Vol. 5 No 10 - Pi Mu Epsilon

Pto6uhofi P/u-eL+p c^ited the Teachv~'~ !,lanuat 6o/i Excursions Int,-llathemat'vos by Beck, W.~ichefi and Cfiowe, pp, 271 -272. Gibbh no-tid tliegenvLoJL fiuuJU 6ound .in 8. 1.1. Stwatt, l.laanite.a.11 1962, p. 234.302. [Spring 19731 Pfiopmed by Vauid L. SU.vvman, We-it Loi Angde-i,CaH.6ofii'u.a and U.6te.d E.Ne.wnan, l.lu Aiplia VeUa Ffiatvt~wLy, New Yufik.A ta~~-~try i? hung on a wall so that its upper edge is a un.l*.. an?its lower edge b unit;, above the observer's eye-level.Show tha: inorder ti i.btain the mcct fav~rable view the observer should stand at adistance /ab from the waL:.I. Sotu^ion by R. Robire~on Rowe., Sac~.ame.nto, Catif,otiua.In Fig. 8, AB is the tapestry on wall ABC and tht? 2b:-erver'r i-y'-' :-at I a t a distance of IC = d from the wall.angle AIB = 9 should be a maximum.Since 1.'rt= AIC - BI,* = tanla/d - tanlb'd= tan 1 d(a + b)d"- abTor the most favorable view,'s less than go0, it :an be maximized by maximizing itstangent, and hence by maximizing its tangent divided bv (a - b).ting F(d) = d/(d2 + ab), we obtain Ft(d) = (ab d- )'(d- + abl2 = ,whence ab - d2 = ,, and d = ¥/ISComment by Pfiobiem EditofiLet-While this solution is correct in theory, ther.' are practical lim-itations. As C approaches B, b and d approach zero and 1 approaches 90'Thus, if a = 4 and b = .01, we find that d = .2 and even a myopic obser-ver would get a jaundiced view.:onstruct the cir-le thrwgh the top and the bc-tt~m pf the tapestrydnd tangent t. the eye-level line of the ..bserver (Fig. 9). The pointof crntact .f the circle wit:, the line is the optimum pcqition.For allpoints on the line :'ut~ide the circle, the tapestry subtends a smallerangle than at 'he rointis /ab.f ¥'-angency Hence the di-tance from the wallE. ANDERSON, Montana State U~uucuitq; ROBERT C . GEBHARDT, Hopatcong ,N. J.; JOHN M. HOWELL, Lct^fyiock, CaU&ofiiua; DONNELLY JOHNSON, W/u.gld-Patt&uon A^A Fome Bale, 0l~t.o; G. MAVRIGIAM, Youngh.town State U~uu~~lLty;BOB PRIELIPP, The. U~~iumLty 06 W-iiicoiu-in, O~Itko^h; DAN SCHOLTEN, WuteyanUihmLty. AAio hotved by the Pfiopoh&u UA-CII~ &if\vthe,tic ge.ome^iy.Pfiobiem EcLUtofi'ii Cotnmc~vtIt is hard to find an elementary calculus text that has not used;om