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Aschig
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| | Monday, August 04, 2003 - 6:38 pm: | 
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Things can be made even simpler by noticing the point ind ivision when you reach the difference between Numerator and Denomintor and using the "all from nine" sutra from there on.
For example, when doing 1/19:
Rather than doing all of the following
0.0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1
_1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0
stop wehn you reach
0.0 5 2 6 3 1 5 7 8
_1 0 1 0 0 1 1 1 1
Note that the last working dividend is 18(=19-1) i.e. (D-N)
Your quotient so far is 0.052631578
Just subtract all the nine digits from
999999999 and get: 947368421
And indeed your recurring decimal is:
0.052631578947368421
The same applies for the other examples. Try those out.
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Aschig
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| | Thursday, August 07, 2003 - 1:21 am: |
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A similar method works if you wish to divide by a number that is one more than a power of 10 (or multiple thereof).
e.g. 13/21
Here the working divisor is still 2, but now you also reduce the working dividend by 1 to 12 (to 1.2 since 21-1=20 -> 2)
so 13/21 = (1.2/2)
Q=0.6 R=0
as before put the 0 before the 6 (like a carry).
Now to get the next dividend you use the
9's complement of 6 i.e. your working dividend is 03. Do the 9's complement taking at every step.
(3/2) = 1 R 1 (Q so far 0.61)
(18/2) = 9 R 0 (Q so far 0.619)
(00/2) = 0 R 0 Q 0.6190
(09/2) = 4 R 1 Q 0.61904
(15/2) = 7 R 1 Q 0.619047
(12/2) and the decimal repeats.
Another example: 17/61 = (1.6/6)
Q 0.2 R 4 Complement of Q =7 new D=(47)
Q 7 R 5 Comp 2 new D = (52)
Q 8 ...
Hence 17/61=0.278...
Lets take 19/91
It becomes 1.8/9
(1.8/9) = 0.2 R 0
0.2 0 8 7 ...
0.7.7.8
19/101
Here (1.8/10) can be made into 0.18/1 and we do things in groups of 2
0.18 are the first digits of the quotient,
R=0
Complement of 18 is 81 those are the next digits. R is 0. complement of 81 is 18 and in fact the decimal repeats 0.188118811881...
127/1001 groups of 3 (126/1)
0.126873 and the decimal repeats
73/121 = (72/12)
0.6 0 3 3 ....
0.3.3.0
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Zakki
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| | Thursday, August 07, 2003 - 4:31 pm: |
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Ashish, have you programmed any of these algorithms? When I was in college (in 1980's) I was writing code for microprocessors with very limited memory and two four byte registers etc. The code to add two three digit numbers with carry, went on for eight pages. With today's processing speeds and memories, do you think these algorithms will be faster than conventional ones used by Windows, Unix or IBM/OS etc.?
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Aschig
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| | Thursday, August 07, 2003 - 9:16 pm: |
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zakki, just last week I had exactly that thought. But I think it will not work for two reasons:
(1) the modern computers (microprocessor based) are hardwired for quickness in binary
manipulation of numbers (mainly doubling and halving which is what is used in most opeartions inthe form of bit shifts), and
(2) vedic methods seem easy because our brain can quickly grasp the special situations and particular sutras that will be required. For a program to do that a lot of conditionals will be required which are time consuming.
So with some specific hardwiring, it could be used to make computers faster, but it may take a lot of effort (BTW just a couple of days back I heard that CRAY computers are making a come back - they are specialized computing machines rather than networks of cheap chips).
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Zakki
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| | Friday, August 08, 2003 - 9:20 pm: |
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AaXaIXaÊ Qanyavaad. mauLat AaplyaakDo far pUvaI- sava- kahI eokUna paz k$naca iXakayacaI pwt hÜtI. AaiNa
Aaplaa maoMdU ha kuzlyaahI yaM~apoxaa jalad gaitnao caalatÜ. ³Aaplaa mhNajao tuJyaasaar#yaa huXaar maulaaMcaa²
maaJaa navho.´ malaa tr AjaUnaih vaaTto kI jaI kamao maoMdU sahja k$ XaktÜÊ %yaalaa yaM~ vaap$ca nayao.
f> AsalaI XaokDÜ gaiNato ekdma krayacaI AsalaI trca yaM~acaa ]pyaÜga hÜtÜ.
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Alhad
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| | Friday, August 22, 2003 - 8:53 pm: |
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vaOdIk gaiNatavar search krta krta BaartIya gaiNatacyaa [ithasaavarIla ek caaMgalaI link imaLalaI ..
http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/index.html
... Aalhad
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Kaua
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| | Thursday, June 10, 2004 - 4:39 am: |
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Mi ithalaa nava member ahe...Ani Vaidik Ganita var charcha pahun atishay bare vaatale...
Mi swataha Vaidik ganitacha course kela ahe ani pariksha hi dilyaa ahet.
vaidik ganita baabat kahi mahiti det ahe.
Bharatiy sanskruti madhe zatapat calculations karataa kahi ganiti sutra phaar purvi pasoon vaparali jaat. Ti mukhyatwe karoon sanskrit madhe lihoon thevaleli hoti. Jene karoon ti phakt kahi uchchabhru vargala kalatil ani tyannach tyacha phayada hoiil.
Asha kotya manovrutti mule eka mahan ganiti padhdhatila aapan phaar varsha mukalo.
Europian deshancha phaar motha phayada mhanaje tyanni (swataha hoon kinva na ilajane) kelele "Sharing of Knowledge". Tya mulech audyogik krantila chalanaa milali. Pan aapalya ithe matra dnyaana swataha kade theoon tyacha laabh ghyayacha prayatna kela gela.
19 vya shatakaat Vaidik ganit ya nava khali tyala parat ekda manyata prapt zali ani tyacha prasaar hou lagalaa.
Pan tyacha ani Vedancha kahihi sambandha nahi.
Ekoon 16 mukhya Vaidik sutre ani barich up-sutre vaidik ganitaat sangitali aahet.
Tyaat beejganita pasoon, basic Integration, derivatives ityadi sarva prakar namood kele ahet.
Vaidik ganitacha ajoon prasaar honya sathi matra agadi shaley staraa pasoon te shikavale gele pahije.
- Kaustubh
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Zakki
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| | Thursday, June 10, 2004 - 4:15 pm: |
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kaua, Aata hI 16 mau#ya va barIca ]psaU~o kuzo imaLtIlaÆ maaiht Asalyaasa kLvaa. Qanyavaad.
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Kaua
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| | Tuesday, June 15, 2004 - 8:16 am: |
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Vaidik ganitachi sagali pustake bajaraat upalabdha ahet. marathi pustakanche 4 bhaag ahet, pan English madhe matra te sarva ekaach pustakaat sankalit kelele ahe.
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Hemantp
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| | Tuesday, June 15, 2004 - 11:40 am: |
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kaua : hI pustko kuzo imaLtIla to saaMgaala kaya ?
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Vaatsaru
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| | Tuesday, June 15, 2004 - 12:05 pm: |
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Hemant, Majestic bookstall madhun mi gelya varshi ghetali hoti... pan kuthalyahi mothya book depo madhe upalabdha asaavit.
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Maanus
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| | Saturday, November 03, 2007 - 2:39 am: |
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gr8 हाच BB शोधत होतो.
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Maanus
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| | Friday, March 21, 2008 - 1:40 pm: |
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वैदीक नाही, पण संगणकातील गणित कसे काम करते हे माहीत करुन घ्यायचे असेल तर हा ivdeo जरुर बघा http://www.youtube.com/watch?v=GcDshWmhF4A
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