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The Relationship Between the Different Central Hexagons Formed by Odd/Even-secting the Lengths of Equilateral Triangles

8/26/2016

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By OSAMA HASAN MUSTAFA HASAN ABDALLA, Doha, Qatar
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Abstract

We shall come up with two formulae, one for odd and another for even, to calculate the maximum number of central hexagons that are formed by section-ing an equilateral triangle’s lengths equally into any given parity number and then connecting each of the sections made to their opposite vertex. We shall also construct several area-ratio generalizations between the different central hexagons and their triangle with use of the number of odd or even-sections made to the triangle. Finally, we shall make use of such generalizations to craft two final formulae that can calculate the area-ratio of any specified central hexagon in comparison to the triangle through which they are occupying, provided the number of odd or even-sections made is given.
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1991 Mathematics Subject Classification. Primary: 52C99, Secondary: 51M05 51M15 51D20
51M20.
This paper may be accessed via Google Drive: https://drive.google.com/file/d/0B6fYIQxjoVuTMnQ3ckxvUWFzMDQ/view?usp=sharing
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