H607

Paji Panjiang, Sujira Simsuwat

Advisor Naphat Youngmeesuk

Abstract

Mathematics Art is combination that make a pattern that has mathematical relationship in there. Mathematics Art that we choose to study is the pattern created from the circle that have dots on its circumference. Each dot has same distance between each other. Measured from size of angles at the center of circle.Then draw lines to connect each dot. Every line must be the longest chord that isn’t the diameter and every line must have same length. From the above pattern will form a circle with many triangles inside. So we study about the relationship between amount of triangles that caused by intersection of chords that connect each dots on circumference and size of the angles that lead to the dots on the circumference.

In studying of that relationship use 5 circles with 10 units of diameter length for the experiment. Each circle has different size of angles at the center include 60, 45, 30, 15and 10 degrees and each circle have same chord length. In finding amount of triangles inside each circle based on the condition of triangle that every triangle will has 3 sides. Each side will be a part of chord that drawn to intersect. Which means 3 chords can make only one triangle. The parallel chords won’t intersect and doesn’t form any angles or polygons.

The result of the experiment is

1.There are 8 triangles in the circle with 60 degrees angles at the center.

2.There are 32 triangles in the circle with 45 degrees angles at the center.

3.There are 158 triangles in the circle with 30 degrees angles at the center.

4.There are 1,760 triangles in the circle with 15 degrees angles at the center.

5.There are 6,528 triangles in the circle with 10 degrees angles at the center.

From the result will observe that the relationship between amount of triangles that caused by intersection of chords that connect each dots on circumference and size of the angles that lead to the dots on the circumference tend in the same direction.