The problem and geometric application of infinite sequences formed from three given numbers by calculating their pairwise means Victor Oxman, Moshe Stupel International Journal of Mathematical Education in Science and Technology, 2024 We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in several stages and involve various technological tools and various fields of mathematics. The activities can be useful for the instruction of pre-service and experienced mathematics teachers.
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
107.10 Trapezia whose side-lengths form an arithmetic progression Moshe Stupel, Victor Oxman Mathematical Gazette, 2023 An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
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.
106.10 PWW: Trigonometric inequality Victor Oxman, Moshe Stupel Mathematical Gazette, 2022 An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Generalization of the Pappus theorem in the plane and in space Journal for Geometry and Graphics, 2018
"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
