705000 An ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960). JULY 05, 2014 PUBLIC LEARNING-FACEBOOK VEDIC MATRIX -GROUP PLEASE SEND A LIST OF STUDENTS WITH A REQUEST TO ADD THEM AND MARK 5 MAY, -2014 ON YOUR ADD LIST. ALL TOPICS ARE IMAGINED, CREATED AND PUBLISHED BASED ON VEDIC MATHEMATICS BY SHRI JAGADGURU SANKARACHARYA (1884-1960) A HUMOROUS SENTENCE (ANY LANGUAGE) AND A RELATED FUNNY FIGURE TOGETHER MAKES A CARTOON, WE LIKE AND GRASP IT. EACH LESSON OF LEARNING OF VEDIC COMPUTING IS A CARTOON. AVEDIC SITRA (SENSIBLE LANGUAGE) AND VEDIC 2-DIMENSIONAL MATRIX (FUNNY FIGURE) ARE THERE IN EACH LESSON. GRASP BOTH THESE VERY WELL ANCIENT INDIAN MEDIUM TO SEE AND LEARN MATHEMATICS IS VEDIC MATRIX (1D, 2D AND/OR 3D). SIMPLER 2D WILL BE EXPLAINED HERE. LANGUAGE USED IS ENGLISH. COPY/TRANSLATE/ PUBLISH.FREELY. RAGHUTHAMAN.K.K MANAGER TOOL ENGINEERING (RETIRED-2006) BAJAJ AUTO LIMITED. AKURDI 411 035... INDIA BASED ON MY VEDIC MATRIX AND VEDIC MATHEMATICS AWARENESS *************************************************************************************** I SHARED MY VIEWPOINTS ON INFINITY (IDEA EXCHANGE ON INFINITY) *************************************************************************************** October 14, 2008 Basics of ‘infinity’ (A my viewpoints on infinity shared on internet) 1) Your explanations are very good. 2) “1/0 = infinity” is wrong 3) “1/ (infinitesimal) = infinity” too is an ‘indefinite relation’ 4) ‘Infinity’ and ‘infinitesimal’ are mutually related concepts! 5) Whole numbers (say a-unit increases) are 1, 2, and 3…infinity 5) A unit less than ’1, 2, 3…infinity’ is ’0, 1, 2… (Infinity-1)’ 6) (Infinity-1) is” endless all 9 digits” number. 7) Infinity is {(endless ‘all 9′) +1}. It is (1& endless ‘all 0′) 8) Difference in between infinity and (infinity-1) is one. 9) Infinity cannot be used as a “definite/fixed” number 10) A theorem that relates ‘infinity’ confuses a user! 11) 2D square matrices are visual matrix positions 12) 2D has equal-digit ‘row’ and ‘column’ numbers 13) 2D matrix positions are merged row-column numbers 14) Matrix 0…9 has 10 0 positions 00…99 15) Matrix 00…99 has 100 00 positions 0000…9999 16) Matrix 000…999 has 1000 000 positions 000000…999999 17) Matrix n 0s…n 9s has 1& (n 0s) (n0s) positions. 18) Just ahead of last matrix position (all 9) lay a related infinity! 19) 100(matrix 0…9), 100000 (matrix 00…99) etc are ‘infinity’ 20) Either ‘a-zero’ or ‘a related-infinity’ can be used to compute. 21) Vedic 2D matrix virtues have been compiled as Vedic sutras. 22) Vedic sutras help all users “to compute” in a best possible manner 23) Vedic sutras are few but each one of it works in many ways! 24) Related Number application is too simple and straightforward! 25) Least matrix 0…9 and any huge (n 0s… n 9s) has ‘similar’ virtues! 1/9^2= 0.0 1 2 3 4 5 6 7 9 & (second last 8 missing) 1/99^2=0.00 01 02 03 04…95 96 97 99 & (second last 98 missing) 1/999^2= 0.000 001 002 003…995 996 997 999 & (998 is missing) 1/(thousand times 9)^2= (1000 times 0)(999 times 0 & 1)(999 times 0 & 2)(999 times 0 & 3)à number groups increases by a-unit ß (999 times 9 & 6)(999 times 9 and 7) & (1000 times 9). Each bracketed ‘number group’ is part of ‘a huge digits number’. It has {(1000 times 9) ^2 -1000) digits in it and each digit can be remembered accurately! This example shows that ancient Indians had analyzed/used infinity far more sensibly. Vedic ‘matrix by matrix’ number application reveals it! Ancient Indians have used relations like these for mental computing! Vedic sutras that have been disclosed by Shri Jagadguru Sankaracharya (1884-1960) are proof to “infinite digits related mental computing” by ancient Indians! It is simplest of logical computing! We can apply practical matrix-by-matrix number application even today. Computers will help us to do it! Vedic Mathematics is a classic example of using endlessly recurring number groups. They perfectly knew ‘sense infinity’, which differ from modern mathematics knowledge (infinity). I have already