Here's my TI-Nspire™ page

What a machine: the TI-Nspire and TI-Nspire CAS change the way we teach, learn, and do mathematics and science.

The files available here are mostly *.tns files which can be used either in the computer software or in the handheld. Most of the files incorporate CAS functions. Recall that these functions will not 'work' on the TI-Nspire (without the CAS), but you can still view the results of the CAS commands and you can work with the programs in these documents.

For more information on TI-Nspire, see the official TI-Nspire website.

A 'Select' Program

By request of the science teachers, I have written a 'select' program for the TI-NSpire. You graph a scatter plot of your data then place and move two points on the screen to choose a range of data to extract. Run the select program and it will create two lists, temp1 and temp2, which contain only the desired data.
More detailed instructions are included in the file, including the procedure for making this a Library program so that you can use it in your own documents.
This file works on both the TI-NSpire and the TI-NSpire CAS.

Plot Differential Equations

This file is included with OS v1.6 (Dec, 2008) in the Examples folder. The CAS OS has the "CAS" version, but the files are identical.

The document is used to produce slopefields for differential equations and is a little easier to use than the Slopefields document that you will find further down on this page.

I have produced a demonstration video that explains the use of this document. Be sure your audio is turned on so you can hear the explanations.

CAS Around the World

My TI-Nspire CAS file used at the 'From Our Classroom to Yours' Conference, January 31, 2009 at the William Penn Charter School, Philadelphia, PA.

Soggies: The Breakfast of Nerds!

Here's a treatment of "The Cereal Box Problem". This classic probablility problem is based on the 'prizes in the box' issue: if there are N prizes in the collection, what is the Expected Number of boxes of cereal you need to buy in order to collect all of the prizes?

The TI-Nspire CAS document utilizes a program, soggies(a, b, t), that performs a simulated sampling of boxes (the number of prizes in the set ranges from a to b) until all the prizes have been collected and stores the number of prizes and the average number of boxes needed into lists that are used to create a scatter plot of the data.

I also include a brief analytic explanation of E(N), the expected value for N prizes and a function that graphs the expected value function over the scatter plot. Despite the appearance of the image on the right, this is not a linear function!

I am very happy to have had help from Lee Kucera, Marc Garneau, especially George Reese's web pages, and Jesse "Jay" Wilkins' great article on the derivation of E(N).

When I taught CS, I used this problem as a great graphics programming project, but did not know the general function until now (Dec, 2008). A big THANK YOU to the WWW!

DERPT
This document is a revision of my TI-84 program "DERPT" (short for 'derivative at a point') and is a demonstration of computing and plotting the slope of a curve at selected points in order to determine the pattern of the derivative function.
Use this activity when making the transition from calculating the slope of a curve at a point to determining the derivative function using the definition of the derivative as the limit of a slope expression. It is one of those 'aha' moments for some students.

Programming in TI-Nspire 1.3

This document examines the new Program Editor in TI-Nspire v1.3 released January 2008. It covers an overview, basic programming concepts, and some stuff for 'experts'. Also, see the Tower of Hanoi program later on this page.

The image to the right is a sample page.

Well, it's January, 2009 and the programming features have not changed much, so this document is still relevant!

Slopefields and Initial Conditions programs
This document contains programs that generate a slopefield for a differential equation (by creating a stat plot) and then allows you to select (graphically/geometrically) an initial-condition point to create another stat plot of a particular solution. The Notes page also explains how to use the desolve( )command on a Calculator page to solve the differential equation and how to make that function's graph go through and be controlled by the initial contition point graphically. Very powerful interactive graphics here! The Slopefield program was originally written by Doug Roberts. The tweaks to slopefield( ), the IC( ) program, and the desolve( ) technique are my work. There are other ways of generating slopefileds. If you are interested in them, email me.

Click the image on the right to see the Flash movie.

Implicit function grapher
This document has an implicit function graphing program in it. The graph produced is actually a stat plot. Instructions are contained in the Notes page in the document. The example shown here is demonstrated on the Calculator page.

Note that there is also a very efficient method for graphing implicit relations using the zeros( ) function in the CAS unit, but the numeric unit does not have that function.

Hanna's Banana
A graph that I discovered while playing around one day. Generates strange pictures as you move a point around on the graph page. How does it work? Read and learn!

Click the image on the right to see the Flash movie.

Largest Triangle - Paper Folding
This paper-folding problem was originally presented by Arne Engebretsen. This document, originally built by Dr. Stephen Arnold of Kiama, NSW, Australia, contains a very slick geometry construction simulating the folding of the upper left corner of a piece of paper down to the bottom edge. I tweaked the shading a bit, changed the dimensions of the paper, and limited the movement of point H. The problem is to find the fold - determined by the location of point H - that makes the area of the triangle formed in the lower left corner a maximum.

Steve has additional TI-Nspire resources at http://compasstech.com.au/TNSINTRO/

Paper Fold - Shortest Fold

Here's another problem related to paper folding: if you fold a corner of the paper to the opposite side, determine the shortest fold length. This problem can be tackled analytically in several different ways. How many different ways can you arrive at the soution? Can you see why the height of the paper is not an issue?

In the picture on the right, you can drag point Drag to change the length of the fold (L) and the distance from the lower left corner of the paper to the point Drag (w). The document contains pages of notes, this construction, a spreadsheet for data capture, a graph for the scatter plot, and CAS. Note that a regression algorithm is not appropriate for this problem.

