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Math Links

Non-Analytic Geometry | Linear Graphing | Triangles, Trigonometry, Vectors & Complex Plane |
Analytic Geometry | Calculus | Statistics | Fractals and Chaos | Math Miscellaneous | Unit Conversion

This page is mainly arranged in the typical curriculum order.

Special Mention

Math Awareness Month 2000
Follow the cornucopia of mathematics and its uses from 0-dimensions to 4-dimensions and hyperspace. The link is not directly to an applet. It is to the exciting and novel April 2000: Math Awareness Month interactive poster. The site has many deep links and unusual applets involving mathematics. Similarly, the current Math Awareness Month poster and prior ones may be see/downloaded also. They are generally attractive but not interactive. Highly recommended.
Joint Policy Board for Mathematics

Java Sites of Math Forum Library
The Math Form Internet Mathematics Library Resource (Types: Software: Web Interactive/Java) lists over 700 links to sites with java applets related to mathematics but with a huge range of content level and pedagogical usefulness. The Math Forum also hosts a library called Math Tools that can be searched by subject and a large variety of resource/applet types.
webmaster@mathforum.com


Non-Analytic Geometry

Density Lab
Why do some things float and others don't? Learn about mass, volume, and density.
Raman Pfaff

Theorem of Pythagoras
Fu-Kwun Hwang

Stereo Icosahedron
A 3-D stereo visualization of an icosahedron (using red/blue 3-D goggles) that is a JavaSketchpad applet arising from a Geometer's Sketchpad sketch.
Nick Jackiw

Les Cinq Polyèdres de Platon (The five Platonic solids)
Animation 3D des cinq polyèdres réguliers. Scroll up after it loads, select a solid, color, & view to see it rotate. Use red/blue 3D goggles to see the 3D stereoscopic effect. Tables and figures of Platonic solids properties are also provided.
Gérard Chevet

Hypercube
An explanation of the process of visualizing n-dimensional space that is a JavaSketchpad applet arising from a Geometer's Sketchpad sketch.
Nick Jackiw

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Linear Graphing

Points in the x-y Plane
Manipulate points and their coordinates in the x-y plane.
Ramon Pfaff

Distance Formula
Manipulate points and measure the distance between them using a ruler or with the distance formula.
Ramon Pfaff

Defining a Line With Two Points
Manipulate points. Compute the slope of the line between them, view the equations in slope-intercept and point-slope form.
Raman Pfaff

Slope-Intercept Form
Experiment with the slope and intercept of a line. See how the slope of a line is calculated.
Ramon Pfaff

Point-Slope Form
Experiment with a line in point-slope form. See the relationship to slope-intercept form.
Raman Pfaff

Reflections of a Linear Function
Explore and compare the graphs of y = f(x), y = -f(x), y = f(-x), and y = -f(-x) for linear functions in slope-intercept form.
Raman Pfaff

Absolute Value of a Linear Function
Explore and compare the graphs of y = f(x), y = |f(x))| and y = f(|x|) for linear functions in slope-intercept form, f(x) = mx + b.
Ramon Pfaff

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Triangles, Trigonometry, Vectors & Complex Plane

Triangle Centroid
In this construction of triangle medians and centroid, drag the vertices of the triangle to alter it. This is a standard interactive that come from a Geometer's Sketchpad sketch.
Nick Jackiw

9 Point Circle
In any triangle, one can locate a circle which passes through the midpoints of that triangle's edges, the midpoints of its perpendicular segments, and the feet of a given triangle's perpendiculars. In this sketch, drag the vertices of the triangle to alter it. Another geometric gem that come from a Geometer's Sketchpad sketch.
Nick Jackiw

Points in The x-y Plane
Manipulate points and their coordinates in the x-y plane.
Ramon Pfaff

Points in Polar Coordinates
Manipulate points and their coordinates in the polar plane.
Ramon Pfaff

Unit Circle
Explore the relationship between the unit circle and the graphs of the sine, cosine, and tangent functions.
Ramon Pfaff

Sine Waver
Sine-wave animations via JavaSketchpad applets that come from familiar Geometer's Sketchpad sketches of points moving on a circle
Nick Jackiw

Shifting and Scaling Sine and Cosine Curves
Experiment with the graphs of trigonometric functions of the form y = a sin [b (x - c)] + d. Relate the equation and graph to amplitude, period, and frequency.
Ramon Pfaff

IES Menu of Trig Applets
IES's Manipula Math - Trigonometry menu of over 20 applets has nice icons.
IES, Inc.

