How Math Explains the World.pdf
(^5) i The Hope Diamond of Mathemat cs The Curse The Hope Diamond is probably the most famous diamond in the world. Its fame com ...
diamonds, but not forestall tragedy. Her firstborn son died at age nine in a car crash, her daughter committed suicide when she ...
sides by 8 to show that x^19 / 8. Algebra was unavailable to Ahmes of Egypt, who contributed a section entitled “Directions for ...
Duels—of an intellectual nature—were one method by which up- and- comers of the time would obtain prestigious academic positions ...
goes into establishing a result such as the solution of the depressed cubic, a nd most of t h at is er ror. We k now t h at g re ...
table to the top of the table—these equations reduce to a quadratic! Solv- ing 3stC for t in terms of s yields tC/3s, and subs ...
sponded with the sixteenth-century equivalent of “Sorry, my agent is working on a book deal,” but Cardano persisted, and finally ...
expansion of (yB/3)^3 , and the term By^2 that occurs in the expansion of B(yB/3)^2 ; these terms cancel so the result is a de ...
lot to root for back in the sixteenth century). Ferrari, naturally, felt that his own brilliance was responsible for his victory ...
including Leonhard Euler and Joseph-Louis Lagrange. The latter pub- lished a famous paper, Ref lections on the Resolution of Alg ...
tive inverse x^1 that satisfies xx^1 x^1 x1. These are the key properties used to define a group G, which is a collection o ...
the shuff le that doesn’t change the position of any card—the “phantom shuff le” that is sometimes performed by magicians or car ...
ple, 3 5 5 3. The same cannot be said of shuff les. If shuff le g simply f lip-f lops the top two cards (and leaves the othe ...
to Abel, his papers had been generating increasing excitement in the mathematical community, and two days after his death a lett ...
have solutions. Remarkably, Galois theory also provides clear explana- tions of three compass-and-straightedge impossibilities w ...
gives the original two (true) statements AB 6 and AB4. If a deck of two cards is shuff led, where A is initially on top and B ...
proven to have solutions by radicals, but one can say with some assurance that mathematics is a lot more interesting a subject b ...
or eight decimal places. Numerical analysis is not, as its name would sug- gest, the analysis of numbers; it is the branch of ma ...
obtained from triangle 1 by performing R first, then F, denoted RF; trian- gle 6 is likewise obtained by performing F first and ...
analysts, defined by f(x) 0 if x is rational and f(x) 1 if x is irrational, can be calculated for every valuable of the variab ...
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