An Educational Consideration on the Condition that Four Points lie on a Circle

• Journal title : The Mathematical Education
• Volume 55, Issue 2,  2016, pp.233-249
• Publisher : Korea Society of Mathematical Education
• DOI : 10.7468/mathedu.2016.55.2.233
Title & Authors
An Educational Consideration on the Condition that Four Points lie on a Circle
Kang, Jeonggi;

Abstract
In this study, we extracted the background meaning of the condition that four points lie on a circle, analyzed textbooks critically and proposed the orientation to improve the content in the textbook. As results, the condition has a realistic background meaning which is `mathematical modeling of finding a fair location`. The condition has a mathematical background meanings which are `a first complex situation distinguished from two points and three points`, `the condition described in the perspective of side and angle in order to overcome the disadvantages of the perpendicular bisectors context` and `being possible to transfer more than five points`. However it is difficult to understand the reason why the condition is on four points in the current textbook. In addition, it is difficult to recognize the connectivity of a circumcenter of triangle. To overcome these problems, we proposed five orientations to improve the content in the textbook.
Keywords
Condition that four points lie on a circle;Background meaning;Realistic background meaning;Mathematical background meaning;
Language
Korean
Cited by
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