National Curve Bank: A Math Archive

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Shaw Prize

NSF Poster Sessions

2003 - 2014

Math on the Web

Mapping the Landscape of Mathematics:

*Newest*
Sums of Infinite Series ~Logistic Model~^{Deposit #169} Sums of Infinite Series ~DDS~^{Deposit #168} The Möbius Strip^{Deposit #31 - Update} Sierpinski Triangle^{Deposit #2 - Update} Parabolicon: A Sphericon-Oloid Relative ^{Deposit #167} A Simulation of Pursuit Curves ^{Deposit #66 - Update} Goodstein's Sequence ^{Deposit #34 - Update} Sums of Infinite Series ~ Baravelle Spirals ^{Deposit #69 - Update} Radioactive Curves and Calculations^{Deposit #68 - Update} Function Grapher including Rational Function Option^{Deposit #108 - Update} Agnesi on her 300th Birthday Celebration^{Deposit 05/16/2018} Cœur de Cye or Waldman's Heart^Deposit #166Tricurves and Tessellations^Deposit #164 Vector Fields^{Deposit #64 - JavaScript Update} Fractal^{JavaScript Update} 2017 Gnomon is an Island^{Deposit #161}Brave New Whorled^{Deposit #162}The Incomplete Gamma Function for Log-Aesthetic Curves^{Deposit #122}A Collection of Calculus Animations^{Deposit #160} Fractals Reimagined: Original Variations on Mandelbrot and Julia Sets^{Deposit #158} Superconics: Hypergeometric Functions^{Renie 2017: Deposit #149}Superconics: Hypergeometric Spirals - From Euler to 2017^{Deposit #163} 2016 Volume of an Open Box: A Tribute to Jaime Escalante^{Deposit #154}Sphericon: Animation and Construction^{Renie 2016: Deposit #150} Möbius Animations^{Deposit #151}Gnomons Land^{Deposit #152}Fibonacci Spiral Reimagined^{Deposit #155}Animated Fractals^{Deposit #157} 2015 Method of Archimedes: MATHEMATICA, MATLAB & 3-D MODELS^Renie^{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} 2014 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 GeoGebra^{Deposit #133}Hypocycloid in GeoGebra^{Deposit #134}Hypotrocoid in GeoGebra^{Deposit #135}Epitrocoid in GeoGebra^{Deposit #136} 2013 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} 2012 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 2011 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} 2010 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} Mittag-Leffler Institute^{Deposit #100} 2009 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) 2008 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 2007 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}

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 in JavaScript ^{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 in JavaScript ^Deposit
#26
Gibbs Phenomenon ^{Deposit #25}
Logarithmic Spiral ^{Deposit #20}
Unit Circle ^{Deposit #18}

Sphericons ^{Renie Award 2003}

Cissoid of Diocles

Trigonometry:
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.}

San Deigo thumb

Baltimore '14

San Deigo thumb

San Diego '13

Boston '12

New Orleans icon

New Orleans '11

San Francisco icon

San Francisco '10

*Enrichment*
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}

Welcome!

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 Jonathan Sahagun, Department of Mathematics
California State University, Los Angeles.

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