Geometry

Advanced Geometry Courses & Lectures (Differential Geometry, Geometry & Quantum Field Theory, etc.) Non Specific Advanced Geometry Calculators & Applets High Performance Calculators for Advanced Geometry 3D Geometry Computer Aided Geometric Design Periodic Billiard Paths in Triangles Evaluation of Euler Sums Geometric Calculator ~ Hyperbolic Geometry ~ Spherical Geometry Computational Geometry

Advanced Geometry ADVANCED GEOMETRY COURSES Undergraduate DIFFERENTIAL GEOMETRY - Matt Visser, Gravity Group, Mathematics, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, New Zealand Multimedia Differential Geometry Notes - PDF - 224 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Differential Geometry Chapters & Subchapters include Chapter 2: Fundamentals "...Basis and sub-basis for a topology; Discrete and indiscrete topologies; Hausdorff and non-Hausdorff topologies; Elementary metric spaces; etc..." Chapter 3: Affine Connexions "...Parallel transport; Geodesics; Torsion; Basic Curvature Identities; Weitzenbock connexion; etc..." Chapter 6: Metric tensor "...Riemannian geometry; Finsler/pseudo-Finsler geometry; The Weyl tensor; etc..." Chapter 8: Lie derivatives "...Lie derivatives on covariant vectors; Lie derivatives on general tensors; etc..." For more information see Lecture Notes; Math 464: Differential Geometry; Teaching; Matt Visser's Home Page or the School of Mathematics, Statistics and Computer Science DIFFERENTIABLE MANIFOLDS (MATH 250A) - Hans Lindblad, Department of Mathematics, University of California, San Diego (UCSD) Multimedia Differentiable Manifolds Course - Differential Geometry Course (Text & Images). Differentiable Manifolds Course "...is roughly vector calculus on manifolds. An example of a manifold is a surface in space when you ignore the rigid structure of space. Many things in geometry and physics, such as Einstein's equations of general relativity, are best stated independent of a particular coordinate system. A manifold together with invariantly defined differential operators is the natural setting for many nonlinear equations of physics..." Example of Differentiable Manifolds Course Chapters include "...Differentiability; Inverse and implicit function theorem; Submanifolds of Euclidean space; Topological and smooth manifolds; Tangent space and bundle; Vector fields, existence for ODE, Lie bracket and derivative, Frobenius theorem; Tensors and differential forms; etc..." For more information see Hans Lindblad's Home Page or the Department of Mathematics RIEMANNIAN GEOMETRY (MATH 250B) - Hans Lindblad, Department of Mathematics, University of California, San Diego (UCSD) Multimedia Riemannian Geometry Course - Differential Geometry Course (Text & Images). Riemannian Geometry Course "...Riemannian geometry is designed to describe the universe of creatures who live on a curved surface and who are unaware of space outside and can only measure distances and areas on the surface. This lead to the modern notion of a manifold independent of a surrounding space..." Example of Riemannian Geometry Course Chapters include "...Curvature of curves, surfaces and submanifolds of Euclidean space; Riemannian metric on a manifold. Riemannian connection; Geodesics; Curvature, Sectional curvature; Bianchi identities; Jacobi fields; etc..." For more information see Hans Lindblad's Home Page or the Department of Mathematics GEOMETRY AND QUANTUM FIELD THEORY - P. Etingof, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Geometry and Quantum Field Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Geometry and Quantum Field Theory Course is "...a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams...." Examples of Geometry and Quantum Field Theory Lectures include "...Generalities on Quantum Field Theory; The Steepest Descent and Stationary Phase Formulas; Feynman Calculus; The Euler Characteristic of the Moduli Space of Curves; Matrix Integrals and Counting Planar Diagrams; Quantum Mechanics; Operator Approach to Quantum Mechanics; Quantum Mechanics for Fermions; etc..." For more information see Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics GEOMETRY OF MANIFOLDS - T. Mrowka, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Geometry of Manifolds Course (Text & Images). VERY VERY VERY...EXTENSIVE. Geometry of Manifolds Course is "...analyzes topics such as the differentiable manifolds and vector fields and forms. It also makes an introduction to Lie groups, the de Rham theorem, and Riemannian manifolds..." Examples of Geometry of Manifolds Lectures include "...Smooth Maps and the Notion of Equivalence; Vector Bundles and the Differential: New Vector Bundles from Old; Vector Bundles and the Differential: The Tangent Bundle; Sard's Theorem; Stratified Spaces; Smale's Sard Theorem; etc..." For more information see Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics Graduate TOPICS IN GEOMETRY - M. Gualtieri, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Topics in Geometry Course (Text & Images). VERY VERY VERY...EXTENSIVE. Topics in Geometry Course is "...an introductory (i.e. first year graduate students are welcome and expected) course in generalized geometry, with a special emphasis on Dirac geometry, as developed by Courant, Weinstein, and Severa, as well as generalized complex geometry, as introduced by Hitchin..." Examples of Topics in Geometry Lectures include "...Smooth manifolds, geometry of foliations, and symplectic structure; Comments on previous lecture, symplectic manifolds, and Poisson geometry; Spinors, the spin group, a bilinear pairing on spinors, and pure spinors; Dirac structures, and geometry of Lie groups; Integrability and spinors, and Lie bialgebroids and deformations; Generalized Kahler geometry, and Hodge theory on generalized Kahler manifolds; etc..." For more information see Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics ADVANCED GEOMETRY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ADVANCED GEOMETRIC CONFIGURATIONS (JAVA APPLETS) - Saltire Software, Beaverton, Oregon For more information see Geometry Gallery or Saltire Software Some examples from over "8" Advanced Geometric Applets include Area of the Triangle Formed by the Intersection of Common Tangents to 3 Circles Applet Quadrilateral Configuration Applet 4 Point Circle Applet CONVERTING TRIANGULATIONS TO QUADRANGULATION (JAVA APPLET) - Sam Sanjabi, Rachel Potvin, The Computational Geometry Lab, School of Computer Science, McGill University VERY VERY EXTENSIVE. Converting Triangulations to Quadrangulations Calculator: "...We obtain a variety of characterizations for when a triangulation admits a quadrangulation without the use of (or with a bounded number of) Steine r points. We also examine the effects of demanding that the Steiner points be added in the exterior of a triangulated simple polygon..." For more information see Projects; Teaching Activities or The Computational Geometry Lab DIHEDRAL ANGLE OF 2 PLANES (JAVA APPLET) - E.M.S. Hitzer Department of Mechanical Engineering, Faculty of Engineering, University of Fukui, Japan VERY EXTENSIVE. For the Dihedral Angle of 2 Planes Calculator "...type in the coordinates of three points each for plane 1 and plane 2 and the press the bar "Get angle!" You get the angle in degree, rad, the cosine and sine and the direction of the line of intersection of the plane, ..." For more information see Geometric Calculus; Eckhard M. S. Hitzer's Home Page or the Department of Mechanical Engineering HIGH PERFORMANCE CALCULATORS FOR GEOMETRY MAGMA COMPUTATIONAL ALGEBRA SYSTEM CALCULATOR - Computational Algebra Group, School of Mathematics & Statistics, University of Sydney VERY VERY VERY...EXTENSIVE. MAGMA Computational Algebra System Calculator is a "...High performance software for Algebra, Number Theory, and Geometry..."