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mathspassion

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  1. we took here 123,456..... not 123,234,345.....mean no repaeting of digit. my question is why for this........ always 6(sum of digits) at the end. For example 123=6 234=9 345=12=3 456=15=6 567=18=9 678=21=3 789=24=6 at the end sum of digits repaeating. and if we do with one more example 12=3 23=5 34=7 45=9 56=11=2 67=13=4 78=15=6 89=17=8 910=19=10=1 1011=21=3 at the end sum of digitis repeating.
  2. Numbers are amazing ,if we deep study about we get a lot miracle which we have to bring out ,in this view one more article see and observe why is it so……….why always 6. (2,2,3....2,2,3......) 123-----1+2+3=6=0+6=6 456-----4+5+6=15=1+5=6 789-----7+8+9=24=2+4=6 101112----10+11+12=33=3+3=6 131415-----13+14+15=42=4+2=6 161718-----16+17+18=51=5+1=6 192021-------19+20+21=60=6+0=6 222324------22+23+24=69=15=1+5=6 252627------25+26+27=78=7+8=15=1+5=6 282930-----28+29+30=87=8+7=15=1+5=6 313233------31+32+33=96=9+6=15=1+5=6 343536------34+35+36=105=1+0+5=6 373839------37+38+39=114=1+1+4=6 404142------40+41+42=123=1+2+3=6 434445------43+44+45=132=1+3+2=6 464748------46+47+48=141=1+4+1=6 495051-----49+50+51=150=1+5+0=6 525354-----52+53+54=159=1+5+9=15=1+5=6 555657-----55+56+57=168=1+6+8=15=1+5=6 585960----58+59+60=177=1+7+7=15=1+5=6 616263----61+62+63=186=1+8+6=15=1+5=6 646566----64+65+66=195=1+9+5=15+1+5=6 676869----67+68+69=204=2+0+4=6 707172----70+71+72=213=2+1+3=6 737475---73+74+75=222=2+2+2=6 767778---76+77+78=231=2+3+1=6 798081---79+80+81=240=2+4+0=6 828384---82+83+84=249=2+4+9=15=1+5=6 858687---85+86+87=258=2+5+8=15=1+5=6 888990---88+89+90=267=2+6+7=15=1+5=6 919293---91+92+93=276=2+7+6=15=1+5=6 949596---94+95+96=285=2+8+5=15=1+5=6 979899---97+98+99=294=2+9+4=15=1+5=6 100101102--100+101+102=303=3+0+3=6 103104105--103=104+105=312=3+2+1=6 106107108—106+107+108=321=3=2+1=6 109110111—109+110+111=330=3+3+0=6 copyright to PiyushGoel
  3. http://gonitsora.com/author/piyush/
  4. sir whatever you trying to write i also know but i just try to prove hw it is .........
  5. sir figure is right AB=3,AC=4 AND BC=5 as per figure find DE=? only two seconds question if you know the particular theorum which recently obtained by .....................
  6. thnxs Happy New Year 2017 to all my math lovers.......
  7. Very Interesting Number Nine Two Numbers (10 a+b) and (10 x+y) For two digits numbers, numbers can be written in four ways like this 1. (10 a+b) and (10 x+y) 2. (10 a+b) and (10 y+x) 3. (10 b+a) and (10 x+y) 4. (10 b+a) and (10 y+x) Multiple with each other  (10 a+b)*(10 x+y) = 100 ax + 10 bx + 10 ay +by  (10 a+b)*(10 y+x) = 100 ay + 10 by + 10 ax + x b  (10 b+a)*(10 x+y) = 100 bx + 10 ax + 10 by + a y  (10 b+a)*(10 y+x) = 100 by + 10 ay + 10 bx + ax Subtract each one respectively 1.100 ax +10 bx + 10 a y + by - 100 a y - 10 by- 10 ax - x b = 90 ax + 9 bx - 90 a y – 9 by = 9(10 ax+bx-10 a y- by) 2.100 ax +10 bx + 10 ay + by – 100 bx – 10 ax- 10 by - a y = 90 ax - 90 bx -9 a y – 9 by = 9(10 ax-10 bx- a y-by) 3.100 ax +10 bx + 10 a y + by – 100 by – 10 a y- 10 bx - ax = 99 ax – 99 by = 9(11 ax -11 by) 4.100 a y + 10 by + 10 ax + x b -100 bx - 10 ax -10 by –a y = 99 ay -99bx = 9(11 a y-11 b x) 5.100 a y + 10 by + 10 a x + x b -100 by - 10 a y -10 b x –ax = 90 a y -90 by+ 9 ax -9 x b = 9(10 a y-10 by +ax –x b) For example 25 & 32, we can write them in four ways like 25, 32, 52 and 23and now multiple with each other like this (25*32),(25*23),(52*32) and (52*23) 25*32=800 25*23=575 52*32=1664 52*23=1196 1664 – 1196 = 468 =4+6+8 =18 =1+8=9 1664 – 800 = 864 =8+6+4 =18 =1+8=9 1664 – 575 = 1089=1+0+8+9=18 =1+8=9 1196 – 800 = 396 =3+9+6 =18 =1+8=9 1196 – 575 = 621 =6+2+1=9 800 – 575 = 225 =2+2+5=9 Nine always Remain Copyrighted
  8. is it for 345 only or for 5 12 13 as well..... my mean is to everyone can solve it (it is still too lengthy) , it can be too short if you know there is a new formula recently obtained. study deep
  9. In a Right angle triangle ABC AB=3,AC=4 & BC=5 at BC,E is middle point and D is altitude AD Find distance DE=? it is not a difficult question eveyone who know maths can solve easly but question is solve it in one line...........
