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Sanatan Dharma teaches not only the procedures to realise the Supreme Reality, the causeless Cause of the Universe, it also abounds in practical tips to run the earthly life, be it researching Nature,Scientific concepts, lifestyle and ways to develop skills. One such is the Katapayadi system that helps one to enhance memory and recall.Ancient Hindus have developed systems to enhance memory and recall by designing techniques to learn by heart and recall instantly throughout one’s life what one has Learned. This technique is used to learn the Vedas, the Sacred text of the Hindus. Sacred texts of Hindus have been transmitted only orally over the past five thousand years and the Vedas are being transmitted by this method even now. Vedas are to be learnt only by hearing them. So they are called Sruthi, which is heard( Srothram).

Another technique iska·ṭa·pa·yā·di system (Devanagari: कटपयादि, also known as Paralppēru, Malayalam: പരല്‍പ്പേര്) of numerical notation is an ancient Indian alphasyllabic numeral system to depict letters to numerals for easy remembrance of numbers as words or verses. Assigning more than one letter to one numeral and nullifying certain other letters as valueless, this system provides the flexibility in forming meaningful words out of numbers which can be easily remembered. Katapayadi.This system was also used for passing secret messages.

Katapayadi System.

ka·ṭa·pa·yā·di system : कटपयादि, also known as Paralppēru, Malayalam: പരല്‍പ്പേര്) of numerical notation is an ancient Indian alphasyllabic numeral system to depict letters to numerals for easy remembrance of numbers as words or verses. Assigning more than one letter to one numeral and nullifying certain other letters as valueless, this system provides the flexibility in forming meaningful words out of numbers which can be easily remembered.

Rules of Katapayadi .

Following verse found in Śaṅkaravarman’s Sadratnamāla explains the mechanism of the system.

नञावचश्च शून्यानि संख्या: कटपयादय:।
मिश्रे तूपान्त्यहल् संख्या न च चिन्त्यो हलस्वर:॥

Transliteration:

nanyāvacaśca śūnyāni saṃkhyāḥ kaṭapayādayaḥ
miśre tūpāntyahal saṃkhyā na ca cintyo halasvaraḥ

Translation: na (न), ña (ञ) and a (अ)-s, i.e., vowels represent zero. The nine integers are represented by consonant group beginning with ka, ṭa, pa, ya. In a conjunct consonant, the last of the consonants alone will count. A consonant without a vowel is to be ignored.

Explanation: The assignment of letters to the numerals are as per the following arrangement (In Devanagari, Kannada, Telugu & Malayalam respectively).

Demo of the system in mathematics and Astronomy.

• Mādhava’s sine table constructed by 14th century Kerala mathematician–astronomer Mādhava of Saṅgama·grāma employs the Kaṭapayādi system to enlist the trigonometric sines of angles.
• Karaṇa·paddhati, written in the 15th century, has the following śloka for the value of pi (π)

അനൂനനൂന്നാനനനുന്നനിത്യൈ-സ്സമാഹതാശ്ചക്രകലാവിഭക്താഃചണ്ഡാംശുചന്ദ്രാധമകുംഭിപാലൈര്‍-വ്യാസസ്തദര്‍ദ്ധം ത്രിഭമൗര്‍വിക സ്യാത്‌Transliterationanūnanūnnānananunnanityaissmāhatāścakra kalāvibhaktoḥcaṇḍāṃśucandrādhamakuṃbhipālair

vyāsastadarddhaṃ tribhamaurvika syātIt gives the circumference of a circle of diameter, anūnanūnnānananunnanityai (10,000,000,000) as caṇḍāṃśucandrādhamakuṃbhipālair (31415926536).

• Śaṅkara·varman’s Sad·ratna·mālā uses the Kaṭapayādi system. The first verse of Chapter 4 of the Sad·ratna·mālā ends with the line:

(स्याद्) भद्राम्बुधिसिद्धजन्मगणितश्रद्धा स्म यद् भूपगी:Transliteration(syād) bhadrāmbudhisiddhajanmagaṇitaśraddhā sma yad bhūpagīḥSplitting the consonants in the relevant phrase gives,भ bhaद् dरा rāम् mबु buद् dधि dhiसि siद् dध dhaज jaन् nम maग gaणि ṇiत taश् śर raद् dधा dhāस् sम maय yaद् dभू bhūप paगी gī4–2–3–97–98–5356–2–9–51–413Reversing the digits to modern-day usage of descending order of decimal places, we get 314159265358979324 which is the value of pi (π) to 17 decimal places, except the last digit might be rounded off to 4.

• This verse encrypts the value of pi (π) up to 31 decimal places. Reference.https://en.m.wikipedia.org/wiki/Katapayadi_system

Indian mathematics is the discipline of mathematics as it developed in the Indian subcontinent. The mathematics of classical Indian civilization is an intriguing blend of the familiar and the strange. For the modern individual, Indian decimal place-value numerals may seem familiar—and, in fact, they are the ancestors of the modern decimal system¹.

In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, and Varāhamihira2. Ancient Indian mathematicians have contributed immensely to the field of mathematics. The invention of zero is attributed to Indians and this contribution outweighs all other made by any other nation since it is the basis of the decimal number system, without which no advancement in mathematics would have been possible

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