Dattatreya Ramachandra Krapeker (1905 – 1986)

D R కప్రేకర్ ముంబైకి ఉత్తరాన 100 కి.మీ దూరంలో భారతదేశంలోని పశ్చిమ తీరంలో ఉన్న దహను అనే పట్టణంలో జన్మించాడు. ఎనిమిదేళ్ల వయసులో తల్లి చనిపోవడంతో తండ్రి వద్ద పెరిగాడు. అతని తండ్రి జ్యోతిష్యం పట్ల ఆకర్షితుడైన గుమాస్తా. జ్యోతిష్య శాస్త్రానికి లోతైన గణితశాస్త్రం అవసరం లేనప్పటికీ, సంఖ్యలతో లెక్కించడానికి దీనికి గణనీయమైన సామర్థ్యం అవసరం, మరియు కప్రేకర్ తండ్రి ఖచ్చితంగా తన కుమారుడికి గణించడంలో ప్రేమను ఇచ్చాడు.

కప్రేకర్ థానేలోని సెకండరీ స్కూల్‌లో చదివాడు . అతను గణిత పజిల్స్ సాల్వ్ చేస్తూ గణిత పరిజ్ఞానాన్నిపెంపొందించుకునేవాడు . అతను 1923లో పూణేలోని ఫెర్గూసన్ కాలేజీలో తన తృతీయ విద్యను ప్రారంభించాడు. అక్కడ అతను రాంగ్లర్ R P పరంజ్‌పే గణిత బహుమతిని 1927లో గెలుచుకున్నాడు.

కప్రేకర్ ఎల్లప్పుడూ అతను ఆలోచించిన సంఖ్య సిద్ధాంతపరమైన ప్రశ్నలలో గొప్ప వాస్తవికతను చూపించాడు. అతను B.Sc పట్టభద్రుడయిన తరువాత, దేవ్‌లాలిలో గణిత శాస్త్ర ఉపాధ్యాయునిగా నియమితుడయ్యాడు, 1962లో 58 సంవత్సరాల వయస్సులో పదవీ విరమణ చేసే వరకు అతను తన కెరీర్ మొత్తాన్ని దేవ్‌లాలిలో ఉపాధ్యాయుడిగా గడిపాడు.

చాలా మంది భారతీయ గణిత శాస్త్రవేత్తలు కప్రేకర్ యొక్క సంఖ్యా సిద్ధాంత ఆలోచనలను చిన్నవిగా , అప్రధానమైనవిగా భావించి నవ్వేవారు. అతను తన ఆలోచనలలో కొన్నింటిని తక్కువ స్థాయి గణిత జర్నల్స్‌లో ప్రచురించగలిగాడు, అయితే ఇతర పత్రాలు ప్రైవేట్‌గా ముద్రించిన, దేవ్‌లాలి లేదా రచయిత, ఖరేస్‌వాడ, దేవ్‌లాలి, ఇండియా ద్వారా ప్రచురించబడిన శాసనాలతో ప్రైవేట్‌గా కరపత్రాలుగా ప్రచురించబడ్డాయి. ఈ రోజు కప్రేకర్ పేరు బాగా ప్రసిద్ధి చెందింది మరియు చాలా మంది గణిత శాస్త్రజ్ఞులు కప్రేకర్ చాలా వ్యసనపరుడైన సంఖ్యల గురించిన ఆలోచనలతో ఆసక్తిని కనబరిచారు.

1. Zero ( 0 ) is the only number which can not be represented by Roman numerals.

2. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion.

3. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D

4. 2 and 5 are the only primes that end in 2 or 5

5. An icosagon is a shape with 20 sides

6. Among all shapes with the same perimeter a circle has the largest area.

7. Among all shapes with the same area circle has the shortest perimeter

8. 40 when written “forty” is the only number with letters in alphabetical order, while “one” is the only one with letters in reverse order

9. ‘FOUR’ is the only number in the English language that is spelt with the same number of letters as the number itself

10. From 0 to 1,000, the letter “A” only appears in 1,000 (“one thousand”)

11. 12,345,678,987,654,321 is the product of 111,111,111 x 111,111,111. Notice the sequence of the numbers 1 to 9 and back to 1.

12. Have you ever noticed that the opposite sides a die always add up to seven (7)

13. Trigonometry is the study of the relationship between the angles of triangles and their sides

14. Abacus is considered the origin of the calculator

15. Here is an interesting trick to check divisibility of any number by number 3.A number is divisible by three if the sum of its digits is divisible by three (3)

16. Do you know the magic of no. nine (9)? Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9).

17. If you add up the numbers 1-100 consecutively (1+2+3+4+5…) the total is 5050

18. A ‘jiffy’ is an actual unit of time for 1/100th of a second

19. Have you heard about a Palindrome Number? It is a number that reads the same backwards and forward, e.g. 12421

20. Have you heard about Fibonacci? It is the sequence of numbers wherein a number is the result of adding the two numbers before it! Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on

Srinivasa Ramanujan ( 22 December 1887 – 26 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: “He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered”. Seeking mathematicians who could better understand his work, in 1913 he began a postal partnership with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognizing Ramanujan’s work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Hardy commented that Ramanujan had produced groundbreaking new theorems, including some that “defeated me completely; I had never seen anything in the least like them before”, and some recently proven but highly advanced results.

During his short life, Ramanujan independently compiled nearly 3,900 results. Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Nearly all his claims have now been proven correct.] The Ramanujan Journal, a scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan, and his notebooks—containing summaries of his published and unpublished results—have been analyzed and studied for decades since his death as a source of new mathematical ideas. As late as 2011 and again in 2012, researchers continued to discover that mere comments in his writings about “simple properties” and “similar outputs” for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death.He became one of the youngest Fellows of the Royal Society and only the second Indian member, and the first Indian to be elected a Fellow of Trinity College, Cambridge. Of his original letters, Hardy stated that a single look was enough to show they could only have been written by a mathematician of the highest calibre, comparing Ramanujan to mathematical geniuses such as Euler and Jacobi.

In 1919, ill health—now believed to have been hepatic amoebiasis (a complication from episodes of dysentery many years previously)—compelled Ramanujan’s return to India, where he died in 1920 at the age of 32. His last letters to Hardy, written in January 1920, show that he was still continuing to produce new mathematical ideas and theorems. His “lost notebook”, containing discoveries from the last year of his life, caused great excitement among mathematicians when it was rediscovered in 1976.

A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess Namagiri Thayar. He once said, “An equation for me has no meaning unless it expresses a thought of God.”