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© 1996: The University of Newcastle: Faculty of Education


Sample Problem 2

Use a graph plotter to look at the graph of the function

f(x) = sin(tan(x))

What is happening at each of the "fuzzy bits"?

If the function is periodic, then why do each of these appear different?

Figure 5: Viewing f(x) = sin(tan(x)) using xFunctions 2.3 on the Macintosh

This is an example of a mathematical situation ideally suited to the use of computer technology, and yet the very problem itself may be an artefact of the technology, rather than the mathematics itself. The nature of the computer as a "rational number machine" means that it plots graphs by joining many points - but these are always rational points! If something unusual happens at an irrational point (as is the case here) how can we be sure that the computer is not simply "stepping over" the point and missing the "real picture"?

Sample Problem 1. Sample Problem 3.


Last updated: 1st May, 1996
Stephen Arnold
crsma@cc.newcastle.edu.au
© 1996 The University of Newcastle


Challenge and Support Index

Courses | Software | Readings | Links | Comments?

© 1996: The University of Newcastle: Faculty of Education