Imagine a single piece of string that can be wound back and forth. In the illustration, the string is bent so that it has three "layers." It is still one piece of string at this point. Imagine now that you take scissors and cut through the wound string, as indicated by the dotted line. The result will be four separate pieces of string, as shown in the next illustration. You can make more than one cut across the layers of string, creating more pieces. You can also start with more layers of bent string. Draw your own pictures of string with different numbers of layers and different numbers of cuts. Now suppose that the number of layers is I, the number of cuts is c, and the number of pieces is p. Find a rule, an equation, for describing the relationship between the number of layers, the number of cuts, and the number of pieces.
Imagine a single piece of string that can be wound back and forth. In the illustration, the string is bent so that it has three "layers." It is still one piece of string at this point. Imagine now that you take scissors and cut through the wound string, as indicated by the dotted line. The result will be four separate pieces of string, as shown in the next illustration. You can make more than one cut across the layers of string, creating more pieces. You can also start with more layers of bent string. Draw your own pictures of string with different numbers of layers and different numbers of cuts. Now suppose that the number of layers is I, the number of cuts is c, and the number of pieces is p. Find a rule, an equation, for describing the relationship between the number of layers, the number of cuts, and the number of pieces.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Imagine a single piece of string that can be wound back and forth. In the illustration, the string is
bent so that it has three "layers."
It is still one piece of string at this point. Imagine now that you take scissors and cut through the
wound string, as indicated by the dotted line. The result will be four separate pieces of string, as
shown in the next illustration.
You can make more than one cut across the layers of string, creating more pieces. You can also
start with more layers of bent string. Draw your own pictures of string with different numbers of
layers and different numbers of cuts. Now suppose that the number of layers is I, the number of
cuts is c, and the number of pieces is p. Find a rule, an equation, for describing the relationship
between the number of layers, the number of cuts, and the number of pieces.
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