1729 has a special place in the Number world thanks to the genius of Ramanujan
Let's explore the neighbourhood of 1729 as I am sure some of those will exhibit special attributes as well being closer to GOD Number!
1728 is in Focus in this Blog
- For starters 1728 is multiple of two cubes - 3 ^ 3 x 4 ^ 3 (27 x 64)
- Now take the two factors (27 and 64) - Add both and you get 91. 91 multiplied with 19 (reverse) gives back Ramanujan Number!
- 1728 is also difference of two perfect squares - 1764 - 36. Now add the digits of 1764 in pairs (17 + 64 = 81) and subtract 36. The result is 45 which is sum of the digit pairs of 1728 (17 + 28)!
- One of the anagrams of 1728 is 2187 which 3 ^ 7 (refer to Blog No.91)
- Multiply 18 and 72 (digit pairs of 1728) and you get another perfect square - 1296
As always the best is reserved for the last
Sum of the cubes of its digits - 1 ^ 3 + 7 ^ 3 + 2 ^ 3 + 8 ^ 3 = 864 which is exactly half of 1728. Very few numbers exhibit this
The neighbourhood of Ramanujan number looks amazing and watch out this space for more!
Let's explore the neighbourhood of 1729 as I am sure some of those will exhibit special attributes as well being closer to GOD Number!
1728 is in Focus in this Blog
- For starters 1728 is multiple of two cubes - 3 ^ 3 x 4 ^ 3 (27 x 64)
- Now take the two factors (27 and 64) - Add both and you get 91. 91 multiplied with 19 (reverse) gives back Ramanujan Number!
- 1728 is also difference of two perfect squares - 1764 - 36. Now add the digits of 1764 in pairs (17 + 64 = 81) and subtract 36. The result is 45 which is sum of the digit pairs of 1728 (17 + 28)!
- One of the anagrams of 1728 is 2187 which 3 ^ 7 (refer to Blog No.91)
- Multiply 18 and 72 (digit pairs of 1728) and you get another perfect square - 1296
As always the best is reserved for the last
Sum of the cubes of its digits - 1 ^ 3 + 7 ^ 3 + 2 ^ 3 + 8 ^ 3 = 864 which is exactly half of 1728. Very few numbers exhibit this
The neighbourhood of Ramanujan number looks amazing and watch out this space for more!
No comments:
Post a Comment