Browse > Article

http://dx.doi.org/10.14477/jhm.2015.28.3.151
###

On integration of Pythagoras and Fibonacci numbers |

Choi, Eunmi
(Dept. of Math., HanNam Univ.)
Kim, Si Myung (Daejeon Dongsin Science High School) |

Publication Information

Abstract

The purpose of this paper is to develop a teaching and learning material integrated two subjects Pythagorean theorem and Fibonacci numbers. Traditionally the former subject belongs to geometry area and the latter is in algebra area. In this work we integrate these two issues and make a discovery method to generate infinitely many Pythagorean numbers by means of Fibonacci numbers. We have used this article as a teaching and learning material for a science high school and found that it is very appropriate for those students in advanced geometry and number theory courses.

Keywords

Pythagoras number; Fibonacci number;

Citations & Related Records

Times Cited By KSCI :
4 (Citation Analysis)

- Reference
- Cited By KSCI

1 | W. BOULGER, Pythagoras meets Fibonacci, Mathematics Teacher 82(4) (1989), 277-282. |

2 | B. A. BURNS, Pre-service teachers' exposure to using the history of mathematics to enhance their teaching of high school mathematics, Issues in the undergraduate mathematics preparation of school teachers, The Journal 4 (2010). |

3 | D. M. BURTON, Elementary Number Theory, McGraw-Hill, 2010. |

4 | M. de VILLIERS, A further Pythagorean variation on a Fibonacci theme, Mathematics in School 31(5) (2002), 22. |

5 | R. FOGARTY, Ten ways to integrate curriculum, Educational Leadership 49(2) (1991), 61-65. |

6 | H. FREUDENTHAL, Revisiting mathematics education, China Lectures, Dordrecht: Kluwer Academic Publishers, 1991. |

7 | U. T. JANKVIST, A categorization of the 'whys' and 'hows' of using history in mathematics education. Educational Studies in Mathematics 71(3) (2009), 235-261. DOI |

8 | D. KALMAN, R. MENA, The Fibonacci numbers-exposed, Math. Magazine 76(3) (2003) 167-181. DOI |

9 | KIM M. K., Review and interpretations of Plimpton 322, The Korean Journal of History of Mathematics 20(1) (2007), 45-56. 김민경, 고대 바빌로니아 Plimpton 322의 역사적 고찰, 한국수학사학회지 20(1) (2007), 45-56. |

10 | E. A. MARCHISOTTO, Connections in mathematics: an introduction to Fibonacci via Pythagoras, Fibo. Quart. 31(1) (1993) 21-27. |

11 | D. PAGNI, Fibonacci meets Pythagoras, Mathematics in School 30(4) (2001) 39-40. |

12 | PARK W. B., PARK, H. S, On the Pythagorean triple, J. Korean Soc. Math. Ed. Ser. A: The Mathematical Edu. 41(2) (2002), 227-231. 박웅배, 박혜숙 (2002). 피타고라스의 세 수, 한국수학교육학회, 수학교육 41(2) (2002), 227-231. |

13 | PAULANO, Fibonacci and Pythagoras unite mathematicians, artists, musicians, naturalists, architects and beauticians, http://paulano.wordpress.com/2008/09/21/. |

14 | E. ROBSON, Words and pictures: new light on Plimpton 322, The Amer. Math. Monthly 109 (2002), 105-120. DOI |

15 | D. ROBINSON, Pythagoras meets Fibonacci, New Zealand Math. Magazine 43(2) (2006), 44. |

16 | ROH M. G., JUNG J. H., KANG J. G., On the general term of the recurrence relation , J. Korean Soc. Math. Ed. Ser. E: Comm. Mathematical Edu. 27(4) (2013), 357-367. 노문기, 정재훈, 강정기, 점화식 의 일반항에 대하여, 수학교육논문집, 27(4) (2013), 357-367. |

17 | YANG Y. O., KIM T. H., A study on generalized Fibonacci sequence, The Korean Journal of History of Mathematics 21(4) (2008), 87-104. 양영오, 김태오, 피보나치 수열의 일반화에 관한 고찰, 한국수학사학회지 21(4) (2008), 87-104. |