The Golden Ratio Pages

Web pages that exploit JavaScript to do animated explanations about the golden ratio.

Compatibility

Some of the features of these pages (notably “canvas”) are new in HTML 5. Your browser must be up-to-date.

Brief Explanation

These web pages illustrate graphically some of the interesting ideas connected with the famous golden ratio. The basic idea is that they follow a plan, and you go through them from first to last, using the links at the top or bottom of the pages. This is a good idea if you haven’t seen them before.

But you can also visit them in arbitrary order. In the section below, there are links for each page, so you can jump to them directly.

Navigate yourself

• Introduction — An explanation of the golden rectangle.
• Solution — Some algebra to find the value of the golden ratio. (No animation yet. ☹)
• Continued Fractions — Another way of representing rational — and irrational — numbers.
• Rational Approximation — Explains why the golden ratio is the “least rational” number.
• The Fibonacci Numbers — What’s the connection?
• Fibonacci Pairs — More about the connection.

Remarks

Although this set of pages comprises a linear narrative, at each page we could turn off toward a multitude of related topics. Perhaps this set of Web pages will eventually more resemble a tree than a line! Of course, eventually the large-scale connectivity would be web-like. This is just a start a getting the simple things illustrated. Each page is self-contained, and no code is hidden or obfuscated, so inquiring minds can inspect the programming and learn further.

See Also

• The Chaos Pages — A similar series of pages exploring iterated systems.
• The 3D Pages — My JavaScript implementation of interactive 3D graphics .
• Combinatorial Music Theory — A lecture connecting graph theory with musical scales and chords.
• The DSP Pages — Explaining the Fourier transform in the discrete domains.
• 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.
• 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.