Hexagon is a form of a polygon which consists of six edges
and six vertices. And 720◦ is the total of the internal angles of any hexagon.
The hexagon patterns are the most prevalent in the nature
due the strong efficiency which they have, if we take on consideration their
existence either in bees’ honeycombs or the Giant’s Causeway.
If we talk about hexagonal structures we find that each line
in the hexagonal grid is short but in the same time it can be if a large area
to fill with the fewest number of hexagons, this mean that it is required less
wax by honeycombs to construct and gain lots of strength under compression.
All the internal angles of the regular hexagon are 120◦ and
have the same length of all its sides.
It has six lines of symmetry, and the longest diagonals are
twice of the length of one side, and which are connecting opposite vertices.
The regular hexagon can be divided into six equilateral
triangles, so we can see as triangle with a vertex at the middle of regular
hexagon. And the regular hexagon gives the strength and the large space and
building materials.
The regular hexagons, like squares and equilateral
triangles, fit together without making gaps in the tile of the plane, as well
as the reason resides behind the hexagonal shapes of cells of a beehive and
makes efficient use of space and building materials.
Although it is equilateral, but it is not considered a
triambus:
The upper equation gives the area of a regular hexagon of
side length T.
And there is another formula which considered alternative
formula for the area where A= 1.5dt and in which the length d is the distance
between the parallel sides in the regular hexagon.
The alternative formula and which known flat to flat
distance for the area is:
We can find the area by the two formulas:
Any hexagon in the circle is a cyclic hexagon, where all the
three main diagonals intersect in a single point.
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