explained it! Related basics I have also published on a site (please web search Vedic matrix). Concerned number applications are given on ‘Orkut’ forum NUMBER ZERO, link kk Raghuthaman, and community/forum. Vedic Mathematicians have used whole number-unit to arrive at infinity and infinitesimal -unit to arrive at one. Infinite a-units (ones) make ‘infinity’ Infinite least-units (infinitesimal units) make ‘one’ 26) To understand a-infinity we have to grasp number of ‘a-units’ in it 27) An increase from “0 to 1″ is like an increase from “1 to infinity”! Both are digital a-unit increases 28) ‘One’ has infinite ‘infinitesimal-units’ within it and ‘infinity’ has infinite ‘a-units’ within it. When both said infinites are technically same both ‘infinitesimal’ and ‘infinity’ becomes an easier to grasp knowledge! 29) Please don’t ignore one (which is made up of infinite*infinitesimal units). Your conclusion, “infinity is not a number” will pose a new question “is one a number?” 30) Zero, infinitesimal, (1- infinitesimal), which is 0.999…endless digits…999 and ‘one’ is a ‘zero to 1′ decimal number range. 31) Zero, one, (infinity-1), which is ’999…endless digits…999′ and ‘infinity’ is a ‘zero to infinity’ whole number range! There is no need to use ‘numbers less than zero’, which is not-liked number application! 32 A number system includes all numbers in a range 0 to infinity. Mathematics binds all numbers, (which includes zero and infinity). 33) 0 to (infinity-1) which is ‘all 9′ numbers is good enough for practical number applications. ‘Vedic mathematics’ makes use of virtues of all 2D square matrix positions (excluding infinity). Vedic sutras carry ‘sense of doing it’! //////////////////////////////////////////////////////////////////////////////////////////////////////////////////// 0 PRIME-NUMBERS PRIME- BASE AND VEDIC-MATRIX 705011 An ANCIENT INDIAN VEDIC MATHEMATICS A WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960). (1)Prime-number by table of 6 (+/-) 1 in 2D square ////////// ////////// ////////// ////////// ////////// ////////// matrix 0…9 Left top far corner of a “cube 0…9” is 2D ‘00-start’ and 3D ‘000-start ‘. All 2D ‘00…99’ (top 10x10) and 3D ‘000…999 are completely within 10x10x10. Visible ‘layer-0’ is a 2D plane and related ‘table of 6’ positions are shown. Each “shown position (+/-1)” is a prime-base (can have more than 1 prime numbers as factors). Prime-bases and prime-numbers are equally useful. In 6 (+/-) 1 cases “prime base” divided by “confirmed prime number of row-0 (5 and 7 only)” is a ‘division check’. If there is ‘no remainder’ to at least one ‘division check’ it does confirm ‘NOT A PRIME NUMBER’.49 is prime base by 48(+/-) 1. Division check is by 49/5 and 49/7. 49/7= 7.Therefore 49 is NOT PRIME NUMBER. ...0......1......2......3.......4......5.......6......7......8.......9 x 00- ------ ------ ------ ------ ------ x 06- ------ ------ ------ 0 ------ ------ x 12- ------ ------ ------ ------ ------ x 18- ------ 1 ------ ------ ------ ------ x 24- ------ ------ ------ ------ ------ 2 x 30- ------ ------ ------ ------ ------ x 36- ------ ------ ------ 3 ------ ------ x 42- ------ ------ ------ ------ ------ x 48- ------ 4 ------ ------ ------ ------ x54- ------ ------ ------ ------ ------ 5 x 60- ------ ------ ------ ------ ------ x 66- ------ ------ ------ 6 ------ ------ x 72- ------ ------ ------ ------ ------ x 78- ------ 7 ------ ------ ------ ------ x 84- ------ ------ ------ ------ ------ 8 x----- ------ ------ ------ ------ ------ x 96- ------ ------ ------ 9 In this case each 6 (+/-)1 is used as an x-reference Principle followed to fix a prime number is “x-reference (+/-)1” 705012 An ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960). (2)Prime-number by table of 6 (+/-) 1 in 2D square ////////// ////////// ////////// ////////// ////////// //////// matrix 00…99 Left top far corner of a “cube 00…99” is 2D ‘0000-start’ and 3D ‘000000-start ‘. All 2D ‘0000…9999’ (top 100x100) and 3D ‘000000…999999 are completely within 100x100x100. Visible ‘layer-00’ is a 2D plane and related few ‘table of 6’ positions are shown. Each “shown position (+/-1)” is a prime-base (can have more than one prime numbers as factors). Prime-bases and prime-numbers are equally useful. In 6 (+/-) 1 cases “prime base” divided by “confirmed prime numbers of row-00 (05…97 only)” is a ‘division check’. If there is ‘no remainder’ to at least one ‘division check’ it does confirm ‘NOT A PRIME NUMBER’. 