ERIC Number: EJ993833
Record Type: Journal
Publication Date: 2012
Pages: 18
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0020-739X
EISSN: N/A
A Thing of Beauty Is a Joy for Ever
Srinivasan, V. K.
International Journal of Mathematical Education in Science and Technology, v43 n4 p521-538 2012
Three unheralded results, two in Coordinate Geometry and the other in Plane Geometry, provide three proofs of a theorem dubbed by this author as "The Fundamental Theorem". The above theorem offers a uniform proof establishing the positive integral nature of the radii of the incircle and the three escribed circles associated with the right triangle corresponding to any Pythagorean triplet of natural numbers. Another special selection of Pythagorean triplet ensures the positive integral nature of the radii of six circles namely; the incircle, circumscribing circle, the three escribed circles and the nine point circle of the right triangle that comes from the specialized Pythagorean triplet. Through these connections some other new results that can be deduced from the Pythagorean triplet are presented in this article. (Contains 2 figures.)
Descriptors: Geometric Concepts, Plane Geometry, Mathematics Instruction, Validity, Mathematical Logic, Aesthetics, Numbers
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A