Spherical shape:
When a clay like mass spins about itself(pot making), it is likely to attain spherical shape. That is why all the celestial bodies are spherical.
All liquids have a property called surface tension. That is, the liquids contract its surface area and try to occupy smallest area. The sphere has a smallest surface area for a given volume. Hence all liquid drops and water bubbles are spherical.
For the same reason, most fruits are spherical. They try to contain good volume of food in efficient packages.
Parabolic shape:
Parabolic mirrors efficiently reflects radiation as a parallel beam or focus the parallel beam of radiation to a point accurately. Hence parabolic shape is used in antenna, telescope mirrors, car head light etc,. Parabolic shape is also used in construction of buildings and bridges for its weight bearing character.
Egg shape:
Egg has a peculiar shape. But it has a purpose. Roll down an egg on a table slowly, it may not fall down on the other side of the table but will make a U turn and come towards you. The shape is responsible for this motion. Bird's eggs are mostly in the nest on high trees. The eggs will not mostly fall down , but revolve within the nest due to its shape. Also, the parabolic shape of egg shell gives strength to it.
Hexagonal shape:
Honey bees' hive is mainly made up of hexagonal structures using bee's wax. These structures closely fits each other without living any gap between them. They can withstand some heavy force even if they are made up of light material. Hexagonal tiles are used in construction also.
There is a purpose for everything in nature.
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