Page 22 - Abstract book - TJSSF-2020

Thailand – Japan Student Science Fair 2020 (TJ-SSF 2020)
“Seeding Innovations through Fostering Thailand – Japan Youth Friendship”

Finding the relationship of a curved pattern from the substitution of x
by the positive integer in the Fibonacci polynomial function

Kwanchanok Siritan , Chananchida Sudsa-ard
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Advisors: Chitpong Neuakorwai , Daoruang Butsap
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Princess Chulabhorn Science High School Pathumthani
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Abstract

The purpose of this study is to create a curved pattern relationship by substituting x with a
positive integer in the Fibonacci polynomial function. To be applied in the pattern design and building
as a guideline in the design of products or decorations. Beginning with the study of the form of the
Fibonacci polynomial and analyze the relationships of each number sequence that result from
substituting x values with positive integers in the Fibonacci polynomial function. After that, take the
resulting numbers and create a relationship in the form of curves associated with the number sequence
generated by the Fibonacci polynomial function. By creating curves based on the arrangement of
isosceles and equilateral triangles, which have side lengths in the order of number sequence produced
by the Fibonacci polynomial function and considered the ratio of the side lengths of each of the
connected triangles. And create the equation for the length of a curve in a general form. Which is come
from a circle surrounds an equilateral triangles n triangle, which has lengths from each number
sequence, which is caused by substituting x with the integer into the Fibonacci polynomial function by
determine the range of the numbers from 1 to n, it is found that the ratio of the lengths of each triangle
caused by substituting x with one positive integer in the Fibonacci polynomial function will be
following one of the Metallic means produced by the x order, and the general curve length can find
th
from the equation Ls=239(1na) by a is the length of equilateral triangles that follow the Fibonacci
sequence and n is the number of equilateral triangles. And able to use the resulting curves to create a
further image.

Keywords: Fibonacci polynomial function, Fibonacci sequence, Metallic means

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