Eneström–Kakeya Theorem and Some of Its Generalizations

On the Eneström–Kakeya theorem and its various forms in the quaternionic setting

“…the papers [1], [3], [10], to mention only a few. For an exhaustive survey of its extensions and refinements, we refer the reader to the comprehensive books of Marden [12], Milovanović et al [13] and Gardner and Taylor [5]. We get the following equivalent form of Theorem 1.1 by applying it to the polynomial…”

104.34 The beauty of mathematics — the connection between the areas of three squares

“…The side-length of the middle square can be changed by rotating the angle of 45º and accordingly the side-lengths of the other two squares vary. A Geogebra applet [1] has been prepared, where the angle of can be rotated by means of a slide bar and for each rotation angle it is found that the area of the central square is equal to the sum of the areas of the two squares in the opposite vertices. At each stage, the following values appear on the screen: , , , .…”

Generalization of an Eneström-Kakeya type theorem to the quaternions

“…Most of them involve weakening the condition on the coefficients. For a survey of such results up to 2014, see [5]. For example, Gardner and Govil [4], inspired by a result of Aziz and Mohammad [1] for power series, presented the following statement [4,Theorem 8].…”