१.१ (छन्दःशास्त्र ८.३४)
परे पूर्णमिति ॥
pare pūrṇamiti ||
मेरु-प्रस्तार (Pascal's Triangle Construction)
\[ \binom{n}{k} = \binom{n-1}{k-1} + \binom{n-1}{k} \]
English Pingala's Meru Prastara: Place 1 at the peak. Below it, write two 1s. Then each interior entry is the sum of the two numbers directly above it—forming Pascal's Triangle 1800 years before Blaise Pascal.
१.२ (छन्दःशास्त्र ८.२३-२५)
द्विरर्धे । रूपे शून्यम् । द्विर्द्विने तु ॥
dvirardhe | rūpe śūnyam | dvirdvine tu ||
द्विआधारी रूपान्तरण (Binary Conversion Algorithm - Naṣṭa/Udggiṣṭa)
English Pingala's algorithm for converting decimal numbers into binary strings of Laghu (0) and Guru (1): If divisible by 2, divide by 2 and write 0 (rūpe śūnyam). If odd, subtract 1, divide by 2 and write 1. This is the exact modern binary arithmetic algorithm.