Conserved properties in polygons obtained by a point reflecting process. Issue 10 (26th November 2021)

• Record Type: Journal Article
• Authors: Oxman, Victor; Stupel, Moshe
• Is Part Of: International journal of mathematical education in science and technology. Volume 52:Issue 10(2021)
• Page Start: 1598
• Page End: 1608
• Publication Date: 2021-11-26
• Subjects: Dynamic investigation of invariant (conserved) properties -- reflection in different polygons -- generalization of properties; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; 510.07
• DOI: 10.1080/0020739X.2020.1850898
• Languages: English
• ISSNs: 0020-739X

Abstract

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.