The Messenger of Mathematics Volume 27-28 - Bookswagon UAE
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The Messenger of Mathematics Volume 27-28

The Messenger of Mathematics Volume 27-28


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: ...radix is of the form 3" + 1.f An exception of quite a different type, discovered by Desmarest, t is the number 487. While 4T repeats in 486 places, the repetend itself divides by 487, so that--_-, also repeats in 486 places. The present writer has fully verified these statements, And finds that both series obey Law 4, and the first one (4J7) obeys his own law of frequency of digits. To verify the latter result for the 488 distinct repetends belonging to the proper fractions with denominator 487', is impracticable, but there is not the least doubt in the mind of the writer that, in these 237168 figures, each digit would occur 23717 times, except 0 and 9, which would occur 23716 times only. Desmarest further states, and few will care to doubt him, that no other number below 1000 possesses the same property as 487 (and 3). The full series for--and-----t are given in Dr. Glaisher's pamphlet before mentioned, where it is also stated that the latter repetend does not divide by 487, so that----, contains 486 x 487 figures. It is easy to see, moreover, that j itself loses this property in the scales of 486 and 488, and doubtless in many other scales. Thus, in the 26-scaIe, -= 5, and-= i. t In the 5-acalc, = 13; i = 023121. J Theorie dcs Nombrts, 1852, p. 20&. Law 3 might easily be remodelled so as to make allowance for these occasional irregularities. Appendix B. Period-lengtlis with different radices, dsc. Keeping the same number, Nt we will consider the length of the period of-.as depending on the radix. Take tf=13. Then the radix-fraction has a repetend of twelve figures, or of n figures (n being any submultiple of 12), according to the radix selected. According as the radix is of the form 13p+l, 13+2, 13p+ 12, so the period consists of 1, 12, 3, 6, 4, 1...


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Product Details
  • ISBN-13: 9781130618082
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 52
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1130618080
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 109 gr


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