Victor Oxman
@wgalil.ac.il
School of Management
Western Galilee College
RESEARCH INTERESTS
Math & Math Education
42
Scopus Publications
Scopus Publications
- PWW (Proof Without Words): In a Right Triangle a + b = 2(R + r)
Victor Oxman
Springer Science and Business Media LLC - On a polygon whose side lengths form a geometric sequence
Victor Oxman
Informa UK Limited - The problem and geometric application of infinite sequences formed from three given numbers by calculating their pairwise means
Victor Oxman and Moshe Stupel
Informa UK Limited - 107.14 Does a trapezium exist whose side lengths form a geometric progression?
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP)
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 and Victor Oxman
Cambridge University Press (CUP) - Two Perpendicular Lines Related to a Circle: PWW accompanied by GeoGebra Applets
Victor Oxman and Moshe Stupel
Research Information Ltd.
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. - Dynamic Investigation of Surprising Situations With Conservation of Areas Described by Functions With Parameters
Victor Oxman and Moshe Stupel
Springer Science and Business Media LLC - Testing the NCTM 2020 Standards Using Rigorous Mathematics and Multiple Solutions to a Single Geometric Problem
Jay Jahangiri, Victor Oxman, and Moshe Stupel
Springer Science and Business Media LLC - 106.10 PWW: Trigonometric inequality
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP) - On One Interesting Property of an Isosceles Triangle Inscribed in a Circle, which HINT Buttons Help to Prove
Victor Oxman and Moshe Stupel
Research Information Ltd.
This note gives an example of an interesting geometric problem whose solution is accompanied by dynamic help using the GeoGebra applet. - Investigation on inscribed circles: one, two, three, four, infinitely many
Victor Oxman and Moshe Stupel
Informa UK Limited
The paper presents a problem that has all the components that make it usable as a research problem for both high school students and in training mathematics teachers at teacher training colleges and universities. The problem contains various geometric curves and shapes: squares, circles, sectors, segments, parabola. It can be developed in stages, asking additional questions that, on the one hand, increase the level of complexity, and on the other hand, reveal the beauty of mathematics. - Illogical use of the converse of a theorem that can cause an incorrect solution
Victor Oxman and Moshe Stupel
Informa UK Limited
ABSTRACT We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16–17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the danger of using a wrong converse, the problem was posed as field research to a group of pre-service teachers and training teachers in the ‘methods (of teaching mathematics)’ course, where similar failures were discovered. The conclusion is that a large part of the students was not aware that the converse is not always true, and its correctness is to be tested before it can be used. The investigation of the problem was accompanied by a dynamic geometry environment software that allowed us to examine the problem in the general case and so to make conclusions for particular cases. - 105.44 A segment inside a square that is equal to the side of the square
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP) - Three Segments on the Diagonal of a Square
Victor Oxman and Moshe Stupel
Informa UK Limited
Summary We present a visual proof for an elegant property of three segments on the diagonal of a square. - Some inequalities in a triangle in which the length of one side and the inradius are given
Victor Oxman
Informa UK Limited
In the article, we prove 18 inequalities involving inradius, a length of one side and one additional element of a given triangle. 14 of these inequalities are the necessary and sufficient conditions for the existence and uniqueness of such a triangle. All proofs are based on standard methods of calculus and can serve as a good demonstration of the relationship between different branches of mathematics (geometry, algebra, trigonometry, calculus). The article can be used by teachers and students in courses on advanced classical geometry. - Conserved properties in polygons obtained by a point reflecting process
Victor Oxman and Moshe Stupel
Informa UK Limited
ABSTRACT The present paper describes a dynamic investigation of polygons obtained by reflecting an arbitrary point located inside or outside a given polygon through the midpoints of its sides. The activity was based on hypothesizing on the shape of the reflection polygon that would be obtained, testing the hypotheses using dynamic software, and finding a justified mathematical proof. The activity was also applied to properties that are conserved or not conserved as a result of the reflection. Additionally, we find the mathematical relation for the ratio between the area of the reflection polygon and the area of the original polygon. The population of the study was pre-service teachers and experienced teachers who study in teaching college. - Surprising relations between the areas of different shapes and their investigation using a computerized technological tool
Victor Oxman, Moshe Stupel, and Shula Weissman
Informa UK Limited
The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified proofs. - An inequality between the area of a triangle inscribed in a given triangle and the harmonic mean of the areas of vertex triangles
Victor Oxman and Avi Sigler
Informa UK Limited
ABSTRACT In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof. The article can be used by teachers and students in courses on advanced classical geometry. - 104.35 Proof without Words: A right triangle ABC with altitude AH = BC
Victor Oxman and Moshe Stupel
Cambridge University Press (CUP) - Dynamic Investigation of Area Conservation Properties Using Computer Technology in a Classroom Activity
Victor Oxman, Moshe Stupel, and Idan Tal
Research Information Ltd.
The article presents some examples of plane geometric variance of an area with the use of computer technology. These tools can offer teachers opportunities for adaptation and preparation of pedagogical presentations which will help students along the process of fruitful conjectures formation and eventually construction of formal deductive proofs. Some of the examples are original, and all are beautiful and insightful. The mathematical proofs of the selected examples are very simple and do not require the use of any "heavy" mathematical tools. All the examples have links to applets prepared in GeoGebra-Tube. The consequences of all the examples can be formulized as mathematical propositions, and vice versa, meaning any mathematical proposition might demonstrate a situation of variance and invariance properties. - Relations between Ceva’s Theorem and the concurrency of midlines of quadrilaterals in a triangle
- The properties of special points on the brocard circle in a triangle
Victor Oxman, Avi Sigler, and Moshe Stupel
Springer International Publishing - Proof Without Words: An Elegant Property of an Isosceles Right Triangle
Victor Oxman and Moshe Stupel
Informa UK Limited - Various solution methods, accompanied by dynamic investigation, for the same problem as a means for enriching the mathematical toolbox
Victor Oxman and Moshe Stupel
Informa UK Limited
ABSTRACT A geometrical task is presented with multiple solutions using different methods, in order to show the connection between various branches of mathematics and to highlight the importance of providing the students with an extensive ‘mathematical toolbox’. Investigation of the property that appears in the task was carried out using a computerized tool. - The concept of invariance in school mathematics
Shlomo Libeskind, Moshe Stupel, and Victor Oxman
Informa UK Limited
ABSTRACT In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change leaves some relationships or properties invariant, these properties prove to be inherently interesting to teachers and students.