000RM.dvi
532 More digital trivia 7.Determine the largest and smallest perfect squares which can be written with the ten digits 0, 1, 2, 3 ...
533 18.Find a number of the formab 0 cdwhose square contains the nine digits 1, 2, 3, 4, 5, 6, 7, 8, 9.^13 19.Find a perfect cub ...
534 More digital trivia ...
Chapter 20 The shoemaker’s knife 1 Archimedes’ twin circles 2 Incircle of the shoemaker’s knife Archimedes’ construction Bankoff ...
536 The shoemaker’s knife 20.1 Archimedes’ twin circles ........... LetPbe a point on a segmentAB. The region bounded by the thr ...
20.2 Incircle of the shoemaker’s knife 537 20.2 Incircle of the shoemaker’s knife .......... 20.2.1 Archimedes’ construction The ...
538 The shoemaker’s knife 20.2.2 Bankoff’s constructions Theorem 20.3(Leon Bankoff).If the incircleC(ρ)of the shoemaker’s knife ...
20.2 Incircle of the shoemaker’s knife 539 Second construction Z Y X ABC Q P 20.2.3 Woo’s three constructions Z Y X ABC Q S P Z ...
540 The shoemaker’s knife 20.3 More Archimedean circles .......... LetUVbe the external common tangent of the semicirclesO 1 (a) ...
20.3 More Archimedean circles 541 Exercise 1.The circles(C 1 )and(C 1 ′)are each tangent to the outer semicircle of the shoemake ...
Chapter 21 Infinitude of prime numbers 1 Fibonacci and Fermat numbers 2 Somos sequences 3F ̈urstenberg’s topological proof made ...
602 Infinitude of prime numbers 21.1 Proofs by construction of sequence of relatively prime numbers Fibonacci numbers^1 Sincegcd ...
21.2 Somos sequences 603 21.2 Somos sequences ................. Define two sequences(an)and(bn)with initial values a 0 =a 1 =1,b ...
604 Infinitude of prime numbers 21.3 F ̈urstenberg’s topological proof made easy ....... There is a famous proof of the infinitu ...
21.3 F ̈urstenberg’s topological proof made easy 605 Appendix: Euclid’s proof^3 The prime numbers or primes are the numbers (A)2 ...
606 Infinitude of prime numbers Appendix: The prime numbers below 20000 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 ...
21.3 F ̈urstenberg’s topological proof made easy 607 Exercise 1.Letpndenote then-th prime number. Find the smallest value ofn fo ...
608 Infinitude of prime numbers Project: Prime links A prime link of lengthnis a permutation of 1, 2,.. .nbeginning with 1 and e ...
21.3 F ̈urstenberg’s topological proof made easy 609 Project: Tuncatable primes Consider the prime number 73939133. The numbers ...
610 Infinitude of prime numbers ...
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