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       Mapping the Landscape of Mathematics:


Method of Archimedes: MATHEMATICA, MATLAB & 3-D MODELSRenie Deposit #147
Supercurves: Superparabola and Superellipse Deposit #148
Waldman-Parquet Tilings Deposit #146
Radial and Spiral Tilings by Rhombus Substitution Deposit #144
GeoGebra Cycloid Family:  A Movie Deposit #145
Pi Day, March 14: A Day to Celebrate Mathematics Deposit #143
Aleph, Infinity, Cantor and Vasarely:  MATLAB Meets Art Deposit #141
Valentines: Beating, Sierpinski, Broken, Vasarely & Fading Hearts Deposit #142
Unique Cornu-Voderberg Tilings Deposit #140
Voderberg Tilings in Matlab Deposit #139
Tautochrone in MATHEMATICA  Renie Award Deposit #138
Lagrange Deposit #137
Cycloid in GeoGebra
Deposit #132      A Quintet of Classics in GeoGebra
Epicloid in GeoGebraDeposit #133
Hypocycloid in GeoGebraDeposit #134
Hypotrocoid in GeoGebraDeposit #135
Epitrocoid in GeoGebraDeposit #136
Fibonacci Spirals in Matlab: Mondrian  Renie Award Deposit #127
Laplace Transform, Voltage Circuits and other calculations Deposit #128
"Other" Fibonacci and Binet Spirals Deposit #129
Polynomial Spirals in Matlab
Deposit #125
Siluroid of de Judicibus
Deposit #124
The 'Compleat' Gamma Pulse: Yin-Yang Deposit #126
The Apple of My  i: Sinusoidal Curves Deposit #117

Volume of a Box Problem with Exponential Regression Deposit #120
Fractal Animation
Renie Award for 2013 Deposit #113
Curves in GeoGebra Deposit #112
On Plane Curves in the Complex Plane Deposit #121
Bhaskara Proof
Deposit #114
Hamilton Circuit: Dodecahedron
Deposit #115
Dodecahedron Deposit #118
Wooden Model of the Conic Sections
Renie Award for 2012 Deposit #111

Online Graphing Calculator Deposit #108
Olga Taussky-Todd Deposit #110
Devil's Curve Deposit #109
Double Devil - Electric Motor Curves Deposit #106
Mathematical Tourist Istanbul: Sundials, Coins and a Palimpsest Deposit #107
Mathematical Tourist Brahe and Kepler: Ven (Hven) and Prague Deposit #119
Feynman Diagrams and Mural Deposit #116

Flight to the Moon: An Early Fantasy Deposit #102
Cannonball Curves of Thomas Harriot Renie Award for 2011 Deposit #103
Bessel Functions Deposit #104
Dandelin Ellipse Deposit #99a
Dandelin Hyperbola Deposit #99b
Dandelin Parabola Deposit #99c
2-D and 3-D Animations: Tunnel Effect-Schrödinger Equation Deposit #101

Number Theory, Baseball and Fiction Deposit #95
Quasi-Spherical Orbitals Renie Award for 2010 Deposit #98
Definition of the Limit: An Epsilon-Delta Streaming Video Deposit #94
A History of Math Class visits the Huntington Library Deposit #93
Sum of an Infinite Series Deposit #96
Leibniz on the Derivative: Acta Eruditorum (1684)
L'Hospital: A Primer on Early Calculus Analyse (1696)
Bernoulli, Permutations & Combinations: Acta Conjectandi (1713)

Catenary with MATHEMATICA®Animation Renie Award for 2009 Deposit #84
The Gaussian Distribution Deposit #92
Polygonal Geometry: Penrose Tilings and Hinged Dissections Deposit #89
Comparison of Descent Times: Brachistochrone vs. Parabola Deposit #88
Circles: From The Nine Chapters to the 21st Century
Deposit #85
Curve Sketching:  Nodes and Singularities Deposit #86
Sea Shells as Mathematics GRAPHER Animation Deposit #83
Ogive - Ogee Curves Deposit #82
Infinite Series in the Calculus: The Harmonic Series - A Video Streaming Video Deposit #75
Brachistochrone:   MATHEMATICA® Animation Deposit #77
Pretzel as a Curve :  GRAPHER Animation Deposit #79
Skew Line on a Torus:   MAPLE Animation Deposit #78
The Conics and Stereographic Projection:  To Infinity and Beyond Power Point Deposit #76
Wankel Engine:  MATHEMATICA® Animation
Revised Deposit #53
The Semicubical or Neile's Parabola:  OCTAVE Animation Deposit #80
Contour Curve or Map: MATHEMATICA®Animation Renie Award for 2008
Renie Award List
Famous Problems button
Thought for the day

