An odd thing about odd numbers

Numbers

Stringing numbers together

Amazing and magical things happen when you string odd numbers together. Take this for example:

Odd Squares

1 + 3 = 4, √4 = 2

1 + 3 + 5 = 9, √9 = 3

1 + 3 + 5 + 7 = 16, √16 = 4

1 + 3 + 5 + 7 + 9 = 25, √25 = 5

1 + 3 + 5 + 7 + 9 + 11 = 36, √36 = 6

See what’s happening? The square root of the sum of the odd numbers always equals the number of odd numbers.  As far as I know this will go on to infinity.

Odd Cubes

If we do it this way and start with the number 3 we get cubes:

3 + 5 = 8, 3√8 = 2

7 + 9 + 11 = 27, 3√27 = 3

13 + 15 + 17 + 19 = 64, 3√64 = 4

21 + 23 + 25 + 27 + 29 = 125, 3√125 = 5

Pretty cool, huh?  This also goes on as far as you want to take it.

Odd Halves

Take any odd number and split it in half:

13 = 6 & 7

Square those numbers and you’ll find they’re always the same number apart as the odd number:

6= 36

72 = 49

49 – 36 = 13

And just a few more:

3+ 43 + 53 = 63

27 + 64 + 125 = 216

32 + 42 = 52

9 + 16 = 25

Unfortunately that’s as far as they go but it’s still pretty cool.  Numbers are amazing things, and the more you explore and play around with them the more cool things like this you’ll find.

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