This is a suggestion for student projects, perhaps leading to animations on Youtube or other video clips archive.
from a Lightning Talk at Linus Pauling House (August 2010)
Having a tetrahedron serve as unit volume means any positive integer N to the 3rd power is modeled by a corresponding tetrahedron of edges N.
Earthlings and Martians share a terraforming project to build a large dam somewhere. They each contribute concrete in "units of volume" but these units are different.
The Martians and Earthlings both calibrate the "scaffolding" (space-filling skeletons) using the Radius and/or Diameter of a ball.
build cubes of edges R, and call this unit.
Click here for further discussion (mathfuture). Spoiler alert: conversion constant given.