Page 27 - Abstract book - TJSSF-2020

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

The Ingenuity of Krathong Designs Using Polygons and Pascal's Triangle

Sirikorn Chanvilainakorn , Tantai Ruenruay
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Advisors: Janjira Khamnan , Dino Alfaro Molano
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Takpittayakhom School
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Abstract

The purposes of “The Ingenuity of Krathong Designs Using Polygons and Pascal's
Triangle”project are: 1) To study the relationship between forms regular polygons constructed on a
circle and Pascal triangle by using the Geometer’s Sketchpad program (GSP). 2) To design the patterns
and creating a decorative Krathong Kala. By integrating mathematical knowledge on binomial theorem,
combination rules and Pascal’s triangle in order to find patterns which were made by creating regular
polygons and all points on the circle from 1 to 7 points by using Geometer’s Sketchpad program then
to design patterns.
1. In finding the relationship between form of regular polygons which constructed on a circle and
Pascal triangle by using Geometer’s Sketchpad program, when n is an element of counting number
result that:
 The number of points on circle has a relation in the second diagonal of Pascal’s triangle,

starting from 1, 2, 3, …, , ...
 The number of line segments has a relation in the third diagonal of Pascal’s triangle,

starting from 1, 3, 6, 10, 15, …, , …
 The number of triangles has a relation in the fourth diagonal of Pascal’s triangle, starting

from 1, 4, 10, 20, 35, …, , …
 The number of quadrilaterals has a relation in the fifth diagonal of Pascal’s triangle,

starting from 1, 5, 15, 35, …, , …
 The number of pentagons has a relation in the sixth diagonal of Pascal’s triangle, starting

from 1, 6, 21, 56, …, , …
 The number of hexagons has a relation in the seventh diagonal of Pascal’s triangle,

starting from 1, 7, 28, 84, …, , …
 The number of heptagons has a relation in the sixth diagonal of Pascal’s triangle, starting

from 1, 8, 36, 120, …, , …
2. In designing the patterns and decorating Krathong Kala by using worked from design, we gained
5 different patterns of Krathong Kala.
Keywords: Polygons, Pascal's Triangle

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