Mandelbrot Set on Geometer's Sketchpad

Computer Resources
for Secondary Mathematics

Law of Cosines
The resources below come with the following caveats:
  • WWW linkThe Web Sites are maintained by various people, organizations, and corporations, who are solely responsible for the material located there. If a link doesn't work or you find inappropriate material there, please let me know.
  • Excel spreadsheetSpreadsheets are generally written for Microsoft Excel 97, and should work in more recent versions of Excel or other spreadsheet programs that can import Excel workbooks. I tried to note exceptions, but if I missed something, please let me know.
  • Sketchpad fileSketchpad files require the Geometer's Sketchpad from Key Curriculum Press. These files come in formats for version 3.0 and version 4.0. In general, they are not compatible across versions.
  • Sketchpad fileSome browsers will try to open Sketchpad (.gsp) files as text rather than sketches. If this happens, change your browser preferences or right-click on the file and save it to your machine.
  • This is perpetually a work in progress. If you think I have something that's not listed here, you're probably right. Contact me.

Functions and Graphs

Graphs a function with sliders for parameters using Sketchpad. GSP 3.0: anygraph.gsp GSP 4.0: any_graph.gsp
Transformations of functions -- translations and scale changes. transformations.xls [by Nils Ahbel]
Inverse functions -- a visual demonstration of the reflection over y = x. inverse.xls [by Nils Ahbel]
Parametric equations with Sketchpad. GSP 3.0: parametr.gsp GSP 4.0: parametric.gsp


Linear Functions

Exploring with slope-intercept and point-slope forms of a line. linear_equations.xls
The accompanying worksheet. linear_equations.doc
Exploring lines, changing slopes and intercepts. GSP 3.0: ymxb0.gsp GSP 4.0: lines.gsp


Quadratic Functions

Exploring vertex form of a parabola. parabolas_vertex_form.xls
The accompanying worksheet. parabolas_vertex_form.doc
A parabola by folding paper (based on focus and directrix definition). GSP 3.0: parafold.gsp GSP 4.0: paper_folding_conics.gsp Also includes ellipses and hyperbolas. Do you know how to incorporate the foci definition of a hyperbola into this sketch? Let me know.


Exponential Functions

Comparing linear growth to exponential growth. linear_vs_exponential.xls
The accompanying worksheet. linear_vs_exponential.doc

Sequences and Series

Exploring Arithmetic Sequences. arithmetic_series.xls [by Nils Ahbel]
Exploring Geometric Sequences. geometric_series.xls [by Nils Ahbel]


Archimedes' estimation of circular area by doubling the number of sides of a polygon. circle_area.xls
All those lovely theorems about chords, tangents, and secants in circles. GSP 3.0: circ_seg.gsp GSP 4.0: circles_and_segments.gsp
The trisectrix of Hippias, in all its glory. GSP 3.0: trisecx3.gsp GSP 4.0: trisectrix_hippias.gsp


How long to pay off that credit card? credit_card.xls
How much will you have to retire on? retire.xls
What mortgage option is best for you? mortgage_options.xls


The Law of Sines, visually GSP 3.0: lawsines.gsp GSP 4.0: law_sines.gsp
Generating a Sine Wave from a Unit Circle: Sketchpad. GSP 3.0: sinwave2.gsp GSP 4.0: sine_wave2.gsp
Add in the cosine and tangent functions. GSP 3.0: sincosta.gsp GSP 4.0: sine_cosine_tangent.gsp
Generating a Sine Wave from a Unit Circle: Spreadsheet. circle_trig.xls
A piano keyboard generating sine waves piano.xls [by Nils Ahbel]
Four parameters on a sine wave. GSP 3.0: asinbxcd.gsp GSP 4.0: a_sin_bx_c_d.gsp
Using a sine wave to fit a model to data (the average temperature in Cleveland). trig_modeling_cleveland.xls

Probability & Statistics

Explore R-squared by moving data points. R-squared.xls
Explore binomial probability. binprob.xls (by Nils Ahbel)

Data Sources

Fedstats, with data from the Census Bureau and other government agencies.
The Information Please Almanac online.
The classic distance calculator: How Far Is It?


Trace along a graph and watch the tangent line, derivative, and area between the curve and the x-axis. GSP 3.0: derivatv.gsp GSP 4.0: tangent_line_and_area.gsp
Calculus In Motion (by Audrey Weeks) -- lots of Geometer's Sketchpad demonstrations specifically for calculus.

Homework Help

The Math Forum's fabulous helpers: Ask Dr. Math. Also has a great archive.
Math Nerds provides "free, discovery-based, mathematical guidance" ... ask them a question, or search the Archive.
Online solutions to many questions from quite a few textbooks! Pretty cool, no?

Calculator Help

TI Resources (homework help, programs to download, FAQ's, and more resources)

F u n     P r o b l e m s

William Wu's Riddles Page -- truly awesome mind-benders.
The Math Forum's Problem of the Week
The USA Mathematics Talent Search -- for some really challenging questions!
But we still don't know everything ... visit some Famous Unsolved Problems!
A wildlife population model. Change the fecundity rate and watch a stable population bifurcate until you have chaos. population.xls [inspired by David Dimsey]


The Candy Problem

A Java Applet with a nice simple description and a great interface, from
A short article by Ivars Peterson
A spreadsheet for five players -- LOTS of different views. candy.xls


The Birthday Problem

A spreadsheet simulation. How many people until the first match? birthday.xls


The Buffon Needle Problem

A spreadsheet simulation. Watch the needles fall onto the hardwood floor! buffon.xls [works better in Office 2000]



The Mandelbrot set on the Geometer's Sketchpad, featuring the first ten orbits of a random walk. Takes a few minutes to generate a useful picture; a few hours to fill most of the screen. mandelbrot.gsp [the image at the top left of this page]
The Mandelbrot set on a spreadsheet, believe it or not. mandel.xls [uses recursive cell references; by Nils Ahbel]

History of Mathematics

The undisputed source: MacTutor History of Mathematics

Mathematics and Popular Culture

Math in the Movies from Sneakers to A Beautiful Mind.

Other Sources for Math Resources

Nils Ahbel's math courses, through Spreadsheets, presentations, data sets, and lots, lots more.
Eric Weisstein's World Of Mathematics is a boundless encyclopedia of mathematical concepts, including many interactive explanations.
101 project ideas for Geometer's Sketchpad
A great source for interactive exploration of fun topics through Java: Cut The Knot.
More interactive exploration through Java, focusing on the high school curriculum: Experiment and Explore Mathematics.
A huge catalog of mathematics related news, books and web resources: Paul Cabay's Mathematics Directory.

If you know of or find any interesting or entertaining mathematics sites or resources, please let me know!