107.14 Does a trapezium exist whose side lengths form a geometric progression? Victor Oxman, Moshe Stupel Mathematical Gazette, 2023 107.14 Does a trapezium exist whose side lengths form a geometric progression? It is known that there is no trapezium whose lengths of consecutive sides form an arithmetic progression [1]. Is this true also for a geometric progression? Let in trapezium with the lengths of consecutive sides form a geometric progression with common ratio . ABCD BC // AD q > 1 Obviously it is enough to consider two cases. In the first case the geometric progression starts at and in the second case it starts at . AB BC
Two Perpendicular Lines Related to a Circle: PWW accompanied by GeoGebra Applets Victor Oxman, Moshe Stupel International Journal for Technology in Mathematics Education, 2023 PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a “mathematical art” that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-bystep help in completing the proof and understand what geometrical properties and theorems it relies on.
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"What if not" strategy applied to open-ended stimulating problem posing in inquiry-based geometry classes International Journal for Technology in Mathematics Education, 2018
A purely geometric proof of the uniqueness of a triangle with given lengths of one side and two angle bisectors Annales Mathematicae Et Informaticae, 2009
