The Relationship Between the Different Central Hexagons Formed by Odd/Even-secting the Lengths of Equilateral Triangles
By OSAMA HASAN MUSTAFA HASAN ABDALLA, Doha, Qatar
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.
1991 Mathematics Subject Classification. Primary: 52C99, Secondary: 51M05 51M15 51D20
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