Vector Calculus Bridge Project JAVA #64
Renie Award 2007  -  A Trio of Contributors:
         Hamilton, Maxwell, Gibbs

 Wavelets #65 Introduction
         Wavelets Part II
#65 Matrix Equations
         Wavelets Applications Compression

AP Calculus Graphing Calculator
         AB Level
#52 A Review
         BC Level #56 A Review

Brachistochrone #58 Renie Award 2006
         Brachistochrone II Derivation and History
         Brachistochrone III Bernoulli's Figures
         Brachistochrone IV #60 Euler-Lagrange
         Brachistochrone V Model from Florence

Pursuit Family of Curves Deposit #59
Pursuit Java Applet Deposit #66

Interactive Trig Applet Deposit #55

Calculus: Area ~Solid of Rev. #37 Renie 2005

Calculus: Solid of Revolution #36 Renie 2005

Polar Animations Using Maplesoft®

Paraboloid Interactive Java 3D & Source Code

Chemistry:  pH  Acid/Base Deposit #28

Coriolis Acceleration Vector Physics

Research on Teaching
     the Calculus
Deposit #21

Twin Primes Deposit #19 Number Theory

Two Classics Deposit #17

Calculus Deposit #15

Steiner Roman Surfaces Deposit #11

Hippopede of Proclus Deposit #12

Derivative Deposit #9  

Graph of the Derivative Deposit #7

Torricelli's Trumpet
    or Gabriel's Horn


Polar Graphs  #73 POVRAY Code

Bombelli IHMT Anniversary Momento

Quartet of 2006 Interactive Applets JAVA
         Areas between Curves #67 For Calculus-Science
         Function Grapher #72 Graphs Any Function
         Radioactive Decay Curves #68 A Comparison
         Baravelle Spirals - Infinite Series #69 Patience!

Oblique Cone Deposit #63 in Spanish

Conchoid of Nicomedes MATHEMATICA® #61

Osculating Circles MATHEMATICA® Deposit #54

Geometric Series Video Deposit #44

Graph Theory PowerPoint Deposit #39

Sequence: Goodstein's Interactive Deposit #34

Curves in MATHEMATICA® Deposit #38

Cycloid Family Maplesoft® - Renie Award 2004

Möbius Strip Maplesoft Code and Java 3D

Sine/Cosine Applet  Deposit #26

Gibbs Phenomenon  Deposit #25

Logarithmic Spiral  Deposit #20

Unit Circle Deposit #18

Sphericons  Renie Award 2003


Cissoid of Diocles

      Sine Function Deposit #1

Lemniscate of Bernoulli  

Sierpinski's Triangles Deposit #2

Cycloid Deposit #5

Quadratrix of Hippias

Folium of Descartes One of a pair.

Calculus of the Folium One of a pair.

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   Baltimore '14

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    San Diego '13

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      Boston '12

New Orleans icon
   New Orleans '11

San Francisco icon
San Francisco '10


Tom Lehrer - New Math   Deposit #10 A Mathematician's Valentine Deposit #130
Cayley Table Quilts Deposit #48 Tour of Newton's England  # 74
More Quilts: A Sierpinski Curve #51 Pascal's Triangle Deposit #46
Menger's Sponge 3-d Analog of Sierpinski's Carpet Baseball
Image Compression Deposit #65 Bat Country: Baseball Tetrahedra Deposit #87
Visit to the Huntington Library Deposit #93 Fibonacci's Pisa Deposit #97
Cambridge Mathematics Deposit #43


The National Curve Bank is a resource for students of mathematics.  We strive to provide features - for example, animation and interaction - that a printed page cannot offer.  We also include geometrical, algebraic, and historical aspects of curves, the kinds of attributes that make the mathematics special and enrich classroom learning.

We welcome participation.  We encourage you to submit your best web animation as a "deposit" in the National Curve Bank.  Also, we welcome information about other outstanding sites that deal with the same subject.  We will provide links to your home site and thus give your work a wide audience.  Please see "Submit Your Curve" on the left for details.

Animation of Famous Curves

This site is maintained by
Shirley B. Gray and Stewart Venit
, Department of Mathematics
Russ Abbott, Department of Computer Science
California State University, Los Angeles.

[ Beta Release: July 4, 2001. National Release: July 4, 2002. ]

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