## Archive for Binomial theorem

## conjugate of a binomial

Posted in Statistics with tags Bayesian statistics, binomial distribution, Binomial theorem, conjugate priors, cross validated, Galois Theory, mathematics on March 25, 2021 by xi'an## Le Monde puzzle [#824]

Posted in Books, Kids, R with tags Binomial theorem, Isaac Newton, Le Monde, mathematical puzzle on June 13, 2013 by xi'an**A** rather dull puzzle this week:

Show that, for any integery, (√3-1)^{2y}+(√3+1)^{2y}is an integer multiple of a power of two.

**I** just have to apply Newton’s binomial theorem to obtain the result. What’s the point?!

## The House of Silk

Posted in Books with tags Binomial theorem, book review, James Moriarty, Sherlock Holmes, Watson on April 6, 2013 by xi'an**A**s surprising as it may sound, *The House of Silk* is a *new* Sherlock Holmes novel. Obviously, it is not a long forgotten piece of Arthur Conan Doyle, but a pastiche commandeered by the Conan Doyle Estate and written by Anthony Horowitz.I was not at all aware of this book when I came upon it in an Oxford bookstore and bought it on a whim, having always loved Sherlock Holmes’ stories (although George Casella was a much more knowledgeable fan than I).

*“I am a mathematician, Dr. Watson. I do not flatter myself when I say that my work on the Binomial Theorem is studied in most of the universities of Europe.” The House of Silk, p.259.*

**E**ven though it would be difficult to confuse the style with Conan Doyle’s, and while the story is more involved and contemporary than the original ones, the book is well-written, reasonably coherent within the early 20th Century, and gripping enough to keep me up late over a few evenings. *The House of Silk* obviously has the advantage to come after the whole sequence of Conan Doyle’s stories and it hence borrows the settings and the characters from this universe: the Baker Street irregulars, Lestrade, Mycroft, and even Moriarty. The story is as usual told by (an old) Watson, recollecting upon events that “were simply too shocking, too monstrous to appear in print” and which could “tear apart the fabric of society”. A clever touch is that Watson describes this story as a mix of two adventures, *The Man in the Flat Cap* and *The House of Silk*, which become linked due to an unfortunate coincidence. As mentioned above, the setting of *The House of Silk*—if not of *The Man in the Flat Cap*—is much darker than in an original Holmes novel and uncovers crimes that could not have been mentioned or even alluded to in a Victorian novel. Even the ill-fatted visit of Holmes to an opium den or his dramatic arrest would have sounded too shocking for his time. However, this contributes to the appeal of the novel. (So does the side entry into Watson’s life after his wedding, esp. the lines when he is ask to swear upon what’s most sacred to him and when Holmes’ friendship wins over his marriage…) It actually becomes difficult to criticise aspects of the book like lack of depth in most characters, short scenes, caricatural mistakes in reasoning by Watson, impossibilities, &tc. without realising they could also be addressed to Conan Doyle himself! Hence, if reading that “the game’s afoot” still conjures for you an addictive flavour of mystery, clever sleuthing, and pipe tobacco, I think you will enjoy *The House of Silk*! As for the Binomial Theorem, I am afraid nothing more is said about it within this book. (In another pastiche, Moriarty actually denies any link with this antique theorem.)