The Polynomial Pages

Web pages that exploit JavaScript to do animated explanations.

Compatibility

Some of the features of these pages (namely “canvas” and “slider”) are new in HTML 5. Your browser must be up-to-date. By slider, I mean a GUI control that you drag back and forth to set a number. If it is rendered like this

you are OK. (This one is just a picture, it won’t actually work.) If the blue knob is missing and there is just a text field to type in, a lot of the interactivity of the Web page will be missing.

Brief Explanation

These web pages let you turn the “knob” that animates the graphs. You change coefficients, and watch the functions and their roots move around.

You can browse the pages sequentially; alternatively, below there are links for each page, so you can jump to them directly.

Navigate yourself

• Linear — Graphs a linear function and plots its root.
• Quadratic — Likewise with roots plural.
• Cubic — And with three roots.

Remarks

This series should to on up to the quintic, and then discuss Galois theory.

See Also

• The Chaos Pages — A series of pages exploring iterated systems.
• The Golden Ratio Pages — A similar series of pages exploring the famous ratio.
• Gear Ratios — These may not be golden, but they are important for people who ride and work with bicycles. Available as a mobile app and a Web page.
• Anagrams — A mobile app and a Web tool for finding anagrams.
• LL(1) Parsing — A Web tool for generating a parse table and using it to construct a leftmost derivation.
• Enumeration — A Web tool for finding permutations and combinations.
• Gaussian Elimination — A Web tool for reducing matrices to row echelon form.
• Combinatorial Music Theory — A lecture connecting graph theory with musical scales and chords.
• The 3D Pages — My JavaScript implementation of interactive 3D graphics .
• The DSP Pages — Explaining the Fourier transform in the discrete domains.
• Graph Clock — A good example of using JavaScript to make a self-modifying Web page, and a little puzzle about elementary connected graphs.
• Regular Expressions — Sometimes a non-match can hang the system.
• The Z-Board — A new kind of MIDI controller.