## Spherical Blackboard

### cosmology - geography - non-Euclidean geometry

** What it shows: **

You can use a spherical blackboard for many things, including the teaching of geographical
coordinates, as a model for a closed Universe, or simply as a mathematical shape.

In the non-Euclidean geometry of the sphere, a circle will have a circumference greater
than 2πr and an area greater than πr^{2}. A triangle’s angles will
add to more than 180°, and two parallel lines, called Great Circles, will converge.

A Universe with a density parameter Ω greater than unity will have too much mass to
overcome its own gravitational attraction. Such a Universe will cease to expand, and will
re-collapse to (maybe) a singularity. The geometry of this closed Universe has a positive
or spherical curvature, and it can be represented two-dimensionally by a spherical surface.

** How it works: **

We have two spherical blackboards, a small bench-top one (diameter 30cm) that is a custom
made blackboard (origin unknown) and a larger (diameter 67cm) that was once a globe (see
*Comments*) but was painted black.

** Setting it up: **

The size globe you want will depend upon the size hall you're teaching in. Use chunky
multi-colored chalk for the big one, such as Prang™ fluorescent lecturer's chalk.

** Comments: **

So, if you have an old globe lying about, paint it black and you have an instant spherical
blackboard. That's exactly what they did at Harvard; they found an old globe, one of a pair
dating from 1757, stripped the paper off the papier-mâché sphere and removed
the six cabriole legs, painted it black and mounted it on a plywood box stand. Its twin, a
celestial globe was restored and currently resides in the Harvard Collection of Historical
Instruments. Originally priced at £35 for the pair, there is now little doubt which
has the greater monetary value. However, which of the twins has the greater educational value
is open to debate. Rating**

** References: **

D. P. Wheatland, *The Apparatus of Science at Harvard 1765-1800* (Harvard University Press 1968)

main categories astrophysics demos quantum/relativity demos math demos