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cess in mathematics is very much a matter of having a feeling

a lways be consider ed as a possible a pproach. gr a phs ther efor e

it is all about, is as much an emotional as an intellectual thing.

human h

what is going on, not blindly following the steps of the for mal

should per meate all mathematical wor k; one should for m the habit

it comes only from r epeated use. it is no use, the first time you see

of giving

cess but seeing the wor k in the fr a mewor k of some intelligible

of per petua lly ask ing oneself. would a gr aph help to m a k e this

a gr aph, mak ing an immense effort to dig out its secr et message.

that str

uation. the first thing to do in approaching an y piece of math-

mor e meaningful? the mor e you do this, the mor e helpful gr aphs

this w ill only discour age you. i can not find an ything to put into


atics is to cast a rou nd for some way of appr eci ating w h at is

become, since you gr adually build up a sort of a lbum of fa miliar

this chapter that str ik es me as at all unusual or profound. but i

t w ins th

olved, some way of m a k ing the question v i v id to yourself so

gr aphs; when you have met the same gr aph in half a dozen situations,

believe that an yone w ho r epeatedly uses the simple ideas in this

gr aphs h

at you w ill be a ble to think a bout it just as you think a bout

it natur a lly con veys mor e to you than it possibly can the first

chapter w ill eventually gain very much in confidence and insight.

w ill be e

miliar things in every day life. gr aphs ar e one way of br inging

time you meet it. it has acquir ed all k inds of extr a associations;

w hat then can w e lear n by look ing at a gr aph? a mong the first

yet w e a

t the meaning of a mathematical situation. they ar e not a magic

it has become fa miliar . it is important to r ealize that this fa mil-

things to look for ar e high points and low points - mountain peaks

a gr aph;


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