Antarctica gives us an idea, how the earth would have been like millions of years ago and how it got divided into various earth masses. The melting and colliding ice masses also give us an insight into how our future is going to be, if we continue with interference in the working of the nature. Moreover, Antarctica holds into the depths of its ice half-million year old carbon records, which are helpful in understanding the past, present and future of the earth. Therefore, Antarctica is the place which reveals our past, shows our present and visualizes our future
What could be the reason for the disintegration of Gondwana? (Journey to the End of the Earth)
Six hundred and fifty million years ago, a giant amalgamated southern supercontinent — Gondwana — did indeed exist, centered roughly around the present-day Antarctica. Things were quite different then: humans hadn't arrived on the global scene, and the climate was much warmer, hosting a huge variety of flora and fauna. For 500 million years Gondwana thrived, but around the time when the dinosaurs were wiped out and the age of mammals got under way, the landmass was forced to separate into countries, shaping the globe much as we know it today.
(Journey to the end of the Earth)
Prove that:
\( \tan^{-1}(\sqrt{x}) = \frac{1}{2} \cos^{-1}\left( \frac{1 - x}{1 + x} \right), \quad x \in [0, 1] \)