TIrdle posted 25 Feb 2022
The word game!
The doc is protected, so
"save as..." a copy for yourself to play and remember to save
your file when done to preserve the stats.
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Checkers19 Mar 2021
The board game vs. the computer. Didier Deses wrote the AI algorithm and I did the GUI. See the Notes app for instructions and details. Requires the textbox module
(available below right) in your Pylib folder. When you store
it there be sure to 'Refresh Libraries'.
The file is write-protected
to preserve the original state, so use Save-As to make a
personal working copy.
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My Nspython Collection
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My Pylib ModulesPut these files in your Pylib folder and 'Refresh Libraries'. Some of the programs on the left need one or more of these modules (as specified). All these files have Notes pages with documentation. All but randfuncs have demos on the left.
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Polynomial Regression
August, 2013 This document requires CAS. I've long wondered what the regression algorithm behind QuadReg, CubicReg, and QuarticReg is. It took me this long to look it up and I was pleasantly surprised to actually 'understand' it (to a point). The result is this pair of programs and a demonstration of their usage embedded in this document. The program polyreg(xlist, ylist, degree) performs a polynomial regression of the desired degree on the dataset (xlist,ylist). The polynomial expression is then stored in the variable regeq so that it can be used as the definition of a function to graph or analyze. The program makes heavy use of matrices and lists and needs CAS to build the function in terms of x. The source code is exposed in one of the pages of the document. As an added bonus, there's also a program called polyfit(xlist, ylist) which is nearly identical to polyreg( ) but only determines the (n-1) degree polynomial for a dataset of n elements. Polyreg( ) does it when p=numpts-1. and you can see how the polynomial regression 'grows' to eventually match the polynomial fit function. Both programs are used on the demo page which is illustrated on the right. There's no error handling, but when the algorithm fails to produce a result you'll see 'Singular Matrix' as it's output and the graph is not updated. This happens when the power you seek is too large (p>numpts-1). |
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page 1.1 page 1.2 page 1.3 |
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version 1 version 2 version 3 |
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not a squircle |
A cone sliced
by a plane
(05/2011) A simple interactive file that uses the new 3D graphing capabilities of TI-Nspire. You have control (sliders) for the angle of the plane (with the x-axis) and the z-intercept of the plane. Take a look at the equation of the plane to see how to convert 'angle' into 'slope'. When a slider controls slope, small values lose detail and large values move slowly. When you drive the angle, everything works smoothly.
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Greater
control of your polar and parametric graphing
Looking for a way to control the rate at which polar and parametric graphs appear? These two files let you expose the graphs using a slider. The polar slider even goes from a negative value to a positive value. The polar graph is defined as r1(theta) but the graph is produced by a parametric relation. (02/2011)These files do not play well on a handheld because of the effort it takes to produce the graph when you use the slider. I'll be working on another method. |
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In version 3.0 this feature is built into the Vernier DataQuest application. By request of the science folks, 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. |
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Version 3.0 has this feature built in: see Graphs/Graph Type/Differential Equation 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. |
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. |
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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! |
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This document explores programming in the 'TI-Basic' language built into the TI-Nspire. First introduced in 2008, the Program Editor allows you to write programs right in the handheld. The TNS file covers an overview, basic programming concepts, and some stuff beyond the bascis such as lists and graphics. Also, see the Tower of Hanoi program later on this page.
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Version 3.0 has slopefields built into the OS. 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. |
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. |
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AP Calculus demo file
Three sample problems that I demonstrated at the AP Calculus Consultants Conference in Dallas, 11/16-18/2007.
- The number of daylight hours on June 21 as a function of latitude
- A limit question from the AP Calculus listserv 10/2007
- AP Calculus 2003AB6c
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! |
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Mesopotamian Tablet - Isosceles Trapezoid Problem
I found this problem at the NCTM Regional Conference in Richmond, VA. Credit is found in the file. The problem is to find a transversal that divides a particular isosceles trapezoid into two equal areas. There's also an interesting extension that's not discussed in the file. Can you figure out what I'm thinking?
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Distance to a Parabola
This zip file contains TWO versions of the activity: a student copy and a teacher copy. The problems investigate the length of a segment drawn from a point to the parabola y=x2. Several problems are included in both files. The investigation of the residuals plot is also addressed and the CAS derivation of the mathematical model is included in the teacher file.
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/ |
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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 file on the right (page 2), 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? |
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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.
This,
and the entire construction process are explained and
demonstrated in this document. |
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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.
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? |
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TI-Nspire DOES have a sequence graphing mode! See Graph Type in the Graphs application.
While the TI-Nspire does not contain a 'sequence' graphing mode, it does have the ability to generate sequences (yep, even recursive sequences) and series (sequence of partial sums) using the Lists and Spreadsheet app and then you can graph the resulting scatter plots. This document explains the seqn function and how to create a sequence of partial sums. It also includes an interesting problem: the limit of the sum of the reciprocals of the Fibonacci numbers.
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... |
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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. |
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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. |
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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. |
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"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. And, speaking of "The Great Courses" -- there's a course called "How the Earth Works" by Prof. Michael E. Wysession of Wash. U, St. Louis, a former student of mine! |
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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. |
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