  10. ok you know how difficult upto the power 6 for this .................as per figure 16 lines shows how much work done by....... some more work still pending ........pl wait......
  11. never say rough working everthing has own existence whatever we do never go waste it reacts......it,s one own choice who play with numbers others with n power ........................
  12. as the work done in digits upto 6 power like that you did ............................wow gr8 in the form of equations everyone says i have done.....................
  13. Today we will see how Piyush Goel discovered something while playing with numbers. Here is the story . One day while sitting idle, and having nothing important to do he was just scribbling on paper. he was writing random numbers and thinking how could link them. To his amazement he discovered this: he wrote down 0, 1, 2, 3, 4, 5. Next to each number he wrote their respective squares, viz. 0,1, 4, 9, 16, 25. Then start subtracting each successive square from the next bigger square. It looks something like this: (1-0), (4-1), (9-4), (16-9) and (25-16). What is the result? he got 1, 3, 5, 7, 9. Now again subtract each successive number from the next one in the order. We are performing this: (3-1), (5-3), (7-5) and (9-7). Surprisingly, he got (2, 2, 2, 2). A 2 in each case. he was amazed and decided to take a step further. This time with cubes. So here go my numbers 0, 1, 2, 3 ,4, 5, 6. And their respective cubes: 0, 1, 8, 27, 64, 125, 216. Time to perform first round of successive subtraction, i.e. (1-0), (8-1), (27-8), (64-27), (125-64) and (216-125). The result: 1, 7, 19, 37, 61, 91. Second round of successive subtraction as performed earlier: (7-1), (19-7), (37-19), (61-37) and (91-61). And this is what he got: 6, 12, 18, 24, 30. Successive subtraction performed the third time: (12-6), (18-12), (24-18) and (30-24). And this time he got the result (6, 6, 6, 6). You see, squaring means ‘to the power 2’ and he got the result 2 after 2 successive subtractions, which is the value of 2! Cubing means ‘to the power 3’ and after performing 3 successive subtraction he got 6 in each case which is nothing but the value of 3! He similarly performed with 4th and 5th powers of the first few whole numbers. He was surprised to find the final value of 24 and 120 which are of course the values of 4! and 5!. It was all right up to 5, but he wanted to go a notch higher and check for 6 just for my personal satisfaction. While doing for 6th power the calculations were massive and numbers so huge that it took him a couple of hours to do his calculations. Just to be sure he also did it for numbers upto 15. Put 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 and their respective 6th powers: 0,1,64,729, 4096, 15625, 46356, 11649, 262144, 531441, 1000000, 1771561, 2985984,4826809, 7829536 and 11390625. He kept on doing successive subtractions till to his contentment he finally got 720 for all which is the value of 6! With little efforts, we can work out algebraic relationship for the above but leave it for some other time.
  14. yes know but if we go deep we get something new.......... now your turn....... find more.........
