By Daniel J. Velleman
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Additional info for American Mathematical Monthly, volume 117, number 3, March 2010
Of course, one has to do so in a plane perpendicular to the planes of sides of the turning square. It is obvious that there are several degrees of freedom, meaning several ways to go wrong. The piece cut off could be the wrong length, or you could cut at the wrong angle, or perhaps the cross section wasn’t square to begin with. So, you start measuring to see how well you have done. In this measurement, though, it seems reasonable to make some assumptions. The basic one of interest here is that the saw cuts off a planar slice.
Lyons and Y. Peres, Probability on Trees and Networks (in progress); available at http://php. html. 11. T. Lyons, A simple criterion for transience of a reversible Markov chain, Ann. Probab. 11 (1983) 393– 402. 1214/aop/1176993604 12. H. M. Mahmoud, P´olya Urn Models, Texts in Statistical Science Series, CRC Press, Boca Raton, FL, 2009. 13. C. St. J. A. Nash-Williams, Random walk and electric currents in networks, Proc. Cambridge Philos. Soc. 55 (1959) 181–194. 1017/S0305004100033879 14. J. R. Norris, Markov Chains, Cambridge Series in Statistical and Probabilistic Mathematics, vol.
If the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent. The SAS, ASA, and AAS theorems are equally well known. The extension to other shapes is not often discussed, but we will have some remarks about the planar problem as well. It is surprising to us that beyond the famous theorem of Cauchy discussed below, we have been unable to find much discussion of the problems we consider in the literature, though we think it is almost certain that they have been studied in the past.
American Mathematical Monthly, volume 117, number 3, March 2010 by Daniel J. Velleman