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Gupta1974j

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Gupta1974j

1. 1. The Mathematics Bdrcrtion SECTION BVo l. V I I I , No.4, D c c . 1 9 74 G L IM P S E S OFA N C IE N T IN D IA N M A T HE M A T I CSNO . 2 1 A lfef\$ht and Dlstance Prolrlem From Tlre AnyanrrATiYA 67 R.C. Gupta, Dept. of Mathcnatics Birla InstitutcdTechnolog2 P,O. Mesra, RANCHI. (Recoived l7 October (1974) l. Introduction Let LO be a lamp-post standing vertically on a level ground at the point O and carry-ing the lamp at its top point.L. Supposethat two equal vcrtical gnomcns (danku) are placed(or the same gnomon is placed succcssively) thc two points P and Q(P being nearer to atthe lamp-post) on the level grourrd such that the horizontal line joining P and Q passesrhro-rrgh O, the foot of the lamppori. Let S and Z be the positionr of the tips (agra) of theshadorvsof the gnomons in the two positions or crses. Thur the tops, M and ,M of thegnonrons will lie on lhe straight lines ZS and LT respectivcly. The points o, P, S, Q, andT n,ill be collinear.z*. t. Let as use the following symbols : First shadow PS:sr Second shadow QT-sz Distance between the tips (or ends) of the slradows ST*d Height of the lamp-post LO:h Lenght or height of each gnomon MP <tr NbC OS:ur - -- r o sq OT:uz FIGUIiE (so that uz-a:d) A rrrle for finding the height of the lampport and distancerof the tips of the shadowsfrom the foot of the lrmp-post is given by qrdCaCqq lryabhata I (born 476 .a.O.| in hisfamols uork cellcd the qrtqqftq Arlebht:ya (abbreviated henceforward as AB;r 1nt *"shall discusr now. Mern b e r . f n t e r n a t i o n a l Co m m issi,r tr o n Hi:to r y o f Il athemati cs