Vector Addition
Basic graphical look at vector addition. Lets you see the "head" to "tail" addition.
Raman Pfaff

Vector Addition
It has a section for displaying 3-dimensional vectors.
Fu-Kwun Hwang

Vector Addition
Surendranath Reddy. B.

Vector Composition
This Macromedia Shockwave is an adding machine for vectors. The vectors to be added can be adjusted by clicking and dragging. The applet displays the polar and rectangular coordinates for the two vectors to be added and for their resultant. The head to tail vector addition principle can be verified graphically.
Pascal Renault

Vector Product
David McNamara, Alan Middleton, and Eric Schiff

Points in the Complex Plane
Experiment with graphical representation of complex numbers in the form z = a + bi. Visualize the conjugate if a complex number.
Ramon Pfaff

Complex Absolute Value
Manipulate a complex number, z, and examine its absolute value, |z|. Use a ruler and the Pythagorean theorem to determine |z|.
Raman Pfaff

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Analytic Geometry

2 X 2 Linear Systems
Define a 2 x 2 linear system and view the corresponding lines and their intersection. Examine the value of the determinant. View the equations in slope-intercept form.
Raman Pfaff

Linear Inequalities
Manipulate and visualize the solution sets of linear inequalities in slope-intercept form.
Raman Pfaff

Systems of Linear Inequalities in Slope-Intercept
Experiment with and visualize solution sets for a system of up to six linear inequalities in slope-intercept form.
Ramon Pfaff

Systems of Linear Inequalities in Standard Form
Experiment with and visualize solution sets for a system of up to six linear inequalities in standard form.
Ramon Pfaff

Linear Programming
Experiment graphically with the value of linear functions of the form f(x,y) = ax + by + c subject to linear constraints on x and y.
Ramon Pfaff

Quadratics: Polynomial Form
Experiment with the graph of a quadratic of the form y = ax2 + bx + c. Calculate the location of the vertex and y-intercepts. Trace the motion of the vertex as a,b, and c are changed.
Ramon Pfaff

Quadratics: Vertex Form
Experiment with the graph of a quadratic of the form y = a(x - h)2 + k. Calculate the location of the vertex and y-intercepts. View the function in polynomial form.
Ramon Pfaff

Quadratics: Polynomial Form in y
Experiment with the graph of a quadratic of the form x = ay2 + by + c. Calculate the location of the vertex and y-intercepts.
Ramon Pfaff

Reflections of a Quadratic Function
Explore and compare the graphs of y = f(x), y = -f(x), y = f(-x), and y = -f(-x) for quadratic functions of the form f(x) = ax2 + bx + c.
Ramon Pfaff

Absolute Value of a Quadratic Function
Explore and compare the graphs of y = f(x), y = |f(x))| and y= f(|x|) for quadratic functions of the form f(x) = ax2 + bx + c.
Ramon Pfaff

4th Degree Polynomial
Experiment with the coefficients of a fourth degree polynomial and their effect on the graph of the function.
Ramon Pfaff

Parabola
Experiment with parabolas from a conic-sections perspective in standard form by manipulating the focus, directrix, and vertex. Visualize the string property.
Ramon Pfaff

Parabola With Horizontal Directrix
Experiment with parabolas from a conic-sections perspective in standard form by manipulating the focus, directrix, and vertex. Visualize the string property.
Ramon Pfaff

Ellipse
Experiment with an ellipse in standard form. Manipulate vertices and foci, show their Pythagorean relationship, and visualize the string property.
Ramon Pfaff

Hyperbola
Experiment with a hyperbola in standard form. View asymptotes, manipulate vertices and foci, and visualize the string property.
Ramon Pfaff

Conic Sections
Perpendicular bisector envelope definition of the conics that is a Java Sketchpad applet arising from a Geometer's Sketchpad sketch.
Nick Jackiw

Coniques
Ellipses, Paraboles, Hyperboles: Illustrations graphiques des propriétés métriques des coniques It is large and thus slow to load. Scroll down after it loads, select a construction, and click 'Compile - Execute'.
Gérard Chevet

Quadratic Inequalities
Manipulate and visualize the solution sets of quadratic inequalities in polynomial form.
Ramon Pfaff

System of Two Quadratic Inequalities
Experiment with the graphical solution of a system of two quadratic inequalities in polynomial form.
Ramon Pfaff

