1. Math
  2. Advanced Math
  3. questions 11 and 12 highlighted in blue...

Question: questions 11 and 12 highlighted in blue...

Question details
Questions 1.1 and 1.2 highlighted in blue
ly arithmetical, as one would expect l. Euclids p the problem seems to belong to arithmetic. IS essential ge r, there is a far more striking solution, which uses the geomet- interpretation of Pythagorean triples. This emerges from the work of However, s, and it is described in the next section. EXERCISES The integer pairs (a, c) in Plimpton 322 are 119 169 3367 4825 4601 6649 12709 18541 97 319 481 2291 3541 799 1249 481 769 4961 8161 45 75 1679 2929 161 289 1771 3229 56 106 or Ple 65 led nt Figure 1.3: Pairs in Plimpton 322 1.2.1 For each pair (a, c) in the table, compute c2 -a, and confirm that it is a perfect square, b2. (Computer assistance is recommended.) ould notice that in most cases b is a rounder number than a or c divisible by 30 or 12. ow that most of the numbers b are divisible by 60, and that the rest are rs were in fact exceptionally round for the Babylonians, because 60 triplsr their system of numerals. It looks like they computed Pythagorean broke aarting with the round numbers b and that the column of b values later was the base for off the tablet. iy, whids formula for Pythagorean triples comes out of his theory of divisibil- We shall take up in Section 3.3. Divisibility is also involved in some es of Pythagorean triples, such as their evenness or oddness
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