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The Vijayanagara Empire was established in 1336 by Harihara I and his brother Bukka Raya I of Sangama Dynasty. The empire rose to prominence as a culmination of attempts by the southern powers to ward off Islamic invasions by the end of the 13th century. The empire is named after its capital city of Vijayanagara, whose ruins surround present day Hampi, now a World Heritage Site in Karnataka, India.
The empire's legacy includes many monuments spread over South India, the best known of which is the group at Hampi. The previous temple building traditions in South India came together in the Vijayanagara Architecture style. The mingling of all faiths and vernaculars inspired architectural innovation of Hindu temple construction, first in the Deccan and later in the Dravidian idioms using the local granite. South Indian mathematics flourished under the protection of the Vijayanagara Empire in Kerala. The south Indian mathematician Madhava of Sangamagrama founded the famous Kerala school of astronomy and mathematics in the 14th century which produced a lot of great south Indian mathematicians like Parameshvara, Nilakantha Somayaji and Jyeṣṭhadeva in medieval south India.Efficient administration and vigorous overseas trade brought new technologies such as water management systems for irrigation.The empire's patronage enabled fine arts and literature to reach new heights in Kannada, Telugu, Tamil and Sanskrit, while Carnatic music evolved into its current form.
The Vijayanagara Empire created an epoch in South Indian history that transcended regionalism by promoting Hinduism as a unifying factor. The empire reached its peak during the rule of Sri Krishnadevaraya when Vijayanagara armies were consistently victorious. The empire annexed areas formerly under the Sultanates in the northern Deccan and the territories in the eastern Deccan, including Kalinga, while simultaneously maintaining control over all its subordinates in the south.Many important monuments were either completed or commissioned during the time of Krishna Deva Raya. Vijayanagara went into decline after the defeat in the Battle of Talikota (1565).