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**

4 -3 -2 o . 1; , ' ..... ,. ~ .. :t'.. , ... f ~ .. : _ ~ ... • :::• • • - ; . 1/2 1/3 1/4 -~ -2 ~1 2 0 4 3' ... , 1/2 ~ ~ U1 <0 ""en 1/3 U1 w 1/-4. U1 4y=l 3y=l 2y=l y=l I '" t . -- ~. ;=1 1/2 -2y=l 1/3 -3y=l ,1/4 -4y=l ;< ~ ..... 1416 and All That Fractions, or rational numbers (the name they go by in number theory), are more ancient than the negative numbers. C. in the Rhind Papyrus of Egypt. The present way of writing fractions (for instance, 7i, %, %3) and the present way of doing arithmetic with them date from the fifteenth and sixteenth centuries.

Jd and Hd consistent: Jd = 1 implies Hd = 1. Our chart now looks like this: SUSPECT HANK JOEY RED SHORTY TONY a b c d t t t f t t t t t t f f f t t t t t t Table 3 Finally, for Hank: abed = 0, b a= O. = e = d = 1, so abed = al = The Logical Lie Detector 39 And with this, we have positively identified Lanky the Merciless, known in the professional circles as Lanky Hank. If we put to use more intricate theorems than those at our disposal, the results may be obtained in fewer steps without the need of picking the statements in the right sequence as we have done.

One day a group of ants met for the purpose of forming a club. The group took up, as the first order of business in this organizational meeting, the questions relating to the ideals and working procedure for the membership. The acting secretary jotted down the following points, which everyone present had agreed were desirable and should be covered by regulations for the members: work to be parcelIed out; promote cooperative spirit among the members; keep the club from being dominated by a small group; provide for interchange of ideas within working groups; keep working groups from being too unwieldy by limiting their size; distinguish the operations of working groups from operations of the entire membership; provide for communication of ideas between working groups.

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