## You are a mathematician: a wise and witty introduction to the joy of numbersWhat is the largest number less than 1? If x and y are any of two different positive numbers, which is larger, x2 + y2 or 2xy? What do you get if you cross a cube and an octahedron? Discover the surprising answers as David Wells conclusively proves that: you Are a mathematician Praise for David Wells's The Penguin Dictionary of Curious and Interesting Numbers. "This is a fascinating, strange, and probably unique book, one that I will look at again and again. As soon as I had taken a good look at it, I went out and bought three more copies to give to friends." —New Scientist. "David Wells's book about curious and interesting numbers is a quirky classic." —William Dunham Author, Journey Through Genius. Are you on friendly terms with numbers? You will be after reading this delightful introduction to the fascinating and challenging world of mathematics. Bestselling author David Wells, a Cambridge math scholar and former teacher, explores the many patterns, properties —and problems —associated with numbers in a witty, thoroughly engaging style that is both entertaining and informative. Whether you are a math aficionado or whether you, as the author puts it, "panic and start sweating at the sight of a sum," Wells makes one point abundantly clear: You Are a Mathematician. From basic arithmetic to algebraic equations, from the purely practical to the abstract, this is an ideal guide to the potential and pleasures of math. Surprising patterns emerge from the simplest groupings of numbers. The many secrets hidden inside of triangles are revealed, as are the origins of a host of mathematical theories and principles, from Aristotle to Euclid and Galileo. On a journey from the ancient Greeks to quantum theory, Wells shares intriguing anecdotes from history, such as how eighteenth-century European military commanders calculated how many cannonballs their enemies had stacked up next to their cannons. David Wells invites us to discover the sense of wonder and fun that is so much a part of mathematics. Mathematical thinking is often very much like a game, relying on cunning tactics, deep strategy, and brilliant combinations as much as on observation, analogy, and informed guesswork. To illustrate, Wells includes over 100 brainteasing puzzles and problems, ranging from Ptolemy's theorem to Euler's famous solution to the Königsberg bridge problem and Koch's snowflake curve. Modern-day computer buffs will also enjoy the underground classic, the Game of Life, invented by Princeton mathematician John Conway. Offering a comprehensive and stimulating look at the myriad aspects of mathematics —whether as a household helper or an invaluable tool of science —You Are a Mathematician covers a wide range of topics and applications. It is an ideal guide to the potential and pleasures to be found in math. |

### From inside the book

Results 1-3 of 15

Page 380

0 Reading the sequence of diagrams backwards suggests to you that

extremely irregular — turn to Frame 27. 0 To see what happens when Buffon's

idea is applied to polyhedra — turn to Frame 16. 11 Buffon's original problem

suggests several natural variations. His observation that the midpoints of the

sides are the centroids of adjacent vertices suggests that you might consider

other centroids.

0 Reading the sequence of diagrams backwards suggests to you that

**Buffon's****process**when reversed will turn a 'normal' looking hexagon into somethingextremely irregular — turn to Frame 27. 0 To see what happens when Buffon's

idea is applied to polyhedra — turn to Frame 16. 11 Buffon's original problem

suggests several natural variations. His observation that the midpoints of the

sides are the centroids of adjacent vertices suggests that you might consider

other centroids.

Page 396

0 It occurs to you that if

regular', or pseudo-regular, then the reverse of

irregular — turn to Frame 26. 25 One set of alternate midpoints is §(A + B), §(C +

D) and §(E + F). The other set is §(B + C), §(D + E) and {(F + A). The average of

either set, which is to say the centroid of either triangle, is the same: §(A + B + C +

D + E + F) which is also the centroid of the original hexagon. 0 It occurs to you

that all ...

0 It occurs to you that if

**Buffon's process**makes a hexagon more and more 'regular', or pseudo-regular, then the reverse of

**Buffon's process**will make it moreirregular — turn to Frame 26. 25 One set of alternate midpoints is §(A + B), §(C +

D) and §(E + F). The other set is §(B + C), §(D + E) and {(F + A). The average of

either set, which is to say the centroid of either triangle, is the same: §(A + B + C +

D + E + F) which is also the centroid of the original hexagon. 0 It occurs to you

that all ...

Page 397

a wise and witty introduction to the joy of numbers David G. Wells. 26 Given five

of the six vertices of a hexagon, you can reverse

any point you choose, because the starting point and the sixth point will then

uniquely define the final, sixth, vertex as the midpoint of the line segment needed

to close the hexagon. In Fig. 13.31, the five vertices are labelled A to E. The first

arbitrarily chosen point is X, and the sixth point is Y. Here F is the midpoint of XY

and the ...

a wise and witty introduction to the joy of numbers David G. Wells. 26 Given five

of the six vertices of a hexagon, you can reverse

**Buffon's process**, starting withany point you choose, because the starting point and the sixth point will then

uniquely define the final, sixth, vertex as the midpoint of the line segment needed

to close the hexagon. In Fig. 13.31, the five vertices are labelled A to E. The first

arbitrarily chosen point is X, and the sixth point is Y. Here F is the midpoint of XY

and the ...

### What people are saying - Write a review

#### You are a mathematician: a wise and witty introduction to the joy of numbers

User Review - Not Available - Book VerdictIf you have ever wondered what makes mathematics so fascinating to a mathematician, this may be the book for you. Wells, a British teacher and author of several books of problems and popular ... Read full review

### Contents

Numbers and patterns | 30 |

Mathematics as science | 49 |

The games of mathematics | 82 |

Copyright | |

10 other sections not shown

### Other editions - View all

### Common terms and phrases

algebra analogy approximation argument average Buffon’s process calculate cells cellular automaton centre of gravity centroid chess circle complex numbers conﬁdent constructed cube curve deﬁned difﬁcult discovered distance divergent series divided edges ellipse equal equation equilateral triangles Euclidean geometry Euler Euler’s relationship example experiment faces fact factors Fermat ﬁgure ﬁnd ﬁnding ﬁrst ﬁt ﬁve ﬁxed formula four G. H. Hardy Galileo geometry happens hexagon hyperbola idea imagine inﬁnite integers length line joining looking mathematicians mathematics midpoints moves odd numbers original triangle pairs parabola parallelogram Pascal path pattern pentagon plane polygon polyhedron position possible prime numbers problem proof properties proved puzzle Pythagoras Pythagorean triples quadrilateral rectangle reﬂection remainder result roots scientiﬁc sequence shape shown in Fig shows sides simple solution solved sphere starting straight line sufﬁcient Suppose symmetry tangent tessellation theorem total number triangular numbers turn to Frame vertex vertices weight