Title The Book of Numbers 3.0 MB 146
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CONTENTS
AUTHOR'S NOTE
ANECDOTES
Also by Shakuntala Devi
Back Cover
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Page 1

SHAKUNTALA DEVI'S

NUMBEBS

Everything you always wanted to know about
numbers but was difficult to understand.

Page 73

to reduce multiplication to addition with the aid
of tables of quarter squares. The method is very
old. There are many tables of quarter squares and
the most extensive table lists quarter squares of
integers upto 200,000. The method is very useful
and economical.

147
WHAT ARE 'QUARTERNIONS' ?

If you do not use the properties of order and the
commutative law of multiplication, we obtain an
interesting further extension of the complex number
system known as Quarternions q.v. in abbreviation.

Quarternions are of the form a + bi + cj + dk
where a, b, c, d are real.

148
WHAT IS THE 'THEORY OF NUMBERS' ?

The Theory of Numbers is concerned with the
study of the properties of integers or whole num-
bers. The proofs of many of the Theory use the
deepest resources of mathematics. However, some
of the most interesting conjectures are still un-
proved.

Topics of the Theory of the Numbers can be listed
as follows?

71

Page 74

I.Divisibility and Primality:

a. Elementary Definitions; Factorizations into
Primes.

b. Residue Classes; Eulers Theorem
c. Congruences in one unknown

city Law
e. Factorization of Numbers; Mersenne Primes

II.Representation by forms:

b. Genera of Quadratic*. forms; Formulas for
Number of Representations

c. The Numbers Represented by a Quadratic
Form: universal forms Representation of
zero.

d. Automorphs and Reduction of indefinite

e. Diophantine Equations

III.Topics in Analytic Number Theory:

a. Gauss's Class-Number Conjencture

b. Distribution of Primes; Asymptotic Formulas

a. Partitions
b. The waring problem and related problems

72

Page 145

Also by Shakuntala Devi

Puzzles to Puzzle You

Match Your Wits with the Human Comput r!

The 150 puzzles included in this book are enjoyable
exercises in reason intended to sharpen your wits.

"Engrossing and entertaining book - there is
something of interest for all".

Statesman

"Provides excitement as well as recreation".

Patriot

More Puzzles to Puzzle You

This book offers over 300 tantalising puzzles, brain-
teasers and riddles. The puzzles include every possible
type of mathematual recreation; time and distance
problems, age and money riddles, puzzles involving
geometry and elementary algebra and just plain
straight thinking.

"She leaves you spellbound with tabulating feats that
could be the envy of the best computers in the world".

l imes of India

Page 146

The Human Computer
explains and simplifies
EVERYTHING YOU ALWAYS WANTED
WAS DIFFICULT TO UNDERSTAND
Little Known Facts

9

99Ninth power of the ninth power of nine is the largest in the world of numbers that can be
expressed with just 3 digits. The answer is mind
staggering!

It will contain 369 mill ion digits. To read it
normally would take more than a year. To write
down would require 1164 miles of paper!

Brain Teasers
A necklace was broken during an amorous

struggle. 1/3rd of the pearls fell to the ground,
1/5th stayed on the couch, 1/6th were found by the
girl, and 1/10th recovered by her lover; six pearls
remained on the string. Say of how many pearls the
necklace was composed.

Numer ica l concepts Simpl i f ied and Explained
Numerals & Digits • Perfect Numbers & Amicab le

Numbers • Algor i thm & Logarithm • Associative &
Commutat ive Laws of Multipl ication • What are
G o o g o l & Googolp lex .

A n d over 20 ready — reference tables to