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![व्यासे वाररधधननहते रूपहृते व्यससागरासभहते ।
त्रिशरादिववषमसुंख्याभक्तुं ॠणुं स्वुं पृथक्रमात्कु याात्॥
vyAse vaariDhinihathe rUpahtRthevyasasAgarAbhihathe
thrisharAdhiviShamasMkhyAbhakthM TRNM svM ptRThakkramAth kuryaath
Meaning :
When the circumference/perimeter of the circle is given in terms of a series (containing d=diameter) then the diameter term i s
divided by the odd numbers (like 1, 2, 3...) and alternately added/subtracted fromthe rest (of the summation of series)
i.e:
Circumference = 4d/1 - 4d/3 4d/5 – 4d/7 ...which is basically the same series as PI/4 = SUMOF [(-1 i 1)/(2i-1)] /* over i from 1 to
infinity */
There were many inventions in the field of science and technology in ancient India. Since many persons of the present generation
does not know them, they will be described briefly to enable the readers to have the basic understanding about them.
Reference:
1) http://sanskritum.blogspot.in/2015/02/katapayadi-sankhya-sanskrit-and-pie.html
2) https://en.wikipedia.org/wiki/Katapayadi_system
3) https://www.facebook.com/BHARAT.untoldstory/posts/610567172308226
4) http://bvsubbaiah.tripod.com/blog/index.blog?entry_id=1400661](https://image.slidesharecdn.com/pivaluefromrigveda-160810182042/85/Pi-value-from-rigveda-5-320.jpg)
Uploaded byCH.PURUSHOTHAM (Aeronautical Engineering)
Pi value from rigveda
The document discusses how ancient Hindu manuscripts contained advanced scientific knowledge, including accurate calculations of pi up to 28 digits. It describes the Katapayadi numerical system used in Sanskrit to represent numbers in a mnemonic way using letters. A sloka from the Rig Veda is shown to give the value of pi to 28 digits through its technical translation, far more accurate than Western mathematicians could achieve until computers. Further, it explains how other ancient Sanskrit texts like the Sad-ratna-mālā also encoded the value of pi within verses using this numerical system, demonstrating sophisticated mathematical knowledge existed in ancient India.
Pi value from rigveda
- 1. SCIENCE OF AERONAUTICS AND ENGINEERINGEDUCATION TECHNICS CH. PURUSHOTHAM AERONAUTICAL ENGG. PI VALUE FROM RIGVEDA
- 2. PI VALUE FROMRIGVEDA Men of older generation used to say that all knowledge is there in the Vedas. Anyone who hears such words will have the first reaction that it is an over confident statement. We should remember here that any sloka in the ancient Hindu manuscripts has more than one meaning. Katapayadi sankhya is a simplification of Aryabhata ‘s Sanskrit numerals , due probably to Haridatta from Kerala. In Malayalam it is also known as ‘Paralperu’ For eg: represents 31415926536 which is _*1000000000000000 The oldest available evidence of the use of Kaṭapayādi ( कटपयादि) system is from Grahacāraṇibandhana by Haridatta in 683 CE. It has been used in Laghu·bhāskarīya·vivaraṇa written by Śaṅkara·nārāyaṇa in 869 CE. A Sloka in the 10th book of Rig Veda appears to be written for praising Lord Indra The technical translation of that Sloka gives the value of pi up to 28 digits accurately. It is not until the invention of the computers that the western mathematicians could get this value up to 16 digits accurately. Here is a test for those who think that a computer can do any calculation. Use the fastest computer available to you and write a program to calculate the value of pi up to 28 digits accurately. You will know how difficult it is. Vedic Numerical Code In Sanskrit, the following Vedic Numerical code was used in many slokas. Means... कादि नव Kaadi nava Kaadi Nava Starting from ka, the sequence of 9 letters represent 1,2,..9 टादि नव Taadi nava Taadi Nava starting from ta, the sequence of 9 letters represent 1,2,..9 पादि पञ्चक Paadi panchaka Paadi panchaka (1-5), starting from pa
