Journal of JASME : research in mathematics education
Online ISSN : 2433-3034
Print ISSN : 1341-2620
Formulas Group Indicating the Relations between the One Area and Sum of the Area in the Pythagoras Triangle ─ The Sequence of Combinations of the Number of Fibonacci Appearing there ─
Fumitaka YAMAMOTO
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2013 Volume 19 Issue 1 Pages 1-8

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Abstract

  The area of the Pythagoras triangle is the sum of area of the Pythagoras triangle that is smaller than it except some exceptions. The exception is the case of M=2N (M,N is an independent variable of the solutions of Euclid).

  Furthermore, these relations are expressed as the sequence and constructed in the Fibonacci series Next, the Pythagoras number is distributed on various parabolas group on the coordinate which assume two axes into two sides sandwiching the right angle. The degree of leaning of the axis of symmetry of the parabola group is 0 in case of the basic formula (Euclid solution) of the Pythagoras number. In addition, it is 0 and ∞ in case of “the unit formula”of sum of area. Furthermore, the axial degree of leaning converges to 2 at an early stage in case of “the general formula”.

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© 2013 Japan Academic Society of Mathematics Education
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