The TI-89 is probably the best calculator ever made by Texas Instruments. In fact, this machine is living proof that the good old rivalry between the world's two premier calculator manufacturers, Hewlett-Packard and Texas Instruments, is still alive and well.

This handheld calculating instrument has just about everything you could ask for in a calculator. A huge amount of memory, even more memory for archiving objects, flash-upgradeable operating system software, a symbolic algebra system, a high-resolution, high-contrast LCD display, just to name a few of its outstanding features.

The TI-89 is actually a close relative of the TI-92. The capabilities of the two machine are nearly identical, except that the geometry application that's a standard feature of the TI-92 is available only as an optional download for the TI-89.

For most calculators, I use a classic computational problem, that of the Gamma function, as a demonstration of the machine's programming capabilities. The TI-89, however, deserves more; it belongs to that exclusive club of calculators on which user-defined functions can take advanced object types, such as algebraic expressions as parameters. (Other members of this club include the HP-28C and HP-28S, the HP-48S/SX/G/G+/GX, the HP-49G, and of course the TI-92 and TI-92Plus.) One very interesting, and practical programming example (used frequently by surveyors, I am told) for such calculators is computing the radius of curvature for an arbitrary function. For any function f(x), the radius of curvature at any x=x₀ can be obtained by evaluating (1+(f'(x)²))^3/2/f''(x). The function below, named roc, can be invoked for instance as follows: roc(x^2,x,0). This will calculate the radius of curvature of a the parabola y=x² at x=0.

:roc(f,z,z0)
:Func
:Return ((d(f,z))^2+1)^(3/2)/(d(d(f,z),z))|z=z0
:EndFunc