Geodesic
Cubic equations and geometric constructions
The Teaching of Mathematics, XXVIII (2025) no. 1, p. 8

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Examples are given of parametric families of equations of the third degree, for which all roots are expressed by square radicals. The problem of constructing a quadrilateral inscribed in a given semicircle by ruler and compass alone is discussed. It is shown that the problem of constructing an isosceles triangle if its three bisectors are given is equivalent to the problem of trisecting an angle. A connection was established between the problem of trisection of an angle and the problem of constructing a regular polygon.
DOI : 10.57016/TM-BZEB4208
Classification : 97H30, 97G40, H34, G44
Keywords: Cubic equation, solution by square radicals, Newton quadrilaterals, angle trisection, regular polygon. 
Nikolay S. Astapov; Natalya K. Noland. Cubic equations and geometric constructions. The Teaching of Mathematics, XXVIII (2025) no. 1, p. 8 . doi: 10.57016/TM-BZEB4208
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