डी. आर. कापरेकर
di. ar. kaparekar
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| poora nam | dattatray ramachandr kaparekar |
| any nam | di. ar. kaparekar |
| janm | 17 janavari, 1905 |
| janm bhoomi | dahanoo, maharashtr |
| mrityu | 1986 |
| mrityu sthan | devळali, maharashtr |
| karm bhoomi | bharat |
| karm-kshetr | ganitajn |
| khoj | kaparekar sankhya aur demalo sankhya |
| shiksha | snatak |
| vidyalay | mumbee vishvavidyalay |
| nagarikata | bharatiy |
| adyatan | 05:58, 11 julaee 2017 (IST) |
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dattatray ramachandr kaparekar (aangrezi: Dattathreya Ramchandra Kaprekar; janm- 17 janavari, 1905, dahanoo, maharashtr; mrityu- 1986 devळali, maharashtr) bharatiy ganitajn the. inhoanne sankhya siddhant ke kshetr mean anek yogadan diya, jinamean se kaparekar sankhya tatha kaparekar sthiraank pramukh haian. dattatray ramachandr dvara kaparekar sankhya aur demalo sankhya ki khoj huee haian.
sankshipt parichay
dattatray ramachandr kaparekar ka janm 17 janavari, 1905 ko dahanoo, maharashtr mean hua tha. unaki prarambhik shiksha thane aur pune mean, tatha snatak ki shiksha muanbee vishvavidyalay se huee thi. lekin unhoanne ganit ya kisi any vishay mean snatakottar digri ki padhaee nahian ki thi. ve nasik mean skool tichar the. ganit mean uchch shiksha n prapt karane ke bavajood unhoanne nanbar thyori par kam kiya. kuchh sthiraank (constant) aur bahut si sankhyayean (numbers) unake nam se jane jate haian. ve manoranjatmak ganit ke kshetr mean jane mane vyakti the.[1] uchch shiksha n prapt karane ke karan bharat mean ganitajnoan ne unhean vah samman nahian diya jo unhean milana chahiye tha. unake pepar bhi nimn shreni ke ganit ki patrikaoan mean chhapate the. ve ganit ke sammelanoan mean apane paise se jate the aur aanko par vyakhyan dete the. unhean kahian se paisoan ki madad nahian mil pati thi chooanki ve keval skool tichar the. unhean bharat mean samman tab mila jab unake bare mean martin gardanar ne saeeantiphik amerikan ke march, 1975 aank mean, unake bare mean likha.
kaparekar sthiraank
ganit mean ek sankhya 6174 hai jise kaparekar sthiraank (Kaprekar constant) kahate haian-
- koee bhi char aank ki sankhya lijiye jisake do aank bhinn hoan.
- sankhya ke aanko ko arohi (ascending) aur avarohi (descending) kram mean likhean.
- isase apako do sankhyayean mileangi. ab b di sankhya ko chhoti se ghatayean.
- jo sankhya mile is par punah 2 nanbar vali prakriya doharaean. is prakriya ko kaparekar vyavahar (Kaprekar’s routine) kahate haian.
- kuchh nishchit charanoan ke bad apako 6174 sankhya milegi. isake sath prakriya kramaank 2 ko apanane par bhi phir yahi sankhya milati hai isiliye ise kaparekar sthiraank kahate haian.
- udaharan
hamane sankhya li 3141.
ab prakriya kramaank 2 ko doharane par aise kram chalega
4311 - 1134 = 3177.
7731 - 1377 = 6354.
6543 - 3456 = 3087.
8730 - 0378 = 8352.
8532 - 2358 = 6174.
7641 - 1467 = 6174…
kaparekar sankhya aur demalo sankhya
ab kaparekar sankhya aur demalo sankhya ki bat karate hai. ye donoan sankhyaye bhi hamare kam charchit maharashtriyan ganitajn kaparekar ji ki khoji huee haian.
kaparekar sankhya : kisi diye huye adhar par (ham samanyataya 10 adhar vali dashamalav pranali ka istemal karate haian ) koee sankhya (shoony ya usase b di) jisake varg ko do aise gunakoan mean vibhajit kiya ja sake ki unhean jo dakar ham punah prarambhik sankhya ko prapt kar sakean, aisi sankhya ko kaparekar sankhya kahate haian.
- kuchh udaharan
| sankhya | varg | gunako me vibhajan |
|---|---|---|
| 703 | 703² = 494209 | 494+209 = 703 |
| 2728 | 2728² = 7441984 | 744+1984 = 2728 |
| 5292 | 5292² = 28005264 | 28+005264 = 5292 |
| 857143 | 857143² = 734694122449 | 734694+122449 = 857143 |
- kuchh aur udaharan
55, 99, 297, 703, 999 adi. visheshakar 9, 99, 999, ……….. shreni ki sabhi sankhyaean kaparekar sankhyaean haian.[2]
demalo sankhya : demalo sankhyaean Repunit sankhyaoan ke varg ka man haian. Repunit sankhyaoan ki ek vishesh shreni ko kahate haian. isaka matalab hai Repeated Unit aur Unit yani ikaee (1), to Repunit sankhyaean haian 1, 11, 111, 1111, ………. aur kramashah
inake varg se jo demalo (demlo) sankhyayean prapt hoti haian vo bhi b di manoranjak haian.
| 1² – 1 |
| 11² – 121 |
| 111² – 12321 |
| 1111² – 1234321 |
- demalo sankhya ke namakaran ki bhi kahani hai. demalo (Demlo) koee relave steshan hai jahaan unhean is sankhya ka vichar aya tha.
harshad sankhya
harshad sankhyao ka ek majedar gun hota hai, ye sankhyaye apane aanko ke yog se bhajy hoti hai. kaprekar ne inhe harshad sankhya arthath anandadayak sankhya kaha tha. udaharan ke liye sankhya lete hai 12. ab 1+2=3 sankhya 12 apane aanko ke yog 3 se bhajy hai arthath vah harshad sankhya hai. in sankhyaoan ko ganitajn Ivan M. Niven ke nam par niven sankhya bhi kahate hai.
nidhan
dattatray ramachandr kaparekar ka nidhan 1986 ko devळali, maharashtr mean hua tha.
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tika tippani aur sandarbh
- ↑ manoranjatmak ganit ke kshetr mean jane mane vyakti - dattatray ramachandr kaparekar (hiandi) unmukt. abhigaman tithi: 11 julaee, 2017.
- ↑ ganitajn kaparekar : kaparekar sthiraank, kaparekar sankhya tatha demalo sankhya (hiandi) vijnan vishv. abhigaman tithi: 11 julaee, 2017.
sanbandhit lekh
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varnamala kramanusar lekh khoj
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