000RM.dvi
11.3 Hofstetter’s 5-step division of a segment in the golden section 325 11.3 Hofstetter’s 5-step division of a segment in the g ...
326 Constructions with the golden section Proof.SupposeABhas unit length. ThenCD= √ √^3 andEG=EF= 2. LetHbe the orthogonal proje ...
11.4 Construction of regular pentagon 327 11.4 Construction of regular pentagon LetOAandOYbe two perpendicular radii of a circle ...
328 Constructions with the golden section 11.5 Ahlburg’s parsimonious construction of the regu- lar pentagon Make use of a given ...
11.6 Construction of a regular 17-gon 329 11.6 Construction of a regular 17-gon To construct two vertices of the regular 17-gon ...
330 Constructions with the golden section Exercise 1.LetABCbe an equilateral triangle. The line joining the midpoints D,Eof two ...
11.6 Construction of a regular 17-gon 331 Project This is a classic problem you should know if you teach geometry. While it is n ...
332 Constructions with the golden section Appendix: Another construction of regular pentagon^6 Given a circle, centerO, let (i)A ...
11.6 Construction of a regular 17-gon 333 ABCDEis a pentagon symmetrically inscribed in a circle such that AB=CD=AE= the radius ...
334 Constructions with the golden section ...
Chapter 12 Cheney’s card trick 1 Principles 2 Examples Exercise A ♠ 2 ♣ 3 ♣ 4 ♠? ? ...
336 Cheney’s card trick 12.1 Principles You are the magician’s assistant. What he will do is to ask a spectator to give you any ...
12.2 Examples 337 12.2 Examples If, for example, you, the assistant, want to tell the magician that he should add 4 to the numbe ...
338 Cheney’s card trick Exercise 1.For the assistant: (a) ♠ 5 , ♠ 7 , ♦ 6 , ♣ 5 , ♣Q. (b) ♥ 2 , ♠J, ♥K, ♣ 2 , ♠ 8. 2.For the mag ...
Chapter 13 Digit problems 1 When can you cancel illegitimately and yet get the correct answer? 2 A multiplication problem 3 A di ...
402 Digit problems 13.1 When can you cancel illegitimately and yet get the correct answer? Letabandbcbe 2-digit numbers. When do ...
13.2 A Multiplication problem 403 13.2 A Multiplication problem A multiplication of a three-digit number by 2-digit number has t ...
404 Digit problems 13.3 A division problem Reconstruct the division problem ∗∗∗∗∗ ∗∗) ∗∗∗∗ 2 ∗ ∗∗ ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ ∗∗ ∗∗ Charles T ...
13.3 A division problem 405 Another division problem: Problem E1 of theMonthly x 7 xxx xxx) xxxxxxxx xxxx xxx xxx xxxx xxx xxxx ...
406 Digit problems One more division problem: not even a single known digit This is Problem E10 of theMonthly, by Fitch Cheney: ...
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