0205 is prime- base by 0204 (+/-) 1. Division check is by 0205/5 through 0205/97. 0205/5= 41.Therefore 0205 is NOT PRIME NUMBER. ..00.....01....02....03....04.....05.....96....97.....98.....99 0000 ------ ------ ------ ------ ------ 0096 ------ ------ ------ 00 ------ ------ 0102 ------ ------ ------ ------ ------ 0198 ------ 01 ------ ------ ------ ------ 0204 ------ ------ ------ ------ ------ 02 0300 ------ ------ ------ ------ ------ 0396 ------ ------ ------ 03 ------ ------ 0402 ------ ------ ------ ------ ------ 0498 ------ 04…Only (step of 6) numbers shown in 2D matrix 00…99 ------ ------ ------ ------ 9504 ------ ------ ------ ------ ------ 95 9600 ------ ------ ------ ------ ------ 9696 ------ ------ ------ 96 ------ ------ 9702 ------ ------ ------ ------ ------ 9798 ------ 97 ------ ------ ------ ------ 9804 ------ ------ ------ ------ ------ 98 x----- ------ ------ ------ ------ ------ 9996 ------ ------ ------ 99 In this case each 6 (+/-)1 is used as an x-reference Principle followed to fix a prime number is “x-reference (+/-) 1” 705013 An ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960). (3)Prime-number by table of 6 (+/-) 1 in 2D square ////////// ////////// ////////// ////////// ////////// //// matrix 000…999 Left top far corner of a “cube 000…999” is 2D ‘000000-start’ and 3D ‘000000000-start ‘. All 2D ‘000000…999999’ (top 1000x1000) and 3D ‘000000000…999999999 are completely within 1000x1000x1000. Visible ‘layer-000’ is a 2D plane and related few ‘table of 6’ positions are shown. Each “shown position (+/-1)” is a prime-base (can have more than one prime numbers as factors). Prime-bases and prime-numbers are equally useful. In 6 (+/-) 1 cases “prime base” divided by “each confirmed prime number of row-000 (005…997 only)” is ‘division check’. If there is ‘no remainder’ to at least one ‘division check’ it does confirm ‘NOT A PRIME NUMBER’. 002005 is prime- base by 002004 (+/-) 1. Division check 002005/5 through 002005/997show 002005/5= 401. (NOT PRIME NUMBER ...000..001…002…003…004…995…996…997…998…999 000000 --- ------ ------ ------ ------ 000996 --- ------ ------ 000 ------ ------ 001002 --- ------ ------ ------ ------ 001998 --- 001 ------ ------ ------ ------ 002004 --- ------ ------ ------ ------ 002 003000 --- ------ ------ ------ ------ 003996 --- ------ ------ 003 ------ ------ 004002 --- ------ ------ ------ ------ 004998 --- 004…Only (step of 6) numbers shown in 2D matrix 00…99 ------ ------ ------ ------ 995004 --- ------ ------ ------ ------ 995 996000 --- ------ ------ ------ ------ 996996 --- ------ ------ 996 ------ ------ 997002 --- ------ ------ ------ ------ 997998 --- 997 ------ ------ ------ ------ 998094 --- ------ ------ ------ ------ 998 x----- ------ ------ ------ ------ ------ 999996 --- ------ ------ 999 In this case each 6 (+/-) 1 is used as an x-reference. Principle followed to fix a prime number is “x-reference (+/-) 1” 705014 ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960). (4)Prime-number by table of 6 (+/-)11 (2D square ////////// ////////// ////////// ////////// ////////// ////////// matrix 0…9) Left top far corner of a “cube 0…9” is 2D ‘00-start’ and 3D ‘000-start ‘. All 2D ‘00…99’ (top 10x10) and 3D ‘000…999 are completely within 10x10x10. Visible ‘layer-0’ is a 2D plane and related ‘table of 6’ positions are shown. Each ‘shown position’ (+/-) 1 is a prime-base (can have more than 1 prime numbers as factors). Prime-bases and prime-numbers are equally useful. In 6 (+/-) 1 cases “prime base” divided by “confirmed prime number of row-0 (3, 5 and 7 only)” is ‘division check’. If there is ‘no remainder’ to at least one ‘division check’ it does confirm ‘NOT A PRIME NUMBER’. @29 is prime base by 18 (+/-) 11. Division check is by 29/5 and 29/7. ‘4’ and ‘1’ are respective remainders. Therefore 29 is PRIME NUMBER. ...0......1......2......3.......4......5.......6......7......8.......9 x 00- ------ ------ ------ ------ ------ x 06-@---- ------ @--- 0 ------ ------ x 12- ------ ------ ------ ------ ------ x 18- ------ 1 ------ ------ ------ ------ x 24- ------ ------ @---- ------ @--- 2 x 30- ------ ------ ------ ------ ------ x 36- ------ ------ ------ 3 ------ ------ x 42- ------ ------ ------ ------ ------ x 48- ------ 4 ------ ------ ------ ------ x54- ------ ------ ------ ------ ------ 5…Indians threw away ‘matrix’ and ‘division check’??? X 60- ------ ------ ------ ------ ------ x 66- ------ ------ ------ 6…Each step of 6 position (including 00) is ‘n’ ------ ------ x 72- ------ ------ ------ ------ ------ x 78- ------ 7… {(n) +/-) 10} means y= ‘1’x10. Remember Vedic z ‘y’ x ------ ------ ------ ------ x 84- ------ ------ ------ ------ ------ 8 ------ ------ ------ ------ ------ ------ x 96- ------ ------ ------ 9 10--- ------ ------ ------ ------ ------ ------ ------ x 108 ------ In this case each 6 (+/-) 11 is used as y-reference pair {(n) +/-) 10} (+/-) 1 Principle followed to fix a prime - base is “strep 6 -reference (+/-) 11” 705015 A ANCIENT INDIAN VEDIC MATHEMATICS A WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960). (5)Prime-number by table of 6 (+/-) 0101 (2D sq ////////// ////////// ////////// ////////// ////////// ///// matrix 00…99) Left top far corner of a “cube 00…99” is 2D ‘0000-start’ and 3D ‘000000-start ‘. All 2D ‘0000…9999’ (top 100x100) and 3D ‘000000…999999 are completely within 100x100x100. Visible ‘layer-00’ is a 2D plane and related few ‘table of 6’ positions are shown. Each ‘shown position’ (+/-) 0101 is a prime-base (can have more than 1 prime numbers as factors). Prime-bases and prime-numbers are equally useful. In 6 (+/-) 0101 cases “prime base” divided by “confirmed prime numbers of row-00 (3, 5… 97 primes only)” is ‘division check’. If there is ‘no remainder’ to at least one ‘division check’ it does confirm ‘NOT A PRIME NUMBER’. @0299 is prime-base by 0198 (+/-) 0101. Division check is by (0299/3, 0299/5 through 0299/97) primes only. After fixing that ‘each division’ has remainder fix as ‘YES’ PRIME NUMBER. ..00.....01....02....03....04.....05.....96....97.....98.....99 0000 ------ ------ ------ ------ ----- 0096 @--- ----- @----- 00 ------ ------ 0102 ------ ------ ------ ------ ------ 0198 ------ 01 ------ ------ ------ ------ 0204 ------ ------ @--- ------ @---- 02 0300 ------ ------ ------ ------ ------ 0396 ------ ------ ------ 03 ------ ------ 0402 ------ ------ ------ ------ ------ 0498 ------ 04 ------ ------ ------ ------ 9504 ------ ------ ------ ------ ------ 95…Indians threw away ‘matrix’ and ‘division check’??? 9600 ------ ------ ------ ------ ------ 9696 ------ ------ ------ 96……Each step of 6 positions (including 00) is ‘n’ ------ ------ 9702 ------ ------ ------ ------ ------ 9798 ------ 97… {(n) +/-) 100} means y= ‘1’x100. Remember Vedic z ‘y’ x ------ ------ ------ ------ 9804 ------ ------ ------ ------ ------ 98 x----- ------ ------ ------ ------ ------ 9996 ------ ------ ------ 99 in this case each 6 (+/-) 0101is used as y-reference pair {(n) +/-) 100} (+/-) 1 Principle followed to fix a prime -base is “strep 6 -reference (+/-) 0101 705016 An ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960). (6)Prime-number by table of 6 (+/-) 001001 in 2D ////////// ////////// ////////// ////////// ////////// sq matrix 000…999 Left top far corner of a “cube 000…999” is 2D ‘000000-start’ and 3D ‘000000000-start ‘. All 2D ‘000000…999999’ (top 1000x1000) and 3D ‘000000000…999999999 are completely within 1000x1000x1000. Visible ‘layer-000’ is a 2D plane and related few ‘table of 6’ positions are shown. Each “shown position (+/-) 1” is a prime-base (can have more than one prime numbers as factors). Prime-bases and prime-numbers are equally useful. In 6 (+/-) 001001 cases “prime base” divided by “each confirmed prime number of row-000 (003, 005…997 primes only)” is ‘division check’. If there is ‘no remainder’ to at least one ‘division check’ it does confirm ‘NOT A PRIME NUMBER’. 