Mathematical Carnival: From Penny Puzzles, Card Shuffles and by Martin Gardner

By Martin Gardner

From Penny Puzzles, Card Shuffles, and methods of Lightning Calculators to curler Coaster Rides into the Fourth size. A round-up of Tantalizers from medical American with a Foreword by means of John Horton Conway and stylish Mathematical Commentaries, Afterthoughts, a brand new Postscript, and a brand new Bibliography by means of Mr. Gardner, Backtalk from Readers, and 1 15 photographs and Diagrams.

Show description

Read Online or Download Mathematical Carnival: From Penny Puzzles, Card Shuffles and Tricks of Lightning Calculators to Roller Coaster Rides into the Fourth Dimension PDF

Similar mathematics books

The Mathematics of Paul Erdos II (Algorithms and Combinatorics 14)

This is often the main complete survey of the mathematical lifetime of the mythical Paul Erd? s, probably the most flexible and prolific mathematicians of our time. For the 1st time, all of the major components of Erd? s' study are lined in one venture. as a result of overwhelming reaction from the mathematical group, the undertaking now occupies over 900 pages, prepared into volumes.

Extra info for Mathematical Carnival: From Penny Puzzles, Card Shuffles and Tricks of Lightning Calculators to Roller Coaster Rides into the Fourth Dimension

Sample text

I n every base notation there are two ways to express an integral fraction by an aleph-null string of digits. 2500000 . . 2499999. . Although it is not necessary for the validity of the diagonal proof in decimal notation, it is customary to avoid ambiguity by specifying that each integral fraction be listed only in the form that terminates with an endless sequence of nines, then the diagonal number is constructed by changing each digit on the diagonal to a different digit other than nine or zero.

FIGURE 16 Straight-line configuration FIGURE 17 How to place thc pennies 6. The sixth configuration of 10 pennies having five straight lines of four coins each is shown in Figure 16. 7. To put penny C between two touchilig pennies A ancl B without touching A or moving B, place a fingertip firmly on R and then slide C against B. Be sure, however, to let go of C before it strikes B. The impact will propel A away from B, so that C can be placed between the two previously touching coins. 8. Three pennies can be placed with two heads on one side of a line and two tails on the other as shown in Figure 17.

The set of all subsets of an aleph-null set is a set with the cardinal number 2 raised to the power of aleph-null. This proof shows that such a set cannot be matched one to one with the counting integers. It is a higher aleph, an "uncountable" infinity. Cantor's famous diagonal proof, in the form just given, conceals a startling bonus. It proves that the set of real numbers (the rationals plus the irrationals) is also uncountable. Consider a line segment, its ends numbered 0 and 1. Every rational fraction from 0 to 1 corresponds to a point on this line.

Download PDF sample

Rated 4.01 of 5 – based on 22 votes