Math E-320: Spring 2011
Teaching Math with a Historical Perspective
Mathematics E-320:Morley's Miracle
Instructor: Oliver Knill
Office: SciCtr 434

This animation (written in Mathematica 7) shows Morleys miracle: The angle tri-sectors define a triangle which is always equilateral.

The background music is the "Flame Dream" song "Nocturnal flight". Recorded in 1980, it is from the album "Out in the Dark" (1981) which features a tetrahedron on the cover art. [By the way, if you look at the animation of Morley, there is the question whether the result could be proved by seeing it in space by cutting three edges away from a tetrahedral shape. This line of thoughts has not led anywhere yet however.] The band "Flame Dream" existed from 1978-1986, was popular in Switzerland in the eighties and I had been at concerts of them. They played so called classic, progressive rock. The members were Peter Furrer (drums) Peter Wolf (vocalist, not the J. Geils band singer), Urs Hochuli (Bass), Roland Ruckstuhl (Keyboard) and Dale Hauskins (Guitar) who was a member of the group for this album. Here is the MP3.

Added July 10, 2011: Peter Wolf wrote me in July 2011 that Volumes 2, 3 and 4 of "flame dream" will be redistributed on CD and will also become available digitally together with more instrumental pieces. Peter also sent more precise details about the band members of the "Out in the Dark" album:
  • Roland Ruckstuhl (piano, keyboards, arrangements)
  • Pit Furrer (drums, percussion)
  • Dale Hauskins (guitars)
  • Urs Hochuli (bass, bass pedals, b-vox)
  • Peter Wolf (voice, flute, saxophones, oboe)
The album was engineered and co-produced by John Acock/London. It was mastered by Kevin Metcalfe and was copyrighted in 1980 by Dark Music Ltd./SUISA. It was originally released and distributed on VERTIGO/Phonogram in 1981.

Added November 16, 2011: Dale Hauskins asked me, whether the Morley movie could be posted on Youtube. here it is. Added January 15, 2013: Dale Hauskins has forwarded me a link to Life performance of Flame Dream fom 1983.
Please send questions and comments to
Math E320| Oliver Knill | Spring 2011 | Extension School | Harvard University