Courbes en Coordonnées Polaires
Lieux géométriques: Rose de Troie, Strophoïdes, Lemniscate de Bernoulli, Cardioïde, Arcs de Samothrace, Spirales, & Coniques It is large and thus slow to load. Scroll down after it loads, select a construction, and click 'Compile - Execute'.
Gérard Chevet

Courbes Parametrees
Lieux géométriques: Astroïdes, Cycloïdes, Strophoïdes, & Hyperbole de Kiepert It is large and thus slow to load. Scroll down after it loads, select a construction, and click 'Compile - Execute'.
Gérard Chevet

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Calculus

Graphics for the Calculus Classroom
This is not a direct applet link. It is a site link to 11 modules which can be used in the study or teaching of calculus: differentials and differences, computing the volume of water in a tipped glass, Archimedes' calculation of pi, how a ball bounces, secants and tangents, zooming in on a tangent line, a trigonometric limit, limits, a nowhere differentiable function, the number e, and the computation of the volume of the region formed by two intersecting cylinders.
Douglas N. Arnold

Visual Calculus
This is not a direct applet link. It is a site link to a large collection of modules which can be used in the study or teaching of calculus. Originally, this collection was designed for instructors to give some ideas how technology, in particular, computers, can be used in the teaching of calculus. Detailed instructions on implementing these ideas with various public domain, shareware and commercial software packages are provided. The collection has been expanded to include tutorials, interactive modules (MathView, Java, and Javascript) which can be used by either students or faculty and now includes detailed instruction for TI-85 and TI-86 graphing calculators. As an additional aid for students, modules containing quizzes and drill problems have also been added.
Larry Husch

Exponential Functions
Experiment with and visualize functions of the form y = Makx. Visually approximate doubling/halving intervals.
Raman Pfaff

Logarithms
Experiment with logarithms by changing the base. View the corresponding exponential function as a reflection across the line y = x.
Raman Pfaff

Write and Plot a Function
Sergey Kiselev and Tanya Yanovsky-Kiselevib

One-D Motion
Fu-Kwun Hwang

Projectile Motion
Fu-Kwun Hwang

Interesting Properties of Projectile Motion
Fu-Kwun Hwang

Racing Balls
Fu-Kwun Hwang

Two-Dimensional Harmonic Motion
In this activity a mass is attached to 4 springs in the x-y plane. Both the x- and y-directions can experience a driving force.
Raman Pfaff

Lissajous Figures
Is it possible to make a figure 8 with electrical signals? Adjust the frequency, amplitude, and phase shift of the x- and y- inputs to an oscilloscope and create varied patterns.
Raman Pfaff

Numerical Integration
See the result of choosing from among five different numerical schemes for integrating experimental data you enter. Visit in the Numerical Integration Lab to learn the mathematical ideas behind modeling functions that produce experimental data.
The Geometry Center Calculus Development Team

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Fractals and Chaos

The Chaos Game
Yes, this is a game. Try to beat the computer by hitting specific targets via the moves of an iterated function system. This game allows students to understand the construction of the Sierpinski triangle via the chaos game.
Robert L. Devaney

Fractalina
This applet allows you to set up the vertices, compression ratios, and rotations associated to an iterated function system, then compute, and view the resulting fractal. If you have black and white monitors, be sure that you choose the appropriate colors for the points from the Color Selection button inside the applet so that you will be able to see the picture!
Robert L. Devaney

Fractanimate
This applet allows you to string together a collection of fractal images generated by Fractalina into a movie. We encourage you to become quite familiar with Fractalina before trying to use this applet.
Robert L. Devaney

Linear Web
This applet allows you to see the results of iteration of linear functions of the form Ax + B in three different ways: as a list of the orbit, as a web diagram (graphical iteration), and as a time series graph.
Robert L. Devaney

Nonlinear Web
This applet allows you to see the results of iteration of nonlinear functions such as the quadratic function x2 + c, the logistic function kx(1 - x), and many others. You can iterate step-by-step or view the entire web diagram.
Robert L. Devaney

Target Practice
This applet allows you to practice graphical iteration in the setting of a game. We give you a target (a particular "itinerary"); your job is to find an orbit graphically that has this itinerary.
Robert L. Devaney

Cycle Practice
This applet is a more advanced version of Target Practice. Your job in this game is to find a cycle (not just an orbit) with a given itinerary. Be sure to master Target Practice first before attempting this game.
Robert L. Devaney