002999 is prime- base by 001998 (+/-) 001001. Division check is 002999/3 through 002999/997 (by primes only). After fixing that ‘each division’ has >0 remainder fix as ‘YES’ PRIME NUMBER. ...000..001…002…003…004…995…996…997…998…999 000000 --- ------ ------ ------ ---000996 @---- ------ @---- 000 ------ ------ 001002 --- ------ ------ ------ ------ 001998 --- 001 ------ ------ ------ ------ 002004 --- ------ @---- ------ @---- 002 003000 --- ------ ------ ------ ------ 003996 ---- ------ ------ 003 ------ ------ 004002 --- ------ ------ ------ ------ 004998 ---- 004 ------ ------ ------ ------ 995004 --- ------ ------ ------ ------ 995…Indians threw away ‘matrix’ and ‘division check’??? 996000 --- ------ ------ ------ ------ 996996 --- ------ ------ 996……Each step of 6 position (including 000) is ‘n’ ------ ------ 997002 --- ------ ------ ------ ------ 997998 --- 997… {(n) +/-) 1000} means y= ‘1’x1000. Remember Vedic z‘y’x ------ ------ ------ ------ 998094 --- ------ ------ ------ ------ 998 999- ------ ------ ------ ------ ------ 999996 ---- ------ ------ In this case each 6 (+/-) 001001is y-reference pair {(n) +/-) 001000} (+/-) 1 Principle to fix prime -base is “strep 6 - reference (+/-) 001001 705017 An ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960).... (7)Prime-number by table of 6(+/-) 101 in 3D cube ////////// ////////// ////////// ////////// ////////// ////////// matrix 0…9 Left top far corner of a “cube 0…9” is 2D ‘00-start’ and 3D ‘000-start ‘. All 2D ‘00…99’ (top 10x10) and 3D ‘000…999 are completely within 10x10x10. Visible ‘layer-0’ is a 2D plane and related ‘table of 6’ positions are row-column numbers. “5, 06” means ‘z’-layer is 5, row-column number 06. There are 17 nos “table of 6” positions 00, 06, 12….84, 90 and 96 X 1) 000, 112, 224, 336, 448, 560, 672, 784 and 896 9 positions # 2) 952, 056, 168, 280, 392, 504, 616, 728 and 840 9 positions. (See 112/2= 056 and further constant increment is 112’) Related to 000, 006, 012… 084,090 and 096 we have 18 positions each. Each position is 3 digit number z=1 digit, y = 1-digit, x= 1-digit. ...0......1.......2......3......4......5........6.......7......8.....9 x000 ------ ------ ------ #5--- ------ ------ ------ ------ ------ 0…Merge a related row-column number to (#)-positions shown. ------ ------ x112 ------ ------ ------ #6--- ------ +618 ------ 1 #3--- ------ ------ ------ x224 ------ ------ ------ #7--- ------ 2 +730 ------ ------ ------ ------ ------ x336 ------ ------ ------ 3 #8--- ------ +842 ------ ------ ------ ------ ------ x448 ------ 4…We have 17numbers of 3D positions, 000 & 506-starts ------ ------ #9--- ------ +954 ------ #0-- ------ ------ ------ 5…Indians threw away ‘matrix’ and ‘division check’??? X560 ------ ------ ------ ------ ------ +066 ------ #1--- ------ 6……Each step of 6(+/-) 1 position (including 000) is ‘n’ ------ ------ x672- ------ ------ ------ ------ ------ +178 ----- 7… {(n)+/-)100} means z is(1)x100 ‘up’ or ‘down’ off 6(+/-)1 #2--- ------ ------ ------ x784 ------ ------ ------ ------ ------ 8 +290 ------ #3--- ------ ------ ------ x896 ------ ------ ------ 9 Each step 6 (+/-) 101 is a prime base pair {(n) +/-) 100}(+/-)1 There are 17x18 ‘step of 6’ positions.(306 number of positions) Principle to fix prime -base is “strep 6 - reference {(+/-) 100} (+/-) 1 Step of 6 increases means z=1, y=1 and x= 2. (Sq root 6 on 3D diagonal) 705018 An ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960).... (8) Prime-number by table of 6 (+/-) 10001 in 3D ////////// ////////// ////////// ////////// ////////// cube matrix 00…99 Left top far corner of a “cube 00…99” is 2D ‘0000-start’ and 3D ‘000000-start ‘. All 2D ‘0000…9999’ (top 100x100) and 3D ‘000000…999999 are completely within 100x100x100 cube. Visible ‘layer-00’ is a 2D plane and related ‘table of 6’ positions are row-column numbers. 