Date: Mon, 6 Apr 1998 09:47:19 -0400
From: Alex Bogomolny
Dear Kris:
I am somewhat uncertain whether "measurement in volume" means "volume measurement" or "a lot of measurements."
Assuming "volume measurement", i.e., measurement of volume:
You can't do better than following in Archimedes' footsteps. Just do not run around naked shouting "Eureka". You may still tell the story.
Assuming "a lot of measurements":
Think of fractals. Take a map and measure border lines using various measurement units. Measure the length of a snowflake.
Best regards,
Alexander Bogomolny
P.S. On second thought, you could use volume measurement to demontsrate the Isoperimetric Inequality: check that shapes made of the same amount of the same material may have different perimeters (or surface areas which is more difficult.) See that the sphere (or the circle) are, in a sense, larger than other shapes.
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