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Why does a circle have 360 Degrees?


A circle is a fundamental premise for many areas of physics and mathematics, such as Geometry, Trigonometry and Calculus. We all know that a circle has 360 degrees. But have we ever wondered why the number is 360, and not 100, or 1000? Phonetically, the word circle is also similar to the Indian word Chakra. What is the Indian connection here? Let us find out.

The vedic hymns also describe the sky as a circle with 360 degrees. This was based on the observation that the sun’s orientation with the earth changes each day and comes to a diametrically opposite direction in 180 days and comes back to the same place in roughly 360 days, which is how a year is also calculated in the calendar. In India this was called a Rashi Chakra based on the division of the celestial path of the Sun, moon and planets into 12 Rashis (or Zodiacs). These were roughly equal segments of the circular path. The number 360 is also an integral multiple of 12 thereby aiding the calculation. Thus the circle came to be divided into 360 degrees. A degree is called Matra in Sanskrit. 

In the Rig Veda, the oldest Vedic text, there are clear references to a chakra or wheel of 360 spokes placed in the sky.

This sloka clearly explains how the circle is divided into 4 quarters each with 90 degrees totalling to 360, using the Sun and its motions as reference. The four divisions refer to 2 solstices and 2 equinoxes. The Sun is compared to the divinity Vishnu and how it holds the planets in orbit around it. This shows how the ancient Indians were able to relate mathematics on paper with the realities of nature. They go ahead by assigning each of these 360 degrees with the names of Vishnu. Also we see how the Sun takes 30 days to travel from one Rashi to another, and 30×12 (rashis) also correspond to the number 360.

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Thus we see how ancient Indians figured out that the best way to represent a circle is in 360 degrees since it comes closest to the natural cycle of the cosmos and is easy to divide by 4, 12, 30 etc. This idea percolated to modern mathematics over millennia of exchanges. 

Also read – The Indian roots of Geometry and The Indian origins of Algebra

Reference: “Roots in India”- Autobiography of India series by D.K. Hari and D.K. Hema Hari by Garuda Prakashan.