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

ISBN-10: 0817633049

ISBN-13: 9780817633042

ISBN-10: 1461585198

ISBN-13: 9781461585190

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**Extra resources for 3.1416 And All That**

**Example text**

Valentine's Day. Shorty was in Mexico City at that time. One of us is guilty. To make up for our lack of acumen, which Sherlock Holmes apparently possessed, we amateurs shall rig up a kind of lie detector to help us put together all the pieces of the puzzle. Ours is simply a "sentence sorter" whose blueprint is based on Tables la and lb. >z -01 0 1 0 1 1 1 ~ 0 1 (a) or 0 1 0 0 0 1 (b) and Table 1 Let's look into how sentences may be sorted. ) Now the statement, "The ground is wet" also has the two The Logical Lie Detector 35 possible truth values: true and false; not both true and false simultaneously.

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. ( 2) between two points is a connection. (4, 5) each connection connects exactly three points. (2, 3, 4, 5) connect each new point to all other points; route the path so that there will be three points on each path.

In New York City, a map of the subway system is posted in every subway car. The relative distances are not accurate, the depth of the tunnel is not indicated, the locations of entrances and exits to the subway have been deleted. But for indicating what train goes where, the order of the stations, and where to transfer, the map is complete. The process of abstraction can be continued further and away What Is an Abstraction? 25 from geometry completely. In Figure IB we designated the places where alternative passages occur by small dots.

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