Mathematical Elegance: An Approachable Guide to by Steven Goldberg

By Steven Goldberg

The center of arithmetic is its beauty; how it all suits jointly. regrettably, its good looks frequently eludes the majority of those who find themselves intimidated by way of worry of the trouble of numbers. Mathematical Elegance treatments this. utilizing countless numbers of examples, the writer offers a view of the mathematical panorama that's either available and fascinating.

At a time of outrage that American early life are bored by way of math, there's renewed curiosity in bettering math abilities. Mathematical Elegance stimulates scholars, in addition to these already skilled within the self-discipline, to discover a few of the unforeseen pleasures of quantitative pondering. Invoking mathematical proofs recognized for his or her simplicity and brainteasers which are enjoyable and illuminating, the writer leaves readers feeling exuberant—as good as confident that their IQs were raised via ten points.

A host of anecdotes approximately recognized mathematicians humanize and supply new insights into their lofty matters. Recalling such vintage works as Lewis Carroll’s Introduction to Logic and A Mathematician Reads the Newspaper through John Allen Paulos, Mathematical Elegance will energize and enjoyment a large viewers, starting from intellectually curious scholars to the enthusiastic basic reader.

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The Powers That Be You may have wondered why a number raised to the zero power is one. You may have thought that a number raised to the zero power should be itself (because the number is not multiplied by anything, so it should just remain itself ). But then you probably then remembered that a number raised to the first power is itself, and you would not want a number raised to the power 0 to equal the same number as the number raised to the power 1. But why couldn’t we have a number raised to the power 0 be 0, just as a number multiplied by 0 is 0?

Etc. Now, draw a diagonal line, beginning with the first digit of the first number, the second digit of the second number, the third digit of the third number, ad infinitum. The unending diagonal number we get will begin 7074553 . . Add 1 to each digit of our diagonal number. The new number will begin 8185664 . . Notice that the diagonal number we end up with cannot be the same as the first number because its first digit is an 8, not a 7. It cannot be the same as the second number because its second digit is a 7, not a 6.

The largest has over 130,000 digits. All are even numbers. Is there an odd perfect number? No one has discovered one or proven that there could not be one. Incidentally, a “sublime” number is one that has the number of divisors (that leave no remainder) that is perfect and the sum of these divisors is perfect. There are only two known sublime numbers. One is 698, 655,567,023,837,898,670,371,734,243,169,822,657,830,773,351,885,970, 528,324,860,512,791,691,264. The other is 12 (1 + 2 + 3 + 4 + 6 + 12, the six divisors, sum to 28).

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