The Delight of Mathematicians

original: "Ganaka Ranjani"

Verse He, known by the name Gopalakrishna, who delights the minds of scholars, was born to the goddess-like Rajalakshmi, ever-observant of poetic inquiry.

Having repeatedly examined the foundations of the Surya Siddhanta The Surya Siddhanta is one of the most important ancient Sanskrit treatises on Indian astronomy., he composed this Delight of Mathematicians for the easy understanding of students.

Calculation of the Shaka Era

original: "Shaka Sadhana"

Verse Sixty (60) multiplied by twenty-three (23), combined with the elapsed years, and added to four hundred and nine (409)—know this to be the time of the Shaka King.

Explanation: Set down 60 and multiply it by 23. To this, add the number of elapsed years in the current sixty-year cycle (starting from the year Prabhava). Then add 409 to the total. The result is the current Shaka Era year.
The Shaka Era is a historical Hindu calendar era beginning in 78 CE. The cycle starting with Prabhava refers to the 60-year Jupiter cycle used in Indian chronology.

Deriving the Constant for Elapsed Kali Years

original: "Kaligatabda Dhruvanayanamu"

Verse Eighty (80) multiplied by sixty (60), combined with two hundred and eighteen (218), and further combined with the years since Prabhava—these shall be the years of the Kali age.

Explanation: Set down 80 and multiply it by 60. Add 218 to the product. Then, add the number of elapsed years from the current cycle beginning with Prabhava. The resulting sum is the total number of years elapsed in the Kali Yuga.
The Kali Yuga is the fourth and current age in the Hindu cycle of cosmic time, traditionally calculated as beginning in 3102 BCE.

Calculating the Epochal Year

original: "Karanabda Sadhanamu"

Verse Subtracting three thousand one hundred and seventy-nine (3179) from the Kali years is said to give the Shaka year. Subtracting four thousand five hundred and forty-eight (4548) gives the Karanabda.

Explanation: If you subtract 3179 from the total elapsed years of the Kali age, the result is the Shaliwahana Shaka year. If you subtract 4548 from the elapsed Kali years, the remaining balance is the Karanabda The "Karanabda" refers to the specific epochal year used as a starting point for simplified astronomical calculations in a Karana text.. These should be understood as the "Constant Years" (Dhruvabda).

Calculating the Savana Day-Count

original: "Savana Dyugananayanamu" - This refers to calculating the Ahargana, or the number of civil days elapsed from a fixed epoch.

Verse Multiply the Epochal Constant by twelve (12) and add the current months... [place in two positions]... add the remainder... divided by seventy (70)... adding the intercalary months resulting from the division by thirty-three (33)...