Sorting and Classifying

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Classify Quadrilaterals. Given a number of irregularly shaped quadrilaterals, devise a scheme for classifying and sorting them. See if the same scheme works for other polygons.

Sorting. You have been hired for a summer job by a local museum which has obtained 50,000 old library cards from a variety of sources to illustrate how library catalogues functioned before computers. Your job: sort and file them. Describe various ways in which you might go about this job. Estimate how long each method would take, and explain which method you would decide to employ.

Consumer Complaints. Consumer complaints at a major department store arrive by letter, e-mail, telephone, and on notes from store employees. Some are about prices, some about service, some about the availability of merchandise, some about quality of goods. A typical job for someone with a bit of mathematical background is to classify these complaints in useful ways and prepare graphs or charts for presentation to store employees and managers.

Puzzle Pieces. Explore the number of types of regular pieces of different types in a very orderly jigsaw puzzle. Draw all possible combinations of pattern interlocks of pieces that are fundamentally rectangular with tabs, including edge pieces.

Musical Pitch. Compare the pitch of notes in the octave above middle C according to the traditional "diatonic" tuning by intervals, the "equal-tempered" system of equal ratios, and the "ideal" tuning by small-integer ratio of frequencies.