This is the story of the Space Shuttle’s Heat Shield. Upon its entry into space, a certain Space Shuttle has lost portions of its very important heat shield. The heat shield protects the craft from the very dangerous buildup of frictional heat caused by contact with the earth’s atmosphere upon a shuttle’s return to earth. Thus, this shuttle cannot safely return to earth unless excellently fitting patches are made and delivered to it via a rescue mission. To accomplish this, a team from the shuttle must take a spacewalk to determine the exact size and shape of the various patches that must be fitted to repair the heat shield. The specifications for these patches are then called into an earth-based manufacturer that then produces the patches and delivers them to the rescue team.
So, for this activity, students are partitioned into teams with an even number of members. For each team, half the team remains with the teacher; the other half (the rescue crew) is sent to a remote location. The team remaining with the teacher (this is the shuttle crew who took the spacewalk) are now handed a cardboard “patch”—a polygon (typically of between five to eight sides, not necessarily convex). This team must now “call in” to their teammates (via a cell phone call) the “specifications” for their particular patch.
The idea is that the shuttle crew should use a coordinate system with, say, centimeter units (thus, a centimeter grid) to determine, to as much accuracy as possible, the coordinates of the vertices of the patch. It is these coordinates (e.g., in a counterclockwise orientation) that are then called into the rescue team that must now reproduce the patch (again, using cardboard) as accurately as possible.
Here we see that:
Q. There is a practical matter at hand (namely, that information regarding the shape and size of objects can be conveyed via a transmission of mathematical data) which
R. requires the use of mathematics (in this case, using ordered pairs to identify vertices).
V. And, the result is easily verified by simply overlaying the original patches with their corresponding reproductions, to determine how well they fit.