In this book the emphasis is on mental calculation, mainly mental
multiplication, but addition, subtraction and division are also covered.
Each chapter focuses on one Vedic formula and shows various ways in
which it can be used. There is a detailed introduction outlining the
benefits of mental mathematics. 102 pages, size 16cm by 24cm, paperback.
2003 (first published 1991); Author: K. Williams; ISBN 978-1-902517-15-5.
Price $12 (including postage).
In the book, The Natural Calculator, the author shows how natural
processes of the mind are associated with mental calculation. Since
multiplication operation reveals remarkably the properties of number,
the book deals mainly with it. Prodigies are recognised by their ability
to give instantly products of large numbers. The book is so written
that it can be gone through, in any desired sequence. Algebraic proofs
justifying the approaches are given at the end of the book. Problem-solving
skills get a boost. The objective is to show how reliance on the calculator
is harmful, as it deprives the mind from exercising its capabilities
which get frozen through repetitive endeavour. Major part of mathematics
education can be directed to give one-line response to basic operations,
singly or combined.
The experience is exhilarating and delightful, once one gets settled
in the Vedic way. Availability of choice and the judgement that it
entails provides one with expertise to shun routineness, the bane
of curricular learning today. As Tirthaji affirms, there is flexibility,
innovativeness and creativity in mathematical computation and this
brings mathematics to life. The criteria for looking upon an activity
as natural are spelled out by advent of increasing speed and accuracy.
To put it in other words, calculation requiring pencil and paper is
objective and external, whereas when resorted to mentally is subjective
and internal and as vouchsafed by transcendental meditation is deeper.
Instructional standards today centre round general methods but Vedic
mathematics emphasises that every problem is unique with its own singularly
arrived at solution. To ignore this tantamounts to underestimating
children's capabilities to hold and remember.
There are nine chapters, each of which is flagged with a bordered
version of the experiences in brief of child prodigies who during
the last four centuries exhibited extraordinary powers of mental calculation
and baffled the audiences. Some of them blossomed into professors
of mathematics like Aitken. The book is presented in prescribable
format with models and exercises for practice with answers given at
the end. It closes with general exercises with hints for two sections.
A list of references is also provided.
"The Natural Calculator" - Contents
1 ON THE FLAG calculating from left to right
2 PROPORTIONATELY multiplication devices involving doubling
3 BY ONE MORE THAN THE ONE BEFORE squaring numbers that end
in 5; a special type of multiplication
4 THE FIRST BY THE FIRST AND THE LAST BY THE LAST calculating
checks; a special type of multiplication
5 ALL FROM 9 AND THE LAST FROM 10 numbers near a base; subtraction;
numbers near different bases; multiplying three numbers simultaneously;
squaring numbers near a base; multiplication by 9's; addition and
6 VERTICALLY AND CROSSWISE general multiplication: multiplying
2-figure numbers, 3-figure numbers, moving multiplier method, 3 and
4-figure multiplication; general squaring; division- divisor near
a base; general division
7 USING THE AVERAGE products using an average
8 BY ADDITION AND BY SUBTRACTION squares from squares; products
9 BY MERE OBSERVATION use of special numbers
"The Natural Calculator" - Back Cover
Vedic Mathematics was rediscovered from ancient Sanskrit texts earlier
this century by Bharati Krsna Tirthaji (1884-1960). He found that
all problems in pure and applied mathematics can be solved easily
with the aid of sixteen simple Sutras, or word-formulae: for example
All From 9 and the Last From 10 or Vertically and Crosswise. This
may sound incredible but the Vedic system offers a very different
approach to mathematics that is both powerful and fun.
The Vedic system is so easy it is really a system of mental mathematics.
It has a coherence and beauty that make it very attractive and some
of the methods are truly amazing in their efficiency and simplicity.
Many schools now teach Vedic Mathematics and a common response from
children is: "Why were we not shown this before?".
The Natural Calculator introduces this system; dealing with mental
mathematics it covers various types of multiplication, addition, subtraction