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<p>In <i>Siddhanta Darpana</i>, a classic of India’s last exponent of Siddhantic astronomy, Samanta Chandrasekhar, four types of sundials are discussed. These are the horizontal sundial, vertical sundial, equatorial sundial, and <i>golardha yantra</i>. We discuss the underlying unity between these sundials and two others: the polar sundial and the analemmatic sundial. Firstly, we derive the mathematical formula for the shadow angle (the time-showing angle) of a horizontal sundial using the geometry of the polar sundial. Next, we derive the shadow angle formula of a vertical sundial using the geometry of the equatorial sundial. We then discuss the underlying unity between the golardha yantra and the analemmatic sundial, from which we deduce the ratio of time-measuring coordinates in the analemmatic sundial. We create a model that integrates various sundials, each characterized by the angle between the gnomon’s side parallel to the Earth’s axis and the dial plate.</p>

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Unification of Various Sundials: Understanding Their Underlying Relations

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Deepak K. Pattanaik,
  • Jatadhari K. Sharma,
  • Bishnupriya Pani,
  • Nachieketa K. Sharma

摘要

In Siddhanta Darpana, a classic of India’s last exponent of Siddhantic astronomy, Samanta Chandrasekhar, four types of sundials are discussed. These are the horizontal sundial, vertical sundial, equatorial sundial, and golardha yantra. We discuss the underlying unity between these sundials and two others: the polar sundial and the analemmatic sundial. Firstly, we derive the mathematical formula for the shadow angle (the time-showing angle) of a horizontal sundial using the geometry of the polar sundial. Next, we derive the shadow angle formula of a vertical sundial using the geometry of the equatorial sundial. We then discuss the underlying unity between the golardha yantra and the analemmatic sundial, from which we deduce the ratio of time-measuring coordinates in the analemmatic sundial. We create a model that integrates various sundials, each characterized by the angle between the gnomon’s side parallel to the Earth’s axis and the dial plate.