- 3. यद्यश्टक Yadyashtaka Yadyashtaka(1-8) starting from ya क्ष शुन्यम् Kshah sunyam ksha represents 0 In detail Na(न), nya(ञ), i.e., vowels represent Zero. The nine integers are represented by consonant group beginning with ka, ta, pa,ya. In a conjunct consonant, the last of the consonants alone will count. A consonant without vowel is to be ignored. KaTaPaYa di for Melakarta Ragam Name & numbers 1 2 3 4 5 6 7 8 9 0 క क Ka ఖ ख Kha గ ग Ga ఘ घ Gha ఙ ङ Gna చ च Cha ఛ छ Cha జ ज Ja ఝ झ Jha ఞ ञ nya ట ट Ta ఠ ठ Tha డ ड Da ఢ ढ Dha ణ ण ~na త त Ta థ थ Tha ద ि Da ధ ध Dha న न Na ప प Pa ఫ फ Pha బ ब Ba భ भ Bha మ म Ma య य Ya ర र Ra ల ल La వ व Va శ श Sa ష ष Sha స स Sa హ ह Ha క్ష क्ष ksha h గోపీభాగయమధువ్రా త-శ ృంగిశోదధిసృంధిగ | ఖలజీవితఖాతావ గలహాలారసృంధర || गोपीभाग्य मधुव्रातः श्ुुंगशोिधध सुंधधगः | खलजीववतखाताव गलहाला रसुंधरः ||
- 4. gopeebhaagya maDhuvraathaH shruMgashodhaDhisaMDhigaH khalajeevithakhaathaava galahaalaa rasaMDharaH 3.1415926535897932384626433832792... The above sloka has actually 3 meanings 1. In favor of Lord Shiva 2. In favor of Lord Krishna 3. The value of PI upto 32 decimals. Śaṅkara·varman's Sad·ratna·mālā uses the Kaṭapayādi system. A famous verse found in Sad·ratna·mālā is भद्राम्बुद्धधससद्धजन्मगणणतश्द्धा स्म यद् भूपगी: Transliteration bhadrāṃbuddhisiddhajanmagaṇitaśraddhā sma yad bhūpagīḥ Splitting the consonants gives, भ bha द् d रा rā म् ṃ बु ba द् d धि dh सि sa द् d ि dha ज ja न् n म ma ग ga णि ṇa त ta श् ṣ र ra द् d िा dha ि् s म ma य ya द् d भू bha प pa धग gi 4 - 2 - 3 - 9 7 - 9 8 - 5 3 5 6 - 2 - 9 - 5 1 - 4 1 3 Reversing 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. Series of PI There is also a sloka for expanding the series of PI. It's given below.
- 5. व्यासे वाररधधननहते रूपहृतेव्यससागरासभहते । त्रिशरादिववषमसुंख्याभक्तुं ॠणुं स्वुं पृथक्रमात्कु याात्॥ vyAse vaariDhinihathe rUpahtRthevyasasAgarAbhihathe thrisharAdhiviShamasMkhyAbhakthM TRNM svM ptRThakkramAth kuryaath Meaning : When the circumference/perimeter of the circle is given in terms of a series (containing d=diameter) then the diameter term i s divided by the odd numbers (like 1, 2, 3...) and alternately added/subtracted fromthe rest (of the summation of series) i.e: Circumference = 4d/1 - 4d/3 4d/5 – 4d/7 ...which is basically the same series as PI/4 = SUMOF [(-1 i 1)/(2i-1)] /* over i from 1 to infinity */ There were many inventions in the field of science and technology in ancient India. Since many persons of the present generation does not know them, they will be described briefly to enable the readers to have the basic understanding about them. Reference: 1) http://sanskritum.blogspot.in/2015/02/katapayadi-sankhya-sanskrit-and-pie.html 2) https://en.wikipedia.org/wiki/Katapayadi_system 3) https://www.facebook.com/BHARAT.untoldstory/posts/610567172308226 4) http://bvsubbaiah.tripod.com/blog/index.blog?entry_id=1400661