Publication Date



Length of a curve, nonlinear differential equations, Abel’s equation, The First Remarkable Limit, interception


Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education


In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are discussed. A new transformation of curves, named “Interception”, is introduced and its approximate construction using GeoGebra is described. Some possible applications include geometry, calculus, ordinary differential equations, and military interceptions.



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