Math is Beautiful Go on, whip out that calculator and confirm the mathemagical equation above. From @Pickover. Comments (6) Newest 5 Newest 5 Comments If you guys like that, consider this:The sum of the first n odd numbers is n^2. For example: 1 + 3 + 5 + 7 + 9 = 25 = 5^2. Abusive comment hidden. (Show it anyway.) So then this raises the question, is there more than one answer for any known value of m, where m is the number of iterations on the left side of the equation? In other words...n^2 + (n+1)^2 + ... + (n+m)^2 = (n+m+1)^2 + ... + (n+2m)^2 Abusive comment hidden. (Show it anyway.) Here are two more:3^2 + 4^2 = 5^210^2 + 11^2 + 12^2 = 13^2 + 14^2 Abusive comment hidden. (Show it anyway.) Thanks, Stan! I appreciate the kind words. Abusive comment hidden. (Show it anyway.) I wonder if there are more, or even infintely many instances of this pattern, or if this is the only one...n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = (n+4)^2 + (n+5)^2 + (n+6)^2I would have no idea how to approach it. Somebody get Numberphile, or Mathologer, or Singing Banana on this!!! Abusive comment hidden. (Show it anyway.) Login to comment. Click here to view up to the first 100 of this post's 6 comments
If you guys like that, consider this:The sum of the first n odd numbers is n^2. For example: 1 + 3 + 5 + 7 + 9 = 25 = 5^2. Abusive comment hidden. (Show it anyway.)
So then this raises the question, is there more than one answer for any known value of m, where m is the number of iterations on the left side of the equation? In other words...n^2 + (n+1)^2 + ... + (n+m)^2 = (n+m+1)^2 + ... + (n+2m)^2 Abusive comment hidden. (Show it anyway.)
Here are two more:3^2 + 4^2 = 5^210^2 + 11^2 + 12^2 = 13^2 + 14^2 Abusive comment hidden. (Show it anyway.)
I wonder if there are more, or even infintely many instances of this pattern, or if this is the only one...n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = (n+4)^2 + (n+5)^2 + (n+6)^2I would have no idea how to approach it. Somebody get Numberphile, or Mathologer, or Singing Banana on this!!! Abusive comment hidden. (Show it anyway.)
The sum of the first n odd numbers is n^2. For example: 1 + 3 + 5 + 7 + 9 = 25 = 5^2.
n^2 + (n+1)^2 + ... + (n+m)^2 = (n+m+1)^2 + ... + (n+2m)^2
3^2 + 4^2 = 5^2
10^2 + 11^2 + 12^2 = 13^2 + 14^2
n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = (n+4)^2 + (n+5)^2 + (n+6)^2
I would have no idea how to approach it. Somebody get Numberphile, or Mathologer, or Singing Banana on this!!!