School: a monthly record of educational thought and progress . \- C,instead of merely the particular line along which itvanishes, and might with advantage be brought rathermore prominently forward in text-books where its appli-cation seems to be limited to the discussion of the positive and negative sides of a straight line. A HP = SimUarly, KP = A Ax -I- By -I- C But PL^ + PL = B I PH2 -r l^pT A^ -f B-[Kx + By -h CfAx + By + C. JW+W Hence, any one of the three values , ,A- + may be taken as the geometrical equivalentfor Kx 4- By + C. As for the application of graphs to the solut
School: a monthly record of educational thought and progress . \- C,instead of merely the particular line along which itvanishes, and might with advantage be brought rathermore prominently forward in text-books where its appli-cation seems to be limited to the discussion of the positive and negative sides of a straight line. A HP = SimUarly, KP = A Ax -I- By -I- C But PL^ + PL = B I PH2 -r l^pT A^ -f B-[Kx + By -h CfAx + By + C. JW+W Hence, any one of the three values , ,A- + may be taken as the geometrical equivalentfor Kx 4- By + C. As for the application of graphs to the solution ofordinary arithmetical or algebraical problems, we areof Mr. Halls opinion that they should be used sparingly,and rather as illustrations than for investigation. Asa specimen of the way in which they may be used, ratherto illustrate the arithmetical solution than to supplantit, the following simple case may serve : A man who livestwo miles from his office finds that if he rides to it by tram,starting at , he is four minutes early, but that if he. FIG. 6 142 SCHOOL : A MONTHLY RECORD OF walks all the way he would he seven minutes late. Findhow much he should ride in order that by walking the resthe may be just in time. Here, if the pupil has once realised the general prin-ciple that in such cases the time saved by riding anydistance instead of walking it is proportional to thatdistance, and can state it intelligently, it would be ablameable waste of time to force him to work the problemby means of a figure which would take far longerthan the arithmetical solution, but he may beenabled to grasp the principle if a rough graph is drawnin Fig. 6. Time being marked along OX and distance alongOY, let OA represent the time taken to walk at a uniformrate the whole distance, OB. So that the diagonal OCis the graph for the complete walk. At the end of atime shown by BN let him take a tram and, traveUinguniformly, arrive at B at the end of a further intervalNQ, saving the inte
Size: 1803px × 1386px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1900, bookidschoo, bookpublisherlondon