  15. Symmetry of Digit "2" In Squaring If we square 11, it is very simple put 1(2*1) (12) get 121 same as square 12 put 1(2*2)(22) get 144 again for 13 we get 169 and for 14 we get 1 8 16=196 and so on. When we go deep, we find that there is symmetry of two types (2, 4, 6, 8, 10, 12, 14, 16, 18, 20 …. Diff is always 2) & (1, 4 , 9 , 16, 25, 36, 49, 64, 81, 100 ) diff. is 3 5 7 9 11 13 15 17 19 and diff. of 3 5 7 9 11 always 2, so there is true symmetry . Up to 19 it is right but at 20 how we can put 1 20 100 just because of symmetry. 112 = 1 2 1 122 = 1 4 4 132 = 1 6 9 142 = 1 8 16 = 100 + 80 + 16 = 196 152 = 1 10 25 = 100 + 100 + 25 = 225 162 = 1 12 36 = 100 + 120 + 36 = 256 172 = 1 14 49 = 100 + 140 + 49 = 289 182 = 1 16 64 = 100 + 160 + 64 = 324 192 = 1 18 81 = 100 + 180 + 81 = 361 202 = 1 102 = 1 20 100 = 100 + 200 + 100 = 400 212 = 1 112 = 1 22 121 = 100 + 220 + 121 = 441 222 = 1 122 = 1 24 144 = 100 + 240 + 144 = 484 232 = 1 132 = 1 26 169 = 100 + 260 + 169 = 529 242 = 1 142 = 1 28 196 = 100 + 280 + 196 = 576 252 = 1 152 = 1 30 225 = 100 + 300 + 225 = 625 262 = 1 162 = 1 32 256 = 100 + 320 + 256 = 676 272 = 1 172 = 1 34 289 = 100 + 34 + 289 = 729 282 = 1 182 = 1 36 324 = 100 + 360 + 324 = 784 292 = 1 192 = 1 38 361 = 100 + 380 + 361 = 841 302 = 1 202 = 1 40 400 = 100 + 400 + 400 = 900 There is a symmetry, a method, which is shown as below for 31, 41, 51 and so on. 312 = 1 212 = 1 42 (1 11)2 = 1 42 (1 22 121) = 961 = 121 + 220 + 100 = 441 + 420 + 100 = 961 412 = 1 312 = 1 62 (1 21)2 = 162 (1 42) (1 11)2 = 1 62 (1 42) (1 22 121) = 1 62 (961) = 961 + 620 + 100 = 1681 512 = 1 412 = 1 82 (1 31)2 = 1 82 (1 62) (1 21)2 = 1 82 (1 62) (1 42) (1 11)2 = 1 82 (1 62) (1 42) (1 22 121) = 1 82(1681) = 1681 + 820 + 100 = 2601 612 = 1 512 = 1 102 (41)2 = 1 102 (1 82) (1 31)2 = 1 102 (1 82) (1 62) (1 21)2 = 1 102 (1 82) (1 62) (1 42) (1 11)2 = 1 102 (1 82) (1 62) (1 42) (1 22 121) = 1 102 (2601) = 2601 + 1020 + 100 = 3721 712 = 1 612 = 1 122 (1 51)2 = 1 122 (1 102) (41)2 = 1 122 (1 102) (1 82) (1 31)2 = 1 122 (1 102) (1 82) (1 62) (1 21)2 = 1 122 (1 102) (1 82) (1 62) (1 42)(1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 22 121) = 3721 + 1220 + 100 = 5041 812 = 1 712 = 1 142 (1 612) = 1 122 (1 51)2 = 1 122 (1 102) (41)2 = 1 122 (1 102) (1 82) (1 31)2 = 1 122 (1 102) (1 82) (1 62) (1 21)2 = 1 122 (1 102) (1 82) (1 62) (1 42)(1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 22 121) = 5041 + 1420 + 100 = 6561 912 = 1 812 = 1 162(1 712 ) = 1 142 (1 612) = 1 122 (1 51)2 = 1 122 (1 102) (41)2 = 1 122 (1 102) (1 82) (1 31)2 = 1 122 (1 102) (1 82) (1 62) (1 21)2 = 1 122 (1 102) (1 82) (1 62) (1 42)(1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 22 121) = 6561 + 1620 + 100 = 8281 1012 = 1 912 = 1 182(1 812) = 1 162(1 712 ) = 1 142 (1 612) = 1 122 (1 51)2 = 1 122 (1 102) (41)2 = 1 122 (1 102) (1 82) (1 31)2 = 1 122 (1 102) (1 82) (1 62) (1 21)2 = 1 122 (1 102) (1 82) (1 62) (1 42)(1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 11)2 = 1 122 (1 102) (1 82) (1 62) (1 42) (1 22 121) = 8281 + 1820 + 100 = 10201
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