The Study on Irrationality of the Square Roots by Using Paper Folding Geometric Proofs

• Main Authors: LIN, JHUO-TING, 林卓廷
• Other Authors: ZUO,TAI-ZHENG
• Format: Others
• Language: zh-TW
• Published: 2017
• Online Access: http://ndltd.ncl.edu.tw/handle/76515955848228465050

碩士 === 國立高雄師範大學 === 數學系 === 105 === The aims of this paper are to discuss the use of origami to prove that the each root number is irrational, and to use both algebra and geometry to make the proof more complete. This paper concludes four parts which illustrate the design of paper folding activities: The first part discusses the geometric proof of the root numbers are irrational. The second part uses origami and algebra to prove square root of two is irrational. The third part uses origami and algebra to prove square root of n^2+4 is irrational. The fourth part uses origami to prove square root of n^2+1 and square root of n^2-1 are irrational. Finally, the origami activities of this paper is expect to provide another way for teachers which can help students on learning root numbers, and to enhance students' learning motivation.