DID you see the Gregory Peck and Omar Sharif starrer classic: MacKenna’s Gold? Both protagonist and antagonist of the movie were after a cache of gold in a hilly terrain but could not succeed in tracing it out. Suddenly a bright flash of light from a crevice dazzled their eyes. It was the reflection of sunlight falling on the gold cache! Although none could ultimately acquire the treasure, the particular angle at which the sunlight fell on the gold was the most impactful scene in the whole movie. Nature thus makes her impact felt with astute sense of geometry. It is a biological truth that the angle between two adjacent lobes of a starfish is 72 degrees. Who has given them such accurate angular sense? While veins on a plant leaf are arranged in acute angles along the midline, angle between the antennas of a cockroach is always obtuse. If you keenly observe the rains coming down the sky during downpour, you will find a series of straight lines. Sunrays trickling through a gap in the window initially demonstrated me how parallel lines look.

Circular shapes are abundant in celestial objects. Staring at the Moon on a full-Moon night many a poet got their first inspiration. But did they notice the geometry of our natural satellite? It appears as if someone has drawn a perfect circle on the canvas. The Sun also looks exactly the same during solar eclipse. As the raindrops hit the surface of a lake, they create tiny circles on water which go on spreading until overlapped by similar circles created by subsequent drops. From an open ground, the rainbow appears like a gigantic semi circle on the horizon. Beehives in a honeycomb are always hexagonal. Why do the bees adopt this pattern? Scientists say that this particular shape wastes the least space between hives. Tree trunks of most of the plant species in our surroundings are of cylindrical type. Branches of plants in hilly areas grow in such a fashion that the plants get a conical profile. This actually helps the plants to shed off the accumulated snow quickly.

Look at the common trifoliate plants like Sugar Maple, Poison Ivy or Wood Apple. If the mid points of the three leaflets of such plants are joined by imaginary straight lines, they form perfect equilateral triangles. Triangular shapes are also observed in the ears of animals, tail-fins of fishes, etc. Celestial bodies follow various geometrical patterns in their motion paths. The Earth moves round the Sun in an elliptical path with one of the foci fixed at Sun. That precisely causes the change in seasons. Other planets of our solar system also follow similar paths. Halley’s Comet revolves the Sun in a large elliptical orbit in every 76 years. However, there are comets which appear for a few days on the night sky and then disappear forever. Orbital paths of such heavenly bodies are either parabolic or hyperbolic in nature. Let us look at our known surroundings. Nature presents her geometrical skill in so many simple manifestations. While snowflakes and fern leaves are of complicated designs, Oranges, Lemons, Cherries and even our eyeballs are of spherical types. If crystals of common salt and sugar are cuboids, clouds in the sky adopt changing shapes to heighten our imagination, as if an artist is always waving her wand to open before us the magical world of geometry!