Sections of a Plane

Materials: Handouts, construction paper, scissors, Scotch tape

To complete before Feb 15:

¨ Consider the sequence 1, 2, 4. Find several different ways to find the next term in this sequence and give an explanation of how each was derived.

¨ Use 2 colors of construction paper to investigate the largest number of regions n lines can divide a plane into for n = 1, 2, 3, 4, 5, . . .. Place the two sheets of construction paper on top of each other. Cut through both pieces along a line. Switch half of each sheet of construction paper for the other color. Tape the pieces back into two sheets. Repeat. Each time you cut the construction paper you should try to divide the plane into as many sections as possible. Keep a table of values and find a pattern. (See me for more details.)

¨ Can you explain geometrically how the patter works.

¨ Do Investigation 1.10 and Discussion on page 34 of Bassarear. Is the pattern the same as for sections of the plane? Why or why not?

¨ Can you find a formula for the nth number in either sequence?