3066 means row-column number 30, 66. There is 10002/6=1667“table of 6” positions (0000, 0006… 9990 and 9996.) Relating each table of 6 positions we have a “99x2 prime base positions”. 000000-start 3D increases by 010102 steps within 999999 (99 positions) 500004-start 3D increases by 010102 steps within 999999 (99 positions) ...00.....01.....02....03.....04.....05.....06....07....08.....99 x000000--- ------ ------ +500004-- ------ ------ ------ ------ 00 ------ ------ x010102--- ------ ------ x510106--- ------ ------ 01 ------ ------ ------ ------ x020204--- ------ ------ @520208 02 ------ ------ ------ ------ ------ ------ x030306--- ------ ------ 03 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 49…We have 1667 3D-positions, 000000 & 506-starts ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 50…Indians threw away ‘matrix’ and ‘division check’??? ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 51…Each step of 6 position (including 000000) is ‘n’ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 52…{(n)+/-)10000} means z is(1)x10000 ‘up’ or ‘down’ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 53…positions ----- ------ ------ ------ ------ ------ ------ ------ ------ ------ 99 Each step 6 (+/-) 10001 is prime-base pair {(n) +/-) 10000} (+/-)1 There are 1667 x 198 ‘= (330066) ‘step of 6’ ref positions Principle that fixes a prime -base is {“strep 6 – ref” (+/-) 100} (+/-)1 @ (520208+10000) (+/-)1=(530209) & (530207) 2 prime bases @ (520208-10000) (+/-) 1= (510209) & (510207) 2 prime bases Division check is by primes in a range 0005...9997 705019 An ANCIENT INDIAN VEDIC MATHEMATICS WORLD WIDE PUBLIC AWARENESS (WITH DUE RESPECT TO SHRI JAGADGURU SANKARACHARYA 1884-1960).... (9) Prime-number by table of 6 (+/-) 1000001 in 3D ////////// ////////// ////////// ////////// ////////// cube matrix 000…999 Left top far corner of a “cube matrix 000…999” is 2D ‘000000-start’ and 3D ‘000000000-start ‘. All 2D ‘000000…999999’ (top 1000x1000) and 3D ‘000000000…999999999 are completely within 1000x1000x1000 cube. Visible ‘layer-000’ is a 2D plane and related ‘table of 6’ positions are row-column numbers. 300666 means row-column number 300,666. There are 1000002/6=166667“table of 6” positions (000000, 000006… 999990 and 999996.) Relating each table of 6 positions we have a “999x2 prime-base positions”. 000000000-start 3D increases by 001001002 steps within 999999999 (999 positions) 500000004-start 3D increases by 001001002 steps within 999999999 (999 positions) ..000..001...002..003..004…005…006..007.008..999 x000000000------ ------ +500000004-- ------ ------ ------ 000 ------ ------ x001001002------ ------ +501001006-- ------ 001 ------ ------ ------ ------ x002002004----- ------ @502002008 002 ------ ------ ------ ------ ------ ------ x003003006---- ------ 003 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 499…We have 166667 3D-positions, 000000000 & 500004004 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 500…Indians threw away ‘matrix’ and ‘division check’??? ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 501…Each step of 999 position (including 000000000) is ‘n’ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 502…{(n)+/-)1000000} means z is(1)x1000000 ‘up’ or ‘down’ ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 503…positions ----- ------ ------ ------ ------ ------ ------ ------ ------ ------ 999 Each step 6 (+/-) 1000001 is prime-base pair {(n) (+/-) 1000000} (+/-)1 There are 166667 x 1998 ‘= (333000666) ‘step of 6’ ref positions. Principle that fixes a prime -base is {“strep 6 – ref” (+/-) 1000000} (+/-)1 @ (502002008+1000000) (+/-)1=(503002009) & (503002007) 2 prime bases @ (502002008-1000000) (+/-) 1= (501002009) & (501002007) 2 prime bases Division check is by primes in a range 000005...999997 //////////////////////////////////////////////////////////////////////////////////////////////////////////////// PRIME NUMBER FIXING RELATE FOLLOWING ‘3’ VEDIC SUTRAS (1) KEVALAI: SAPTHAKAM GUNYAT ( ‘by 143 steps’ 1/7 through 6/7) ////////// ////////// ////////// ////////// ////////// ////////// 6/7 start-groups). Each ‘143 step’ x 999 is a 6 digits recurring number group. 