Animating Web Pages with the TI-92 David Bowers, University College Suffolk, UK |

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## Application 1: Illustrating Dynamic ProcessesWhen studying the graphs of functions, it is important to understand the effect on the graph of varying certain function parameters. This introduces the idea of a "family" of curves, each of which can be deduced by applying a sequence of transformations. The most well-known graphical transformations of the "basic" graph *y = f(x) + a**y = f(x - a)**y = a.f(x)**y = f(a.x)*
a.
The case An animation which cycles through such a family of curves is shown below: Click here to see a sample page from the | |||||||||||||||

## Application 4: Visualising Practical Problems
Problem solving in applied maths is often little more than using standard formulae to set up a system of equations, and then solving them algebraically. Traditional textbooks do little to encourage a "feeling" or insight into the nature of the problem, since the visual representation there is restricted to static diagrams. Web pages, on the other hand, can include animation in the images, which can help to illustrate the inherent dynamical nature of many problem. A common topic in applied maths courses concerns the motion of projectiles. For
example, consider the situation where two objects are projected towards each other with
different initial velocities. The problem is to establish whether they collide. In the
case where the objects are projected from ground level 50 metres apart, the first with
initial velocity 20 m/s at 40 degrees to the horizontal, the second with initial
velocity 18 m/s at 60 degrees to the horizontal, the parametric equations of motion
are given by: The dynamic features of a simulation can be captured in an image which is animated rather than static, and an animated GIF within a web page is a simple way of achieving this. We show below the running of a simulation of the well-known experiment to estimate the value of pi. A quadrant of a circle of unit radius is drawn within a unit square, and a number of points (50, say) are chosen at random within the square. Since the proportion of the area of the square covered by the quadrant is pi/4, the proportion of the points lying in the quadrant may also be taken as an estimate of pi/4, from which an estimate of pi can be deduced. | |

## References
One of the easiest to use GIF Animators is the Version 5 of the popular graphics software package Descriptions of a variety of web graphics tools, including reviews of several GIF
animators, can be found at: An example of online learning material which includes static screendumps from the
TI-92 where animated images might be more instructive, can be found at: And finally, the website of the machine which makes it all possible: | |

## Notes on the Author
David Bowers is Senior Lecturer in Mathematics & Statistics at University College Suffolk, Ipswich, UK. (Click here for more information about the College). He is interested in all areas of technology-assisted learning in mathematics, and is currently manager of the College's newly established resource-based learning and skills support workshop.
Bowers, D. (1995) "Computer Algebra in the Classroom", Mathematics Support Newsletter, 3. Bowers, D. (1995) "What was the Question?", International DERIVE Journal, 2(2). Bowers, D. (1995) "Changing Assessment Criteria in A-level Mathematics with DERIVE", in: Barzel, B. (Ed), Tagungsband der Derive Days Düsseldorf, Landesmedienzentrum Rheinland-Pfalz. Bowers, D. & Townsley-Kulich, L. (1996) "Total Resource Management" in: Monaghan, J. (Ed) The State of Computer Algebra in Mathematics Education, Chartwell-Bratt, UK. Bowers, D. & Beaudin, M. (1996) "Logistics for facilitating CAS Instruction" in: Monaghan, J. (Ed) The State of Computer Algebra in Mathematics Education, Chartwell-Bratt, UK. Bowers, D. (1997) "Computer Algebra and Secret Codes", Micromath, 13(2). Bowers, D. (1997) "What was the Question - A Framework for Investigational Activities using DERIVE" in: Graham, E. (Ed) Mathematical Activities with DERIVE, Chartwell-Bratt, UK. Bowers, D. (1997) "Maths Support for Students with Visual Impairment", Mathematics Support Newsletter, 6. Bowers, D. (1997) "Opportunities for the Use of Computer Algebra Systems in Middle Secondary Mathematics in England and Wales", Zentralblatt für Didaktik der Mathematik 97/4
"Enhancing the quality of student-centred mathematics": 27th International Conference of the Association for Educational and Training Technology, York, UK, 6-9 April 1992. "The use of authoring software to enhance the quality of student-centred mathematics provision": International Conference on Technology in Mathematics Teaching, Birmingham, UK, 17-20 September 1993. "What was the question? Structured investigational activities using DERIVE": The First International DERIVE Conference, Plymouth, UK, 11-15 July 1994. "Customised studyware in mathematics": The Seventh International Conference on Technology in Collegiate Mathematics, Orlando, USA, 17-20 November 1994. "Die Erweiterung des Erwartungshorizonts durch DERIVE": International Council for Computer Algebra in Mathematics Education, Düsseldorf, Germany, 19-21 April 1995. "Attracting teachers to DERIVE": International Symposium of the Austrian Centre for the Didactics of Computer Algebra, Honolulu, USA, 30 July - 3 August 1995. "Computer-based studyware in mathematics": International Conference on Technology in Mathematics Teaching, Edinburgh, UK, 4-7 September 1995. "On establishing a mathematics workshop": Second National Conference on Support for Mathematics in Further & Higher Education, Luton, UK, 14 September 1995. "On Plotting Piecewise Defined Functions": DERIVE/TI-92 Days Leeds, Leeds, UK, 13-15 April 1996. "Exploiting DERIVE's Vector Function": The Second International DERIVE Conference, Bonn, Germany, 2-6 July 1996 "Animating Web Pages with the TI-92": The Third International DERIVE Conference, Gettysburg, USA, 14-17 July 1998 David Bowers The URL of this document is http://website.lineone.net/~davidbowers/Getty98/main.htm | |

This website was created by the Author for dissemination in good faith to the participants at the Third International Derive & TI-92 Conference held in Gettysburg, USA, July 14 - 17 1998. It may be reproduced in whole or in part for bona fide educational use, on the condition that the source is acknowledged.

David Bowers, July 1998