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# musical mathematical journeys

July 6, 2014 10:26 AM Subscribe

Trio for Three Angles (1968) is one of many beautiful acclaimed visually-oriented short films with music by mathematical filmmakers Bruce and Katharine Cornwell, some animated by hand and some using early digital technology. It inspired three sequels: Similar Triangles (1975), Congruent Triangles (1976), and Journey to the Center of a Triangle (1978) (previously).

Other extant films by the couple, recently generously released by their sons Eric and Scott Cornwell under a Creative Commons license "to encourage artists, educators, and others to give these images new life", are:

Other extant films by the couple, recently generously released by their sons Eric and Scott Cornwell under a Creative Commons license "to encourage artists, educators, and others to give these images new life", are:

- The Seven Bridges of Königsberg (1958), on Leonard Euler's famous solution to the topological problem
- Possibly So, Pythagoras (1963), using the patterns of a tile floor to demonstrate the Pythagorean Theorem
- How Do You Count (1963), on counting in bases 2, 3, 4, 10, 12, and more
- Newton's Equal Areas (1967), an elegant visual demonstration of Newton's proof of Kepler's Second Law
- Circle Circus (1978), featuring ten ways to draw a circle
- Dragon Fold (1978), on fractals

Nice indeed! I loved

posted by languagehat at 11:58 AM on July 6 [1 favorite]

*The Seven Bridges of Königsberg*.posted by languagehat at 11:58 AM on July 6 [1 favorite]

Glorious! I loved how the Trio for Three Angles tried to teach geometrical features purely through animation, hoping that the viewer would think things like, "Huh, that's neat. I wonder why those two angles match up so perfectly?" It reminds me of the way a video advertising designer might try to catch an audience's eye by sliding around elements of a brand logo in an interesting way. But here it's used for good. I wonder how far you could go teaching geometry entirely non-verbally?

posted by painquale at 2:49 PM on July 6

posted by painquale at 2:49 PM on July 6

Perfect timing on these. I'm teaching my summer camp kids the Pythagorean theorem and triangle centers in the next two days, and will for sure show them these.

The triangle centers one in particular does a great job showing how angle bisectors are everywhere equidistant from the sides of the angle, and how perp. bisectors are everywhere equidistant form the endpoints, which are some of those intuitive-but-hard-to-explain ideas that trip people up a lot.

posted by Wulfhere at 3:17 PM on July 6

The triangle centers one in particular does a great job showing how angle bisectors are everywhere equidistant from the sides of the angle, and how perp. bisectors are everywhere equidistant form the endpoints, which are some of those intuitive-but-hard-to-explain ideas that trip people up a lot.

posted by Wulfhere at 3:17 PM on July 6

I can remember seeing one of the triangle films some time in the early 70s - I can remember the hall it was projected in, and that it was on a sunny day with the curtains drawn, but nothing more than that - and being entranced. I was almost certainly under ten.

That I can remember it so clearly but didn't take the mental steps to find out more explains why I love mathematics but am a lousy mathematician.

posted by Devonian at 4:15 PM on July 6 [1 favorite]

That I can remember it so clearly but didn't take the mental steps to find out more explains why I love mathematics but am a lousy mathematician.

posted by Devonian at 4:15 PM on July 6 [1 favorite]

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posted by benito.strauss at 10:57 AM on July 6