Geometrical theories were known to ancient Indians and find display in motifs on temple walls, which are in many cases replete with mix of floral and geometric patterns. Basham, an Australian Indologist, writes in his book, The Wonder That was India that “…
The method of graduated calculation was documented in a book named “Five Principles” (Panch-Siddhantika) which dates to 5th Century AD. the world owes most to India in the realm of mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity.
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The natural corollary were emergence of music and other forms of performing arts.
Mechanical & production technology – Greek historians have testified to smelting of certain metals in India in the 4th century BC.
Medical science & surgery – Around 800 BC, first compendium on medicine and surgery was complied in ancient India.
Fine Arts – Vedas were recited and recitation has to be correct, which gave rise to a finer study of sound and phonetics.
In ancient India, roots to mathematics can be traced to Vedic literature, which are around 4000 years old.
Between 1000 BC and 1000 AD, a number of mathematical treatises were authored in India.
He is known to have given a basic idea of the Rolle’s theorum and was the first to conceive of differential calculus.
In 1816, James Taylor translated Bhaskaracharya’s Leelavati into English.
Civil engineering & architecture – The discovery of urban settlements of Mohenjodaro and Harappa indicate existence of civil engineering & architecture, which blossomed to a highly precise science of civil engineering and architecture and found expression in innumerable monuments of ancient India.
Shipbuilding & navigation – Sanskrit and Pali texts have several references to maritime activity by ancient Indians.
He has referred to Algebra (as Bijaganitam) in his treatise on mathematics named Aryabhattiya.