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Aryabhata gave tables of half chords which are now known as sine tables, along with cosine tables. He used zya for sine, kotizya for cosine, and otkram zya for inverse sine, and also introduced the versine.

Brahmagupta used an interpolation formula to compute values of sines, up to the second order of the Newton-Stirling interpolation formula.

Representing a complete system of social, physical, mental and spiritual development; the origins of yoga date to some 5,000 years ago in the Indus-Sarasvati civilization of northern India. The first references to the history of yoga can be found in the Rig Veda.

Indian astronomers has made the important discovery that the stars visible at night are similar to the Sun visible during day time.
There is an old Sanskrit shloka (couplet) which states “Sarva Dishanaam, Suryaha, Suryaha, Suryaha” which means that there are suns in all directions. This couplet which describes the night sky as full of suns. In other words, it was recognized that the sun is also a star, though the nearest one. This understanding is demonstrated in another Sloka which says that when one sun sinks below the horizon, a thousand suns take its place.

The History of metallurgy in the Indian subcontinent dates back to 1700 BCE. Metals and related concepts were mentioned in various early Vedic age texts. The Rigveda already uses the Sanskrit term Ayas (metal).

The Atharva Veda and the Satapatha Brahmana refer to krsna ayas (“black metal”), which could be iron (but possibly also iron ore and iron items not made of smelted iron).
In the Taittiriya Samhita are references to ayas and at least one reference to smiths.
The Satapatha Brahmana 6.1.3.5 refers to the smelting of metallic ore.
In the Manu Smriti (6.71), the following analogy is found: “For as the impurities of metallic ores, melted in the blast (of a furnace), are consumed, even so the taints of the organs are destroyed through the suppression of the breath.”
The Rasa Ratnasamuccaya describes the extraction and use of copper.

The pillar of Delhi, erected by Chandragupta II Vikramaditya (375-413), made up of 98% wrought iron of pure quality is a testament to the high level of skill achieved by ancient Indian iron smiths in the extraction and processing of iron. It has attracted the attention of archaeologists and metallurgists as it has withstood corrosion for the last 1600 years, despite harsh weather.

Metallurgists at IIT Kanpur have claimed that a thin layer of “misawite”, a compound (amorphous phase d-FeOOH) of iron, oxygen, and hydrogen, has protected the wrought iron pillar from rust.

Source:
http://timesofindia.indiatimes.com/articleshow/1058320.cms

India has given the idea of the smallest and the largest measure of time.

Krati Krati = 34,000th of a second
1 Truti = 300th of a second
2 Truti = 1 Luv
2 Luv = 1 Kshana
30 Kshana = 1 Vipal
60 Vipal = 1 Pal
60 Pal = 1 Ghadi (24 minutes)
2.5 Gadhi = 1 Hora (1 hour)
24 Hora = 1 Divas (1 day)
7 Divas = 1 saptaah (1 week)
4 Saptaah = 1 Maas (1 month)
2 Maas = 1 Rutu (1 season)
6 Rutu = 1 Varsh (1 year)
100 Varsh = 1 Shataabda (1 century)
10 Shataabda = 1 sahasraabda
432 Sahasraabda = 1 Yug (Kaliyug)
2 Yug = 1 Dwaaparyug 3 Yug = 1 Tretaayug
4 Yug = 1 Krutayug
10 Yug = 1 Mahaayug (4,320,000 years)
1000 Mahaayug = 1 Kalpa
1 Kalpa = 4.32 billion years