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Ernest Yakovlev
Ernest Yakovlev

Magical Mathematics : The Mathematical Ideas Th... [Extra Quality]

What follow are several tricks, and the basis for each of these tricks is mathematics. It is important to note that I did not come up with any of these tricks. The tricks themselves, or the underlying ideas for the tricks, come from Martin Gardner, Raymond Smullyan((Smullyan, Raymond M., et al. Alice in Puzzle-Land: a Carrollian Tale for Children under Eighty. Dover Publications, 2011.)), Arthur Benjamin((Benjamin, Arthur. The Magic of Math: Solving for x and Figuring out Why. Basic Books, 2016.)), Persi Diaconis((Diaconis, Persi, et al. Magical Mathematics: the Mathematical Ideas That Animate Great Magic Tricks. Princeton University Press, 2016.)), Ron Graham, the wonderful productions at Numberphile, and all of the great minds who came before these people to inspire them.

Magical mathematics : the mathematical ideas th...

Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath Principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem.

The first thing to note is that the authors are both respected mathematicians, so it is perhaps not surprising to learn that the mathematics involved is actually non-trivial. In my undergraduate course on Knots and Surfaces I do a few knot and rope tricks to enliven the lectures and to demonstrate some of the ideas in the course, but these are generally sleight-of-hand tricks unlike the tricks in this book which all have some interesting mathematics underlying them.

The astronomer Galileo Galilei observed in 1623 that the entire universe "is written in the language of mathematics", and indeed it is remarkable the extent to which science and society are governed by mathematical ideas. It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords,scales, and keys can all be demystified and understood logically using simple mathematics.

Your comments echo a lot of my own feelings, but with a different conclusion. How we can take something as beautiful as music and convert it to mathematical formulas is truly wonderful. Before reading this excellent article, I had a feeling that harmony in music has been discovered as something orderly that can be explained by mathematics. Order like that does not come into existence by random chance. It strengthens my faith in God the Creator of the universe who alone deserves recognition for these gifts we enjoy.

Known for his unbounded curiosity and enthusiasm for subjects far beyond mathematics, Conway was a beloved figure in the hallways of Princeton's mathematics building and at the Small World coffee shop on Nassau Street, where he engaged with students, faculty and mathematical hobbyists with equal interest.

"He was like a butterfly going from one thing to another, always with magical qualities to the results," said Simon Kochen, professor of mathematics, emeritus, a former chair of the department, and a close collaborator and friend.

The game was introduced in an October 1970 issue of Scientific American's mathematical games column, whose creator, the late Martin Gardner, was friends with Conway. Conway continued his interest in "recreational mathematics" by inventing numerous games and puzzles. At Princeton, he often carried in his pockets props such as ropes, pennies, cards, dice, models and sometimes a Slinky to intrigue and entertain students and others.

"An extrovert by nature, John liked to be at the center of mathematical discussions and he enjoyed thinking and inventing on the spot," Sarnak said. "To this end he gave up his regular office in the Princeton mathematics department and moved into the big common room where he could always be found holding court on the latest (often his!) mathematical development or invention. On days of little mathematical news he would be challenging others to mathematical games or puzzles and now that I think of it, I can't recall any instance where he did not win.

The Euler Book Prize is awarded annually to an author or authors of an outstanding book about mathematics. The Prize is intended to recognize authors of exceptionally well written books with a positive impact on the public's view of mathematics and to encourage the writing of such books. Eligible books include mathematical monographs at the undergraduate level, histories, biographies, works of fiction, poetry; collections of essays, and works on mathematics as it is related to other areas of arts and sciences. To be considered for the Euler Prize a book must be published during the five years preceding the award and must be in English. The Euler book prize is $2,000.

According to one definition, learning a concept consists of making mental connections to other concepts and ideas. The more connections, the more complete the learning. The creators of the That's Calculus! videos, Dartmouth professors Dorothy Wallace and Marcia Groszek, suggest connections through visual imagery, metaphor and humor, to help students learn mathematical concepts and remember them.

It is here that the case starts to become shaky. The number theorist G. H.Hardy wrote in his Mathematician's Apology in 1940 that "the best mathematics is serious as well asbeautiful", going on to assert that "the 'seriousness' ofa mathematical theorem lies not in its practical consequences ... but in thesignificance of the mathematical ideas which it connects". By thismeasure, magic squares, entertaining though they are, rank mathematicallyjust a little higher than chess problems (Hardy's example of real butunimportant mathematics).

Perhaps Franklin just came too late to pure mathematics, already a maturefield in his era, but early to electricity, where the work of a gentlemanresearcher could still be ground-breaking. It was Franklin's electricalwork, viewed in the light of Maxwell's equations, that gave us genuinemathematical magic.

There are of course also quite nice things to say about this book.First of all there is its very elementary approach, but it is still discussing many mathematical objects and ideas.Sometimes they are only mentioned or briefly touched upon.Not really analytic proofs of course, but sometimes strong suggestionsand indications are given for limiting value.Similarly we meet also Einstein's relativity theory as I mentioned above,but also several different geometric proofs of the Pythagoras theorem,continued fractions, Platonism, complex numbers, $i^i$,Schrödinger's equation, Stirling's asymptotic formula for the factorial, and many others.

There are a few of problems or puzzles to solve (but not many) which get solutions at the end of the chapter, and for the hungry readerthere is a list of references to read more.Thus, if you are interested in mathematical issues andpuzzles of the mathematical type, you willcertainly enjoy this book even if you have only a minimalbackground. Just be aware that numerology is as alien to mathematicsas penguins are to the Amazon jungle. 041b061a72


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