Pascal’s Triangle

Recently I was introduced (or perhaps reintroduced) to Pascal’s Triangle, an arrangement of integers that lends itself to a variety of purposes, including binomial expansion. I’ve written a little program to explore this aspect of the idea.

Features

• Interactively adjust the degree of the expansion to see the corresponding triangle.
• Change the binomial terms for clarity or convenience.
• Show exponents of the first and zeroth power to illustrate that the total degree of each term matches the degree of the initial expression.
• Show plus symbols in the triangle to emphasize how each row is the basis for the next.
• Mouse-over highlight of corresponding terms in triangle and expansion.
• Binomial expansions to any degree can be computed (although the triangle is only displayed for small values due to limitations of the current layout spacing).
• Click and drag in triangle to scroll or drag divider to adjust size of expansion pane.

Screenshots

Download

• Mac OS X: pt.app.zip 2.5M
• Windows: pt.exe.zip 1.3M
• Other: pt.tcl.zip 2.3K or pt.kit.zip 2.8K; requires Tcl/Tk 8.5 or a corresponding Tclkit, respectively. The Mac OS X and Windows versions are self-contained (and hundreds of times larger, unfortunately).

Posted on Monday, February 25th, 2008. Tags: mac, math, tcl.