maths ppt with java applets

8/3/2019 Maths Ppt With Java Applets

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INTRACTIVE INTRODUCTIONINTRACTIVE INTRODUCTION

TheThe followingfollowing conversationconversation willwill helphelp usus toto understandunderstandsomesome basicbasic lessonslessons onon coordinatecoordinate geometrygeometry..

MentorMentor ::-- Please,Please, drawdraw aa straightstraight horizontalhorizontal lineline atat thethe centercenter ofof youryourgraphinggraphing paperpaper.. AsAs wewe countcount:: "Zero,"Zero, one,one, two,two, threethree...."" wewe putput thethe numbersnumbers

onon thethe line,line, oneone numbernumber perper lineline ofof thethe graphgraph paperpaper.. WhenWhen wewe countcountbackwards,backwards, wewe distinguishdistinguish thethe numbersnumbers thatthat comecome beforebefore zerozero byby placingplacingaa ""--"" signsign inin frontfront ofof them,them, soso itit goesgoes:: "Two,"Two, one,one, zerozero......"" MakeMake suresure thatthat youyouevenlyevenly spacespace thethe numbers,numbers, sincesince thethe distancedistance fromfrom 11 toto 22 shouldshould bebe thethesamesame asas thethe distancedistance fromfrom 22 toto 33..



StudentStudent:: MinusMinus one,one, minusminus two,two, minusminus threethree......

MentorMentor:: WhatWhat wewe havehave nownow isis calledcalled aa "number"number line"line" oror"coordinate"coordinate lineline.."" ItIt cancan bebe usedused toto describedescribe wherewhere aa pointpoint isisonon thethe lineline.. ToTo givegive thethe exactexact "address""address" ofof aa point,point, wewe justjust looklook

atat howhow farfar thethe pointpoint isis fromfrom zero,zero, usingusing aa minusminus symbolsymbol forfornumbersnumbers toto thethe leftleft ofof zerozero.. ExceptExcept wewe don'tdon't callcall itit aa minusminussign,sign, wewe referrefer toto thesethese numbersnumbers asas "negative"negative..""

StudentStudent:: SoSo thethe addressaddress ofof thisthis pointpoint ( Student( Student highlightshighlights 44) ) isis

44,, andand thethe addressaddress ofof thisthis pointpoint ( Student( Student highlightshighlights --5 5) ) isisnegativenegative 5 5..



MentorMentor: Excellent. Now we want to get more freedom of: Excellent. Now we want to get more freedom ofmovement. We will let our points be anywhere on the paper,movement. We will let our points be anywhere on the paper,

not only on the line. To give an address for the points thatnot only on the line. To give an address for the points thatare not on the number line we will need to make a verticalare not on the number line we will need to make a verticalnumber line. Draw a vertical line through the zero of thenumber line. Draw a vertical line through the zero of thehorizontal number line. Now label it with positive numbershorizontal number line. Now label it with positive numbersabove the horizontal number line and the negative numbersabove the horizontal number line and the negative numbers

below the horizontal number line. Instead of sayingbelow the horizontal number line. Instead of sayinghorizontal number line and vertical number line all the timehorizontal number line and vertical number line all the timelet's call them by their mathematical names. The horizontallet's call them by their mathematical names. The horizontalnumber line is called the xnumber line is called the x--axis and the vertical number lineaxis and the vertical number line

is yis y--axis.axis.



StudentStudent: Well, I would go up three blocks and then right two: Well, I would go up three blocks and then right twoblocks.blocks.

MentorMentor: Sure. How else can we get there?: Sure. How else can we get there?

StudentStudent: We can first go two blocks to the right, and then: We can first go two blocks to the right, and then

three blocks up.three blocks up.



StudentStudent: Or we can go one right, three up, and one more: Or we can go one right, three up, and one moreright.right.

MentorMentor: There are many ways to get from one point to: There are many ways to get from one point toanother point (how many ways, by the way?). To create aanother point (how many ways, by the way?). To create astandard way of referring to points, mathematicians came tostandard way of referring to points, mathematicians came to

an agreement that they will always name the point after onean agreement that they will always name the point after onespecial way of walking. Starting from zero, we go all the wayspecial way of walking. Starting from zero, we go all the wayto the right or to the left, counting steps: one, two. Then weto the right or to the left, counting steps: one, two. Then wego up or down: one, two three steps up. Then we write thego up or down: one, two three steps up. Then we write thenumber of steps like that: (2,3). Again, the first number isnumber of steps like that: (2,3). Again, the first number is

"left"left--right," the second "upright," the second "up--down." A negative sign meansdown." A negative sign meanseither left or down. So, if our point is ( either left or down. So, if our point is (--2,2, --3), we go two steps3), we go two stepsto the left, and then three steps down. Do you remember theto the left, and then three steps down. Do you remember thenames of our number lines?names of our number lines?



StudentStudent: Yes, the horizontal line is called the x: Yes, the horizontal line is called the x--axis and theaxis and thevertical line is called the yvertical line is called the y--axis.axis.

MentorMentor: Can any one think of a better way to describe the: Can any one think of a better way to describe theaddress of a point instead of (leftaddress of a point instead of (left--right, upright, up--down)?down)?

StudentStudent: Could we call the address by the names of the lines?: Could we call the address by the names of the lines?

