Other Polygons

Polygon any plane figure enclosed by straight lines. We see many types of polygons in nature and in life around us. Except for triangles & quadrilaterals, polygons are named after the number of sides that they have. The word” gon” stands for side.

In geometry we study only convex polygons where every interior angle is less than 180 degrees. In concave polygons, some of the interior angles can be reflex angles.

Polygon – Many sided “gon”, Pentagon – 5 sides, Hexagon – 6, Heptagon – 7, Octagon – 8 sides, Nonagon – 9, Decagon- 10, Dodecagon – 12 etc.

If all the sides of a polygon & all the interior angles are equal, then it is known as a “regular” polygon.

Hence in triangles the “regular” triangle in the Equilateral triangles. In quadrilaterals the “regular” quadrilateral is the Square. Regular polygons are also convex polygons where each interior angle is less than 180 degrees.

In all polygons, except the quadrilateral, equal sides automatically ensures equal interior angles. In quadrilaterals both square and rhombus have equal sides. Hence the additional criterion of equal angles has to be introduced to ensure that there is only one type of “regular” quadrilateral.

A polygon can be divided into a certain number of triangles by joining the vertices. There is a simple relation between the sides of the quadrilateral and the minimum number of triangles it can be divided into.

Hence the total of the internal angles of a polygon can be easily worked out. This also leads to a way of calculating the area of the polygon.

Many structures and shapes in nature are in the form of polygons.

Many flowers and creatures in the sea are similar to pentagons.

Hexagon

Nature seems to love hexagons, possibly because they seem to offer efficient and robust structural solutions at any scale from the atomic to the planetary.

Honey combs, carbon-based structures, basalt stones, the atomic structure of ice and snowflakes, turtle shells, the basic unit in the eyes of insects, bubbles in foam… number 6 is everywhere!

When several air bubbles join together, they form hexagons. Many chemical molecules are found to form shapes of different polygons.

The "Symphony of Stones" is a natural wonder found in the Azat River basin, nestled within Garni Gorge in Armenia. It features towering columns made of basalt, some as tall as 50 meters. These columns, shaped like hexagons and pentagons, formed when basaltic lava cooled and crystallized under intense pressure.

Even on Saturn, a perplexing hexagon, a spinning six-sided jet stream located at its north pole, since the 1980s.