143x999= 142857… 286x999= 285714… 429x 999= 428571 Same 6 digits appears in (in different order) in these ‘cyclic order’ groups. We can also “see and learn” pattern of these number groups …0….1……2…....3…...4…..5…...6……7…...8…..9 x----- ------ ------ ------ ------ ------ ------ ------ ------ ------ 0 ------ x----- ------ ------ + 14- ------ ------ ------ ------ ----- 1....................................142857= 1/7 ------ ------ x----- ------ ------ ------ ------ ------ + 28- ----- 2......................................................................285714= 2/7 ------ ------ ------ x----- ------ ------ ------ ------ ------ ------ 3 ------ ------ x 42- ------ x----- ------ ------ ------ ------ ----- 4..................428571= 3/7 ------ ------ ------ ------ ------ x----- ------ + 57- ------ ----- 5.............................................................571428= 4/7 ------ ------ ------ ------ ------ ------ x----- ------ ------ ------ 6 x---- x 71- ------ ------ ------ ------ ------ x----- ------ ----- 7.........7142 85= 5/7 ------ ------ ------ ------ ------ x 85- ------ ------ x----- ----- 8............................................857142 = 6/7 ------ ------ ------ ------ ------ ------ ------ ------ ------ x----- 9 1/7 recurring group (6 digits) and a related cyclic orders is obvious now. So a related visual learning is possible. (1 a) PARAVARTYA YOJAYET. Repeatedly Joining ‘14, 28 and 57’ //////////////////////////////// Sutra give us a correct idea of ‘cyclic order’ triangle. See 1/7, 2/7 and 5/7 start-points are three vertices same triangle. 71, 42 and 85 make another. This is a solid proof that ancient Indians knew ‘zero’ and 2D square matrix 0…9 (2) KALOV KSHUDRASASOV (‘in 1/13 077-steps x 999) ////////// ////////// ////////// //////////// 077 X (1 through 12) give us start 3-digits of each 1/13 through 12/13. 077x 999= 07 69 23 It is a 1, 9, 3 cycle (1/13, 9/13 AND 3/13) on (upper side of diagonal 00…99) 154x 999= 15 38 46 It is a 2, 5, 6 cycle. (Upper side of diagonal 00…99) …0….1……2…....3…...4…..5…...6……7…...8…..9 x00-- ------ ------ ------ ------ ------ ------ + 07 ------ ------ 0...........................................................076923=1/13 ------ x----- ------ ------ ------ x 15 ------ ------ ------ ------ 1..........................................153846= 2/13 ------ ------ x----- + 23 ------ ------ ------ ------ ------ ------ 2...........................230769=3/13 x 30- ------ ------ x----- ------ ------ ------ ------ x 38- ------ 3...307692= 4/13...................................384615= 5/13 ------ ------ ------ ------ x----- ------ x 46- ------ ------ ------ 4..................................................462315= 6/13 ------ ------ ------ x 53- ------ x----- ------ ------ ------ ------ 5.........................538461= 7/13 ------ x 61- ------ ------ ------ ------ x----- ------ ------+69- 6........615384= 8/13............................. 9/13= 692307 ------ ------ ------ ------ ------ ------ x 76- x------ ------ ------- 7....................................................769230=10/13 ------ ------ ------ ------ x 84- ------ ------ ------ x------ ------ 8................................846152=11/13 ------ ------ x 92- ------ ------ ------ ------ ------ -------x------ 9.................923076=12/13………………………..99 924x 999= 92 30 76 It is a 12, 4, 10 cycle (lower side of diagonal 00…99) 847x 999= 84 61 52. It is a 11, 8, 7 cycle (lower side of diagonal 00…99) Purpose of Vedic sutra is not to remember “digits of 1/7, 1/13 or 1/17. 7x 13= 91 and 91x 11= 001 001. 