Fascinating NUMBER pattern

Fascinating Number Pattern

Number pattern is my weakness. The moment I see the pyramid of number pattern I start jumping and these pattern which I have collected from different sources is presented here for your enjoyment. I do hope you will love it and enjoy.

Amazing Number 142857

While solving the problem of mensuration we generally take the value of pi to be equal to 22/7 which in mixed fraction gives 3 ¹/_7. This fractional part ¹/₇ when changed it will be a non- terminating decimal which is equal to 0.142857 142857…

The number 142857 shows an explicit feature; when multiplied by 1, 2, 3, 4, 5 and 6.

142857 × 1 = 142857

142857 × 2 = 285714

142857 × 3 = 428571

142857 × 4 = 571428

142857 × 5 = 714285

142857 × 6 = 857142

This is not the end of the story. The sum of every digit of the number (if written in a table) column wise or row wise comes to be equal to 27.

×	1	4	2	8	5	7	Row wise sum
1	1	4	2	8	5	7	27
2	2	8	5	7	1	4	27
3	4	2	8	5	7	1	27
4	5	7	1	4	2	8	27
5	7	1	4	2	8	5	27
6	8	5	7	1	4	2	27
Column wise sum	27	27	27	27	27	27

You will be astonished to see more feature of this number. Let’s do the division process of number 1, 2, 3, 4, 5 and 6 by 7 and see the beauty of the number obtained.

1/ 7 = 0.142857 …                  and                   142 + 857 = 999

2/7 = 0.428571 …                  and                   428 + 571 = 999

     3/7 = 0.285714                      and                    285 + 714 = 999

    4/ 7 = 0. 857142                    and                     857 + 142 = 999

    5 / 7 = 0.571428                    and                    571 + 428 = 999

    6/ 7 = 0.714285                   and                     714 + 285 = 999

So far, we did multiplication of number 142857 by number from 1 to 6, let’s do the multiplication of this number by 7.

142857 × 7 = 999, 999

Moreover, 142 + 857 = 999 and 14 + 28 + 57 = 99

(142857)² = 20408122449 and 20408 + 122449 = 142857.

Pattern 2:- Multiplication of Number in recurrence of 9 with 2

Numbers like 9, 99, 999, 9999 … etc. are amazing numbers and it shows a beautiful relation when multiplied by 2. Enjoy the beauty here:-

9 × 2 = 18

99 × 2 = 198

999 × 2 = 1998

9999 × 2 = 19998

99999 × 2 = 199998

999999 × 2 = 1999998

9999999 × 2 = 19999998

99999999 × 2 = 199999998

999999999 × 2 = 1999999998

Pattern 3:- Multiplication of 987654321 by multiples of 9

987654321 is a number written in reverse order from the highest one digit number 9 to the least one digit number 1. This number when multiplied by the multiples of 9 it shows an exceptional beautiful pattern of number. Are you ready to enjoy the beauty?

Did you notice the beauty of pattern?

The sum of digit at both the extreme is 9 and the multiple is placed at both the extreme. As far as the middle part of the product is concerned it is the recurring of number that is 1 less than the number at the unit digit of the multiplier.

Pattern 4:  Here is a pyramid of multiplication of two numbers with equal number of 1’s and 8’s and the result obtained is amazing.

1 × 8 = 8

11 × 88 = 968

111 × 888 = 98568

1111 × 8888 = 9874568

11111 × 88888 = 987634568

111111 × 888888 = 98765234568

1111111 × 8888888 = 9876541234568

11111111 × 88888888 = 987654301234568

Pattern 5:- The below pattern is a very beautiful pattern of numbers that involves the multiplication of number 1, 12, 123 …. 123456789 by 8 and adding number 1, 2, 9 to it making a beautiful decorative pattern.

1 × 8 + 1 = 9

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

123456 × 8 + 6 = 987654

1234567 × 8 + 7 = 9876543

12345678 × 8 + 8 = 98765432

123456789 × 8 + 9 = 987654321

Pattern 6:- Pyramid of 8

This beautiful pyramid of 8’s is formed with the number 9, 98, 987 … multiplied by 9 and adding 7, 6, 5 ….

9 × 9 + 7 = 88

98 × 9 + 6 = 888

987 × 9 + 5 = 8888

9876 × 9 + 4 = 88888

98765 × 9 + 3 = 888888

987654 × 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 × 9 + 0 = 888888888

Pattern 7:- Multiplication of number 12345679 with the multiples of 9’s:- If you multiply 12345679 with the multiples of 9’s the result will be the recurring of the as many times the multiples of 9’s.

12345679 × 9 = 111 111 111

12345679 × 18 = 222 222 222

12345679 × 27 = 333 333 333

12345679 × 36 = 444 444 444

12345679 × 45 = 555 555 555

12345679 × 54 = 666 666 666

12345679 × 63 = 777 777 777

12345679 × 72 = 888 888 888

12345679 × 81 = 999 999 999

Pattern 8:- Multiplication of number 65359477124183 with multiples of 17:- Number 65359477124183 makes astonishing pattern when multiplied with the multiples of 17.

65359477124183 × 17 = 1111 1111 1111 1111

 65359477124183 × 34 = 2222 2222 2222 2222

65359477124183 × 51 = 3333 3333 3333 3333

65359477124183 × 68 = 4444 4444 4444 4444

65359477124183 × 85 = 5555 5555 5555 5555

65359477124183 × 102 = 6666 6666 6666 6666

65359477124183 × 119 = 7777 7777 7777 7777

65359477124183 × 136 = 8888 8888 8888 8888

65359477124183 × 153 = 9999 9999 9999 9999

Pattern 9:- Palindrome Number Pattern with the multiples of 11, 111 ….:- Here is a beautiful pattern formed with the multiples of 11, 111, 1111 …. with itself.

