# 3.1416 And All That by Philip J. Davis, William G. Chinn (auth.)

By Philip J. Davis, William G. Chinn (auth.)

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Additional info for 3.1416 And All That

Example text

IA b. C c. IA C D d. C I. I. ·WWw. IA D IA C D IA C I D FIGURE 1 In the step-by-step explanation below, the numbers in parentheses refer to the relevant bylaws. a. DrawAB,' b. Locate Can AB; c. Locate D outside AB; d. Draw DA, DC, DB; e. Locate E on DA, Fan DB, GonDC; f. Draw EGB and FGA; (2) between two points is a connection (path), (1) there is at least one connecting path. ( 4) any path connects at least three points, (5) no path connects more than three points. (6) there is a point outside the path.

Also, if it is not raining, but the ground is wet (someone tossed a bucket of water), the compound statement remains true. Finally, if it is both raining and the ground is wet, the truth value is obviously true. Using 1 to stand for a true statement and 0 for a false statement, the result of the compound sentence involving the linking word "or" is shown in Table la, where the left-hand column shows the truth value of the first phrase x, the top row the truth value of the second phrase y, and the entry shows the result of the compound statement.

We assume that we are dealing with a set of things, A, B, . . ,which represent the points at which alternative paths branch off. " But we are thinking necessarily of geometric lines. The connection of A with B is simply a certain relationship which is possessed by A and B simultaneously. With this as our raw material, we can proceed to make deductions. Although the original inspiration may have been geometric, we have shed all geometric garments. We have extracted all we need to describe traversings.