A verse that is a number: π to seventeen places in the Sadratnamālā (1819)

# A verse that is a number: π to seventeen places in the Sadratnamālā (1819)

In 1819, in the Malabar country of Kerala, a nobleman-mathematician named Śaṅkara Varman finished the *Sadratnamālā*, a complete manual of astronomy in 211 Sanskrit verses. One of those verses, when its consonants are read through a cipher, *is* the number π. Charles Whish, the East India Company civil servant who reported the Kerala texts to the Royal Asiatic Society, translates the rule the verse completes:

> "…measure the diameter of a great circle by 100000000000000000 > equal parts, the circumference **will be equal to > 314159265358979324 of such parts.**" > > — *Sadratnamālā*, trans. Whish (1834)

Check it: π = 3.14159265358979323846…, so a diameter of 10¹⁷ gives a circumference of 314159265358979323.8 — which rounds to exactly the verse's value. Seventeen figures, correctly rounded, composed into a line of poetry that scans.

The cipher

The encoding is **kaṭapayādi**, the most elegant of Sanskrit's [several number-in-verse notations](/c/6efa0558-3861-597a-a28e-4e020743303f). Each consonant maps to a digit — *ka* through *jha* cover 1–9, *ṭa* and *pa* rows recycle the digits, *ya* onward runs 1–8, and nasals or bare vowels give 0. Vowels carry no value, and where consonants cluster, only the one joined to the vowel counts. The consequence: for every digit the poet has three or four consonants to choose from, and full freedom in vowels — enough freedom to spell *actual words*. A skilled author can therefore write a sentence that means something *and* encodes an arbitrary number, digit for digit, in a fixed meter whose scansion doubles as a checksum against copying errors.

That is what the Sadratnamālā's π-verse is: a metrical line whose surface reading is devotional and whose consonant skeleton is 3-1-4-1-5-9-2-6-5-3-5-8-9-7-9-3-2-4. (The cached 1834 scan carries the verse only in damaged transliteration, so this article describes the mechanism and relies on Whish's own translation of its value — quoted above — rather than reproducing a reconstructed text.)

The honest frame: 1819 is not a record

Let the date do its work. By 1819 Europe was far ahead on sheer digits — Jurij Vega had computed 126 decimals by 1794 with Machin-type arctangent series, and the arithmetization of analysis was in full swing. Śaṅkara Varman's seventeen places set no world record, and this claim does not pretend otherwise.

What the verse attests is two things Europe did not have.

First, **the format**. A number stored as a meaningful, metrical, memorizable sentence — self-checking, transmissible without paper — is a genuinely different technology from a printed digit string, and kaṭapayādi is its most refined implementation. Nobody else's mathematics could *rhyme* its constants.

Second, and more important, **the lineage**. Śaṅkara Varman did not look π up. He computed it with the infinite-series methods of his own school — the Kerala tradition whose [series for π this corpus documents from the Tantrasaṅgraha of c. 1500](/c/55530187-0d22-56de-ae83-1ca4c614833a), and whose founding figure Mādhava worked around 1400. When Whish met him (he calls him "a very intelligent man and acute mathematician," brother of the Raja of Kaḍattanāḍu), he was meeting the *living end* of a four-century unbroken chain of working infinite-series mathematics — a tradition that had reached calculus-grade results [centuries before Leibniz](/c/55530187-0d22-56de-ae83-1ca4c614833a) and was still teaching, computing, and composing when the modern world arrived to take notes. The Sadratnamālā is the document that proves the chain never broke.

The corpus's three π claims now form a deliberate arc: [Aryabhata's 3.1416, flagged as "approximate," in 499](/c/0b862684-d325-5002-b054-169bd2253ef9); the Tantrasaṅgraha's infinite series with corrections around 1500; and seventeen encoded places in 1819. Thirteen centuries of one tradition sharpening one number — and stating, at every stage, exactly what kind of answer it had.

Legacy

Whish's 1834 paper — the source text for this claim — closed with the Sadratnamālā precisely because it demonstrated continuity; the paper then lay ignored for a century before the Kerala school's rediscovery in the 1940s. Śaṅkara Varman thus occupies a curious place: the last major mathematician of the Sanskrit siddhānta tradition, and the first whose work a European learned society heard about within his own lifetime.

The kaṭapayādi habit never died in Kerala — Carnatic music still indexes its 72 melakarta ragas by kaṭapayādi encoding of their names — and the π-verse survives as the tradition's signature artifact: a civilization's favorite constant, carried to seventeen places, in a sentence you can sing.

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Sources

- [Whish, "On the Hindú Quadrature of the Circle…", *Transactions of the Royal Asiatic Society*, vol. 3, 1834](https://archive.org/details/jstor-25581775) — the Sadratnamālā rule and value (pp. 519–520), and Whish's account of Śaṅkara Varman. - Plofker, *Mathematics in India*, 2009, ch. 7 — the Kerala school's later history and kaṭapayādi (secondary synthesis). - Sarma, "Śaṅkara Varman and his Sadratnamālā" — modern scholarship on the text (referenced for context only).

Related claims

- [Kerala's infinite series for π (~1500 CE)](/c/55530187-0d22-56de-ae83-1ca4c614833a) - [Aryabhata's π = 3.1416, called "approximate" (499 CE)](/c/0b862684-d325-5002-b054-169bd2253ef9) - [Moon-eyes-fires-oceans: writing numbers as poetry](/c/6efa0558-3861-597a-a28e-4e020743303f)