Page 28 - Abstract book - TJSSF-2020

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

Some properties of inscribed relation in regular n-gons

Supakit Krailert , Pimlaput Olrankijanun
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Advisor: Nattawoot Doomluck
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Phuketwittayalai School
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Abstract

Some properties of inscribed relation in regular -gon begins with considering regular
polygon inscribed in regular polygon. We use knowledge in Mathematics and Technology in order
to find the theories and prove some properties of regular polygon inscribed in regular polygon
from number theorem. We also use DEV-C++ program to calculate for finding duplicated vertices.
From considering regular polygon inscribed in regular polygon, we bring about the conditions of

regular polygon inscribed in regular polygon if and only if and find that any regular
polygon inscribed in regular polygon has some duplicated vertices if and only if

when is the first vertices, is the interval between the vertices

of any and the number of duplicated vertices is equal to . Furthermore, we can
also find how to calculate the number of areas that result from the blockage of regular polygon or

regular polygon. If the different vertices of regular polygon that are supported by any sides of

regular polygon are equal to where , the number of areas that result from the blockage of
regular polygon or regular polygon where that side of regular polygon passes is equal

to areas. In addition to these results, we can find that if we color the areas that result from the
blockage of regular polygon or regular polygon, the least number of colors is equal to 2.

Keywords: regular polygon, duplicated vertices, the number of duplicated vertices,
congruence equations, DEV-C++ program, face, chromatic number

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