Igor’ E. Pogodin, Igor’ D. Popov
Methodological errors of choosing «simple» solutions
Abstract. The goal of the work is to draw the attention of teachers and students to the danger of choosing the simplest solutions to a wide range of problems, the solutions of which sometimes seem obvious, but turn out to be incorrect when they are more carefully analyzed. Such examples should help to develop the need for in-depth study of the encountered problems and a critical attitude to the advice of the «inner voice» at the first superficial acquaintance. To do this, quite elementary cases from classical programs in Mathematics and Physics are considered here, in which, for reasons of «common sense» and the desire for «simplification», you can come to incorrect results. The following points have been investigated: I) construction of the most economical network for connecting points at the vertices of a square; II) implementation of the fastest descent along a broken trajectory consisting of two segments; III) approximate solution of the scalar equation by linearizing it, leading to the appearance of fictitious roots; IV) calculation of the limit with (incorrect) application of the L’Hospital’s rule; V) solution of the trigonometric equation; VI) ways of estimating the probability of «angle acuteness» of an arbitrary triangle; VII) task of assessing the probability of hitting a target moving along the diameter of the circle with the aircraft; VIII) cause of the fault of the simplest electrical circuit.