Investigating the Circumregion

Often, straightforward notions from one mathematical domain, when altered even slightly, can become rich and rewarding investigations involving numerous additional domains -- particularly when the investigation includes rigorous proof. This study begins with a familiar high school geometry problem (...

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Bibliographic Details
Published inInternational journal of mathematical education in science and technology Vol. 52; no. 6; pp. 857 - 878
Main Authors Byrd, James L., Bossé, Michael J., Spurr, Michael J.
Format Journal Article
LanguageEnglish
Published London Taylor & Francis 03.07.2021
Taylor & Francis Ltd
Subjects
Domains
equidistance
Euclidean space
Exploration and discovery in geometry
Geometric Concepts
Geometry
High School Students
Mathematical analysis
Mathematical Logic
Mathematics education
Mathematics Skills
Measurement
metric space
Plane Geometry
Problem Solving
Secondary School Mathematics
Triangles
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Summary:Often, straightforward notions from one mathematical domain, when altered even slightly, can become rich and rewarding investigations involving numerous additional domains -- particularly when the investigation includes rigorous proof. This study begins with a familiar high school geometry problem (namely finding the circumcentre of a triangle), extends it to the study of equidistance and analyses the problem using geometry in concert with a number of other mathematical areas to construct a new region called the Circumregion. Altogether, the beautiful and intricate interconnectedness of mathematics is both employed and demonstrated.
ISSN:0020-739X
1464-5211
DOI:10.1080/0020739X.2020.1719442