Computational Diversions: The Return of the Spherical Turtle
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Computational Diversions: The Return of the Spherical Turtle Michael Eisenberg
Published online: 9 December 2012 Ó Springer Science+Business Media Dordrecht 2012
Two years ago in this column (time flies!), I discussed the idea of programming a Logo turtle to move about the surface of a sphere. This was an idea explored at length in Abelson and diSessa’s (1980) book Turtle Geometry, and it’s a fun way of introducing many of the seemingly strange ideas of non-Euclidean geometry. In that earlier column, I described a still-embryonic programming system that permitted spherical turtle programs to be drawn on the giant spherical screen, ‘‘Science on a Sphere’’,1 produced by the National Oceanic and Atmospheric Administration (NOAA). The column closed with a photograph of a Logo ‘‘flower’’ drawn on the giant sphere at our local Fiske Planetarium here in Boulder, and I’ve brought back that photograph as Fig. 1 for this column: the flower was a thankyou gift of sorts for Hal Abelson and Andrea diSessa in honor of their remarkable and timeless book. This essay returns to the topic of spherical turtle geometry, but in a more participatory spirit. As of this writing, we now have a Web-accessible programming interface for the spherical turtle, programmed by Antranig Basman and Michelle Redick at the University of Colorado; that’s just a formal, academic way of saying that you, the reader, can now bring up a working spherical turtle interface and write programs for it. (I could refer to the system as a ‘‘spherical Logo interface’’, but that would be inaccurate—since, as you’ll see if you play with the system, the language only has some superficial similarities to Logo.) The spherical programming system is available through the beautiful website created by Dr. Sherry Hsi and her colleagues at the Lawrence Hall of Science in Berkeley, California. Here’s how you can access the system: first, go to the website www.mathsphere.org, and then follow the ‘‘Tools’’ link to get the current web address of the spherical programming interface.; currently, that interface is available at: http://mathsphere.org/mos-client/ client.html.2
1
NOAA website for ‘‘Science on a Sphere’’: http://sos.noaa.gov/index.html.
2
The current web interface works in the latest versions of the Firefox and Google Chrome browsers.
M. Eisenberg (&) University of Colorado, Boulder, CO, USA e-mail: [email protected]
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Fig. 1 A spherical ‘‘Logo flower’’ pattern drawn on the Science on a Sphere installed at the Fiske Planetarium in Boulder
Fig. 2 The spherical programming interface. At upper left, an editor window in which full programs may be written and run (by selecting the ‘‘run commands’’ button underneath the window). At lower left, an interactive command window. At right, a rendering of the sphere, with the turtle icon initially placed at the equator, pointing due north. This sphere may be turned interactively via the mouse to see the surface from any direction
When you bring up the spherical turtle interface, you
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