Relationship between magic fractions and decimals based on Lucas and Fibonacci numbers

ธนิษฐา โกวรรณ์; พิมพ์กมล บัวทอง; ศุภสิทธิ์ ประทีปจิตต์

ผู้แต่ง

ธนิษฐา โกวรรณ์ Division of Mathematics and Statistics, Department of Computational Science and Digital Technology, Faculty of Liberal Arts and Science, Kasetsart University Kamphaeng Saen Campus, Nakhon Pathom, 73140, Thailand
พิมพ์กมล บัวทอง Division of Mathematics and Statistics, Department of Computational Science and Digital Technology, Faculty of Liberal Arts and Science, Kasetsart University Kamphaeng Saen Campus, Nakhon Pathom, 73140, Thailand
ศุภสิทธิ์ ประทีปจิตต์ Division of Mathematics and Statistics, Department of Computational Science and Digital Technology, Faculty of Liberal Arts and Science, Kasetsart University Kamphaeng Saen Campus, Nakhon Pathom, 73140, Thailand

คำสำคัญ:

Fibonacci numbers, Lucas numbers, Fractions, Decimals

บทคัดย่อ

This research aims to study the relationship between fractions and decimals based on Lucas and Fibonacci sequences by considering the decimal values of fractions with digit numbers in the Lucas and Fibonacci sequences. We analyze the pattern of repeated decimals and their special properties. The results show the mathematical relationship and pattern between Lucas and Fibonacci sequences in the occurrence of the decimals. We give the exact number of Fibonacci numbers in decimal forms of remarkable fractions studied by James Smoak (2003). Our theorems may be applied in numerical analysis such as approximations and errors.

เอกสารอ้างอิง

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