Finally, can you generalize the result for any width of the paper?

Function + Polar Trace
     TI-Nspire allows for graphing of parametric, Cartesian and polar graphs on the same axes. What happens when we trace a point in both Cartesian and polar coordinate systems? In this graph/constuction, as you drag point D on the graph of y=sin(3t), the point on the polar rose, r(ø) = sin(3ø), also moves so that you can see or explain the relationship between the two coordinate systems. The coordinates of D and the converted radian-degree angle measure is on the screen, but not 'r'. The clever mathematical conversions are hidden, but easily exposed.
      Do you know that you can graph polar functions in parametric mode? Just define r(ø) = <the polar function> on a Calc page then set up these parametric functions:

x(t) = r(t)*cos(t)
y(t) = r(t)*sin(t)

     This, and the entire construction process are explained and demonstrated in this document.
     This file does work in all versions of TI-Nspire. If you are using version 1.3 released Jan 2008 just replace the parametric (polar) graph with a 'real' Polar graph. The point P is not really 'on' the graph anyway.

The Tower of Hanoi Program

     Well... if you've never heard of the Tower of Hanoi then you can look it up online. This program demonstrates the power of recursive programming. When you run the program you will notice a delay in the display of the output of the program until the program has completed. I guess that's a feature, not a bug. Posted 22JAN2008.
      Arguments to the program hanoi are:

hanoi(numberOfDisks, fromPeg, toPeg, auxPeg)

     It takes 2^N-1 moves to move a tower of N disks. I've tried it in the Computer Software with 10 disks resulting in 1023 moves. How many disks does it take to get a 'Recursion too deep' error?
      I have another version that displays the move number, but it requires an external, global variable. If you can't get it to work by yourself I can send you a copy.

Rabbits and Foxes

A study of the predator-prey mathematical model using the Spreadsheet and Scatter Plot tools. The document allows the user to drag point Init in this picture to change the initial populations of Foxes and Rabbits (but you have to recalculate the spreadsheet manually) and allows you to edit the growth factors on the SS page.

The next version of this document will have sliders on the graph page to control those growth factors. See version 2 below...

Rabbits and Foxes 2 (posted 2FEB08) has all the variables controlled by sliders in the graph screen. It also has a modified function for the Rabbits which incorporates a logistic growth rather than an exponential one.

This model is very sensitive to the variables BR, DF, and AA.

I've concluded through examing some Java applets online that there are just not enough data points available in the TI-Nspire (2500) to see the end behavior of the system. This version only graphs 500 data points. You can produce more data by copying and pasting the last line of the data set in the spreadsheet (in row 500) down to row 2500.

Loans Calculator

This file uses a spreadsheet to calculate the monthly payment on an amortized loan, displays the amortization table (in the spreadsheet) and then displays a graph of the principal payments and the interest payments. Useful to illustrate the TVM principal and the advantage of shorter term loans.

How To Make And Use 'Sliders'

NOTE: This document refers to constructing sliders (pre version 1.4-style). It does not use the 'insert slider' option on the G&G Actions menu. By request: a 'how-to' guide on the construction and use of 'sliders'. For the purposes of this discussion, a 'slider' is a point (usually on a segment, but not necessarily) that controls the value of a variable that is used as a parameter in a function, like the values a, b, and c in the function f(x) = a*x^2 + b*x +c. Moving the sliding point on the segment thus changes the shape of the function. Several different methods and tips are provided in this document for your enjoyment. As always, suggestions for improvement are welcome!

Lissajous curves and Harmonograms

     What are they, you ask? Well peek inside this file and see. The image to the right is a simple Lissajous curve, the result of a 2-axis pendulum under resistance-free movement.
     An important feature in this file is the use of Marc Garneau's method of graphing parametric relations using lists that do a better job than the parametric graphing mode. It gives you better control of the T-Step value as well as Tmin and Tmax if you like.

"The Zeckendorf Decomposition"

Isn't that a cool title? I learned about this while watching a DVD lecture from "The Great Courses" called "The Joy of Thinking" on Fibonacci numbers.
The idea is this: Every Natural number can be uniquely expressed as the sum of a set of (non-consecutive) Fibonacci numbers. I get the 'non-consecutive' part, but the rest is a mystery to me. Anyway...
Write a program that displays the Zeckendorf Representation of a Natural number (considering the limitations of the machine you are using). The image to the right is the output of my program which easily handles 'very large' numbers (the 1000^th Fibonacci number is over 200 digits). If you'd like a copy, though, you'll have to email me. Try it yourself first.

And, speaking of "The Great Courses" -- the latest catalog (March 2008) features a course called "How the Earth Works" by Prof. Michael E. Wysession of Wash. U, St. Louis, a former student of mine!

The "y=3x and point (1,1)" Problem
... for lack of a better title...

A vertex of a triangle is at the origin and one side is on the x-axis. Another side lies along the line y = 3x. The third side passes through the point (1,1). What is the slope of the third side if the area of the triangle is to be a minimum? There's another restriction, but you'll figure it out.

This is a neat optimization problem that lends itself well to Data Capture and a CAS solution. Note that the built-in regressions do not apply to this problem. Lots of great algebraic manipulation going on here.

Gene Olmstead offers two other optimization problems: What line makes the minimum perimeter of the triangle and what line makes the shortest third side, the side through (1,1). Gene says that all three of these have geometric proofs.

The file does not contain a complete solution. If you need one, email me.