Orbit Diagram
This applet allows you to draw the orbit diagram (or bifurcation diagram) for a variety of families of functions. You may also magnify various portions of these complicated sets.
Robert L. Devaney

Attracteurs D'une Famille de Contractions
Un choix de 512 combinaisons de contractions du plan. On obtient entre autres, parmi tous ces attracteurs, le fameux raban de Sierpinski.
Gérard Chevet

One-Dimensional Iteration of the Quadratic Map
Click on any point in the graph window and see the graphical iterates of that x value by the quadratic parameterized curve x2+c. The scrollbar changes c.
Evelyn Sander

The Infinite Fractal Loop
This is the home page of a web ring dedicated to fractal art. To begin browsing fractal galleries in the Loop, click either of the large arrow buttons at the bottom of the page. (A web ring is essentially a list of sites on the web, tied together with simple navigation tools that allow the user to move through the sites in sequence. By repeatedly moving to the next site in the ring, the user can see all sites and eventually return to their starting location.)
Damien M. Jones

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Statistics

Buffon's Needle Monte Carlo Simulation
A simulation of Buffon's Needle, the famous Monte Carlo method for the estimation of pi.
Michael J. Hurben

Real-Time Histogram
This module lets you gather data while clicking your mouse, and creates a histogram while you are clicking. You can then change the bin size, maximum y-value, and you can even edit the data.
Raman Pfaff

Least Squares Fit Line
Manipulate points and fit a line by hand. Visualize the meaning of "least squares" and compute the least squares fit line for your data.
Ramon Pfaff

Least Squares
An interactive exploration of the "least squares" statistical metric that is a JavaSketchpad applet arising from a Geometer's Sketchpad sketch.
Nick Jackiw

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Math Miscellaneous

The Pi Pages
This is not a direct applet link but is a site link. The story here with many links and including some java applets is definitely not pie in the sky.
J. Borwein

Snowflake Designer
Folding a piece of paper and pulling out the scissors is always fun near the holidays. If you want to 'design' your snowflake before slicing the paper, start here!
Raman Pfaff

Snow Flake '6-Sides' Designer
Folding a piece of paper and pulling out the scissors is always fun near the holidays. If you want to 'design' your snowflake before slicing the paper, start here! This version lets you make a six-sided flake, which is how snow flakes form in the actual world.
Ramon Pfaff

Snow Flake '6-Sides' Designer - w/ Copy Feature!
A new and improved version of the previous 6-Sided Snowflake. It has square scissors and a copy feature. Requires Shockwave Plug-in 7 or greater. (The rest of the site only requires version 6.)
Ramon Pfaff

Kaleidoscope
Move the mouse into the figure and watch the changes in 6 small, a medium, or large regular polygon.
David E. Joyce

Vasarely Bubble
A complex construction that was inspired by the works of Victor Vasarely (1908-1997), one of the founders of the Op Art movement. You can make the Vasarely bubble "breathe", or explode, by dragging a single point in a JavaSketchpad applet that comes from a Geometer's Sketchpad sketch.
Nick Jackiw

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Unit Conversion

Google
The Google search window can be used to do calculations and unit conversions. Also, search with Google using the three words "Google", "unit" and "conversion" for much more than is listed below.
Google.com, Inc.

Conversion Factors
Here is a database of conversion factors and a calculator.
Freie Universität Berlin · Institut für Chemie und Biochemie

Martendale's Calculators
An extensive collection of calculators for the sciences, business and everyday measurements. Organized by subject area.
Jim Martindale

Unit Conversions
Select the type of quantity you need to convert from the drop down menu. Type the amount to be converted, including significant final zeroes, in the "Quantity" box, then select its unit from the "Unit" drop down menu. The calculation is made whenever you select the new unit from the drop down menu. The results are shown in a lower panel. They include the conversion factor used in the calculation, an illustration of the procedure followed in the calculation and the result. You may convert a new quantity of the same type by changing the relevant information. When the new unit is not changed, you need to press the "Calculate" button to perform the calculation. You may select a new quantity type by using the "Select Quantity" drop down menu. For temperature conversions the procedure is the same, but the utility shows only the result of the calculation.
Taha Mzoughi

Non-Analytic Geometry | Linear Graphing Triangles, Trigonometry, Vectors & Complex Plane |
Analytic Geometry | Calculus | Statistics | Fractals and Chaos | Math Miscellaneous | Unit Conversion

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