Abstract

A carpet vendor has to measure her customer's living room for some new broadloom. She has forgotten her tape measure, but does have a meterstick. She lays the meterstick on the floor, snug up against the wall, with the left edge of the stick in one corner of the room. She then makes a pencil mark at the right edge. Next she shifts the stick right until the left edge of the stick is at her mark, and again marks the right edge. She does this three times, but then finds that less than a full length remains to be measured. She turns the stick around so that the zero is now at the right side and lays it in the right corner and notes that her last pencil mark is at 70 cm. She concludes that the wall she is measuring is 3.7 meters in length. She then measures the opposite wall and concludes that it, too, is 3.7 meters in length. She then repeats the process for the remaining two opposite walls, and finds that they each measure 4.1 meters. To see if the room is rectangular, she runs a piece of twine from one corner to its opposite, pulls the twine taut and then cuts it to fit exactly. She then uses the same piece of twine on the other two corners to see if they are the same distance apart as the first two. The twine fits exactly. On the basis of these measurements, she..