MentorMentor: Yes, so the address of a point would be described as: Yes, so the address of a point would be described as( (x,yx,y) instead of (left ) instead of (left--right, upright, up--down). The mathematical termdown). The mathematical termfor the address of a point is called coordinates. Now doesfor the address of a point is called coordinates. Now doeseveryone see how the xeveryone see how the x--axis and yaxis and y--axis divide our paper intoaxis divide our paper into

four sections?four sections?



StudentStudent:: YesYes andand II betbet theythey havehave namesnames too!too!

MentorMentor:: YouYou areare right!right! TheseThese sectionssections areare calledcalled quadrantsquadrants..

StudentStudent:: AreAre theythey calledcalled quadrantsquadrants becausebecause therethere areare fourfour ofof themthemandand therethere areare fourfour sidessides toto aa quadrilateral?quadrilateral?

MentorMentor:: GoodGood observation!observation! WeWe getget ourour prefixprefix "quad""quad" fromfrom thethe LatinLatin

wordword ""quattuorquattuor"" whichwhich meansmeans fourfour.. EachEach ofof thesethese quadrantsquadrants arearereferredreferred toto byby aa romanroman numeralnumeral..TheThe firstfirst quadrantquadrant containscontains allall thethe pointspoints withwith positivepositive xx andandpositivepositive yy coordinatescoordinates andand isis representedrepresented byby thethe romanroman numeralnumeral II..TheThe secondsecond quadrantquadrant containscontains allall thethe pointspoints withwith negativenegative xx andand

positivepositive yy coordinatescoordinates andand isis representedrepresented byby thethe romanroman numeralnumeral IIII..TheThe thirdthird quadrantquadrant containscontains allall thethe pointspoints withwith negativenegative xx andandnegativenegative yy coordinatescoordinates andand isis representedrepresented byby thethe romanroman numeralnumeral IIIIII..TheThe fourthfourth quadrantquadrant containscontains allall thethe pointspoints withwith positivepositive xx andandnegativenegative yy coordinatescoordinates andand isis representedrepresented byby thethe romanroman numeralnumeral

IVIV..



INTRODUCTIONINTRODUCTION

FiveFive blindblind menmen foundfound anan elephantelephant.. EachEach feltfelt thethe animalanimal andanddescribeddescribed itit toto thethe othersothers.. AnAn argumentargument ensuedensued.."The"The elephantelephant isis likelike aa rope,"rope," saidsaid thethe firstfirst man,man, feelingfeeling thethe tailtail..

"No,"No, thethe elephantelephant isis likelike aa wall,"wall," saidsaid thethe secondsecond man,man, feelingfeeling thethe sideside.."The"The elephantelephant isis likelike aa blanket,"blanket," saidsaid thethe thirdthird man,man, feelingfeeling itsits earear.."The"The elephantelephant isis likelike aa tree,"tree," saidsaid thethe fourthfourth man,man, feelingfeeling itsits trunktrunk.."You're"You're confusedconfused.. TheThe elephantelephant isis likelike aa spear,"spear," saidsaid thethe fifthfifth man,man, feelingfeelingitsits tusktusk..

ThenThen camecame thethe KingKing.. HeHe sawsaw thethe wholewhole elephantelephant andand hehe alonealonediscerneddiscerned thethe realityreality ofof thethe elephantelephant..

InIn thisthis ProblemProblem ofof thethe Week,Week, wewe willwill exploreexplore howhow thethe looklook ofof aagraphgraph ofof aa functionfunction cancan vary,vary, dependingdepending onon howhow oneone setset thethe domaindomain andandrangerange ofof thethe graphgraph windowwindow..



TO DO AND NOTICETO DO AND NOTICE

OpenOpen thethe applet,applet, belowbelow.. (Note(Note:: TurnTurn upup thethe volumevolume onon

youryour computercomputer..) ) ExperimentExperiment withwith changingchanging thethe numbernumbervaluesvalues forfor thethe minimumminimum andand maximummaximum forfor bothboth thethe domaindomainandand rangerange.. NoticeNotice howhow thethe graphgraph andand axesaxes looklook differentdifferenteacheach timetime afterafter youyou presspress "Zoom"Zoom.."" NoticeNotice thatthat eacheach domaindomainandand rangerange youyou trytry isis recordedrecorded inin thethe tabletable toto thethe rightright ofof thethegraphgraph..

JAVA JAVA APPLET APPLET



THETHE CONCEPT CONCEPT

SamSam thethe ChameleonChameleon illustratesillustrates graphinggraphing pointspoints inin thetheplaneplane.. WhenWhen lookinglooking forfor aa particularparticular point,point, SamSam movesmoves alongalong

thethe xx--axisaxis toto reachreach thethe point'spoint's xx coordinatecoordinate andand thenthen stickssticksoutout hishis longlong tonguetongue toto reachreach thethe point'spoint's yy coordinatecoordinate..



INSTRUCTIONSINSTRUCTIONS

ClickClick onon thethe graphgraph toto makemake SamSam graphgraph thethe pointpoint underunderyouryour cursorcursor.. AfterAfter havinghaving graphedgraphed thethe point,point, SamSam willwill blendblendinin withwith thethe backgroundbackground toto letlet youyou studystudy whatwhat hehe hashas donedone..HoldHold downdown thethe mousemouse buttonbutton andand movemove thethe cursorcursor aroundaround toto

movemove thethe graphgraph..

JAVA APPLET JAVA APPLET

maths ppt with java applets

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