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Chhaya Ganit In Ancient Hinduism

Chhaya Ganit, or Chaya Ganita, are calculations based on the length of the shadows in Hinduism. Chaya Ganita has its roots in man’s observation of the changes in his own shadow during daytime. Starting from the gnomon, the science grew to the extent of using sophisticated astronomical instruments in ancient India. In Atharva-Jyotisha (13th century BCE), muhurtas (time divisions) are defined in terms of the shadow of a gnomon of twelve angula (finger) size.

Details of Chhaya Ganit for determining accurately the cardinal points, time, seasons, length of year, obliquity, ascendant, etc., have been given in all the texts of mathematical astronomy, which appeared around 4th century CE or even earlier.

For instance, when the sun is at the equinox, its meridional zenith distance is equal to the latitude of the observer. This can be obtained by measuring the equinoctial shadow cast by a gnomon, from which destination of the sun can be calculated. Following this, the obliquity of the ecliptic with the equator could be calculated to the 24 degrees. These methods are further elaborated in medieval astronomical works.

Ganesha Daivajna (1522 CE) constructed the Pratodayantra, essentially a horizontal gnomon, for geometrical calculations based on the shadows cast by it. Later, triangular gnomons, in the form of sundials with slanting styles, were also developed, which formed a significant constituent of the Samrat Yantra of Jai Singh (1724 CE).

Another application of Chhaya Ganita lies in understanding the eclipses. Varahamihira (535 CE) explains that the real cause of a lunar eclipse is the entry of the moon into the earth’s shadow and likewise at the solar eclipse the moon enters between the sun and earth. Aryabhata I (476 CE) has described the formulae for calculating the length and diameter of the shadows cast, conditions and the duration of eclipses.

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