11 × 11 = 121

111 × 111 = 12321

1111 × 1111 = 1234321

11111 × 11111 = 123454321

111111 × 111111 = 12345654321

1111111 × 1111111 = 1234567654321

11111111 × 11111111 = 123456787654321

111111111 × 111111111 = 12345678987654321

Pattern 10:- Beautiful pattern of multiplication of 9, 99 …:- Multiplication of number 9 shows a beautiful pattern. Enjoy the beauty of pattern.

Pattern 11:- Pattern of square making a beautiful pyramid: - There are certain numbers which presents a beautiful pyramid pattern when its square is formed. Let’s enjoy the beauty.

4² = 16                                     7² = 49                                     9² = 81

34² = 1156                               67² = 4489                               99² = 9801

334² = 111556                         667² = 444889                         999² = 998001

3334² = 1115556                     6667² = 4444889                     9999² = 99980001

            33334² = 1111155556             66667² = 4444488889             99999² = 9999800001

Pattern 12:- Multiplication pattern with number 76923:- If you multiply 76923 with 1, 10, 9, 12, 3 and 4 you will see a beautiful pattern of result obtained. The number obtained in each case contains the same number of digit.

76923 × 1 = 076923

76923 × 10 = 769230

76923 × 9 = 692307

76923 × 12 = 923076

76923 × 3 = 230769

76923 × 4 = 307692

Pattern 13:- Pyramid of square of number in the recurring of 9:- Square of number 9, 99, 999, 9999, 99999, 999999 … etc. will form a pattern that looks like a pyramid. See the beauty.

9² = 81

99 ² = 9801

999² = 998001

9999² = 99980001

99999² = 9999800001

999999² = 999998000001

9999999² = 99999980000001

Pattern 13: - Circular Prime Pattern: - This is a circular Prime pattern :-A circular prime is a prime number that remains prime as each leftmost digit in turn is moved to the right hand side. For more information you can visit www.

19937

99371

93719

37199

71993

19937

Pattern 14:- Multiplication pattern with the primes makes a beautiful pattern.

                                                    

 Pattern 15:- Division of number 1 to 9 by 11:- Number 1 to 9 divided by 11 gives non ending decimal expansion.

1/11 =0.09090909….                                                  2/ 11 = 0.18181818…

3/11 = 0.27272727…                                                  4/11 = 0.36363636—

5/11 = 0.45454545…                                                  6/11 = 0.54545454….

7/11 = 0.63636363…                                                  8/11 = 0.72727272…

Pattern 16:- Division of number 1 to 9 by 9:- Number 1 to 9 divided by 9 gives non ending decimal expansion.

1 /9 = 0.11111…                                                         2 /9 = 0.22222…

3/9 = 0.33333…                                                          4/9 = 0.44444….

5/9 = 0.55555….                                                         6/9 = 0.66666…..

7/ 9 = 0.77777….                                                        8/9 = 0.88888…

Pattern 17:- Palindrome Pattern:-

Pattern 18:- Square of Palindrome number giving the palindrome result

11² =121

101² = 10201

1001² = 1002001

10001² = 100020001

100001² = 10000200001

1000001² = 1000002000001

10000001² = 100000020000001

100000001² = 10000000200000001

Pattern 19: Product of Palindrome number making a beautiful pyramid: Here palindrome number made with recurring of 1 and 8 are shown making a beautiful pyramid of number.

Pattern 20:- Pattern with number 987654321 :- Number 987654321 when multiplied by the multiple of 9 gives a beautiful pattern of number where the number placed at the  extreme left and extreme right are the digit by which the number is multiplied whereas the middle recurring digits are one less than the number placed at the extreme right.

Pattern 21:- Pascal Triangle: - In Algebra, you must have used the Pascal triangle to obtain the coefficient of binomial expansion. But this is not the end of the game, Pascal triangle when expended for 9 -10 rows shows different number pattern itself. If I say that Pascal triangle has natural number, triangular number, square number, Pentagonal number, Hexagonal number, Fibonacci number etc. then you will simply not believe my words but it is true.

In the above diagram, you can see the second diagonal showing you the Natural numbers like 1, 2, 3, 4, 5 …. Whereas the third diagonal from either side shows you the triangular number 1, 3, 6, 10 … The Square number (1, 4, 9, 16, 25 …), Pentagonal number (1, 5, 12, 22, 35,…)  Hexagonal number (1, 6, 15. 28, 45,…) and Fibonacci sequence (1, 1, 2, 3, 5, 8, 11, …) can be witnessed in this triangle.

Pattern 22:- Pyramid of 1:- See the beauty of number in increasing order making the pyramid of 1’s.

1 × 9 + 2 = 11

12 × 9 + 3 = 111

123 × 9 + 4 = 1111

1234 × 9 + 5 = 11111

12345 × 9 + 6 = 111111

123456 × 9 + 7 = 1111111

1234567 × 9 + 8 = 11111111

12345678 × 9 + 9 = 111111111

123456789 × 9 + 10 = 1111111111

Pattern 23:- Multiplication with 41

If you multiply 41 by any three digit number to produce a five digit number, every cyclic representation of that number formed by moving the last digit to the front is also divisible by 41. 

41*378 = 15,498.

 41 will also divide 81,549; 98154; 49815; and 54,981

 So Explore the beauty and never forget to inform me about your sweet reaction.

Rajesh Kumar Thakur

rkthakur1974@gmail.com