Odd Numbers - Tumblr Posts

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Werid facts about math that I find interesting

If you put all squares in a sequence, you may notice each square can be created if you add up the odd numbers, form smallest to biggest, 1+3=4+5=9+7=16+9=25+11=36+13=49+15=64+17=81+19=100, so on and so forth, multiplying squares or cubes together will get you the square or cube of their multiple, squaring a cube will always give you the square of the cube and the cube of its square.

If you combine a number of objects into unique groups, you will always get the power of two of the number of objects you combined -1, so 2-1=1 for 1, 4-1=3 for 2, 8-1=7 for 3, 16-1=15 for 4, 32-1=31 for 5, 64-1=63 for 6, so on and so forth, but if you add of the previous ones you also get it, since 1 is the only odd power of two, if you add the non negative powers of 2, the result will always be odd, which means the total of all unique groups you can create will always be odd.

Fibonacci numbers, created by adding the 2 previous numbers together to create a new number will eventually converge on the golden ratio, if you divide consecutive numbers in the sequence together, the Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and well it basically continues non stop.