11, 01 01, 001 001 and so on are bases to study a recurring pattern. Understanding mental computing (Vedic math) and actual computing (computers) differ. Vedic manner is logical mental-speed computing (10) VEDIC SUTRAS 1/(7 x 13) AS 1/91. Through 90/91 ////////// ////////// ////////// ////////// Combining (each 143-step x 999 as 1/7 to 6/7), and (each 077-step x 999’ as 1/13 to 12/13) we get 1/91 through 90/91. It is a matrix 0…9 study. Only 45 no’s upper positions of diagonal 00…99 are shown in matrix. These positions make a related 15 cyclic triangles. Not a single triangle will cross over to lower side of diagonal. See and learn and believe all related facts. 1/91= 01 09 89 which is 011x 999. 2/91 is 022x 999= 02 19 78. 1/91 to 90/91 is mental computing when we learn (011, 022, 033…) x 999 Ordinary number users can do it. …0….1……2…....3…...4…..5…...6……7…...8…..9 x ----+ 01- +---- +---- +----- +---- +---- +---- +----+ 09 0..........01 09 89 = 1/91 ------ x----- +----- x----- x----- x-----x----- x-----x-----+---- 1...we have 15 recurring triangles like 1/91= 010989 right top. ------ ------ x----- +----- x---- +---- +---- +----- x-----+---- 2 ------ ------ ------ x----- +---- x----- +---- +-----x-----+----- 3 ------ ------ ------ ------ x----- +-----x---- +----- x-----+----- 4 ------ ------ ------ ------ ------ x----- +---- x----- x-----+----- 5 ------ ------ ------ ------ ------ ------ x----- +-----x-----+----- 6 ------ ------ ------ ------ ------ ------ ------ x-----+-----+----- 7 ------ ------ ------ ------ ------ ------ ------ ------x----- +89-- 8 ------ ------ ------ ------ ------ ------ ------ ------ ------ x----- 9... Bottom left half has another 15 recurring triangles. (Total 15+15) triangles have 90 vertices as start of 1/91...that ends as 90/91. Learn these visually and by actually drawing all 30 recurring triangles. This is a very good practice that will give you a feel of Vedic mathematics (only a pleasing feel) (11) SUTRAS 1/(7 x 13) AS 1/91. And 1/(11x91) IS ////////// ////////// ////////// ////////// ////////// ////////// 1/1001 through 1000/1001 (MENTALLY) Combining (each 143 step x 999 as 1/7 to 6/7), and (each 077-step x 999’ as 1/13 to 12/13) we get 1/91 through 90/91. It is a matrix 0…9 studies. Combining (each 091 step x 999), and (each 011-step x 999’) we get 1/1001 through 1000/ 1001. We get 1000 related 6-digit recurring groups. 1/91= 01 09 89, which is 011x 999. 1/ (91x 11)= .000 999 and 2/ (91x11)= .001998 and 3/ (91x11)= .002 997… 1000/ (91x11) =.999 000 It implies 1/ 1001 is 001x 999; 2/1001 is 002x 999; 3/1001 is 003x 999 and so on. Therefore it is a simple ‘logical’/zero mental computing that gives us dead accurate answer(always) …0….1……2…....3…...4…..5…...6……7…...8…..9 x 00- ------ ------ ------ ------ ------ ------ ------ ------x 09- 0...00 09 99 = 1/1001 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 1 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 2 ------ ------ ------ + 33 ------ ------ ------ ------ ------ ------ 3 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 4 ------ ------ ------ ------ ------ ------ + 56 ------ ------ ------ 5....................................................56 64 33 =567/1001 ------ ------ ------ ------ + 64 ------ ------ ------ ------ ------ 6 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 7 ------ ------ ------ ------ ------ ------ ------ ------ ------ ------ 8 ------ ------ ------ ------ ------ ------ ------ ------ ------ x 99- 9 1/ 1001= 00 09 99. See and learn. 567/ 1001= 56 64 33. See and learn. (3) “1/17= 05882353 x99999999” (Kamse ////////// ////////// ////////// ////////// ////////// ////////// Kshamadahakhalaimalai:) when Kamsa ruled… 1/17= 05882353 and (05882353 x 11) is 0000000100000001. It is a ‘8 times 0s’…”8 times 9 s’ 2D square matrix position”! In a matrix-based prime-base fixing we have seen 17 “2D matrix 0…9 steps”, 1667 “2D matrix 00…99 steps”, and 166667 “2D matrix 000…999 steps” relating these “prime bases. Let us see how 1/17 recurring pattern is visible. We shall also see if more properties relate a 1/17 recurring group. 1/17= 0.05882373 endless recurring. 05882352
Posted on: Fri, 04 Jul 2014 08:49:14 +0000