Power play

Since today is the 27th day of the month, I find my thoughts drifting toward mathematical patterns. That’s because 27 happens to be 3 raised to the power of 3.

Which suggests the idea of raising a number to the power of itself. If we do this with integers, we get a series that starts: 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 10000000000 …

But we don’t need to do this with integers only. We might just as well raise 1.5 to the power of 1.5 (in which case we get a result between 1.8 and 1.9).

If we try it with negative numbers, for example -1.5, things start to get more complex. And what if we start with complex numbers?

If we consider the entire complex number plane, this operation gets very interesting. If you are mathematically inclined, you might want to explore the question: What is the shape formed by raising every complex number to the power of itself?

2 Responses to “Power play”

  1. David A Smith says:

    Your list is wrong.
    Every other number should be even.
    Isn’t that odd.

  2. admin says:

    Thanks for catching that! I was typing the numbers in by hand — fixed now. 66 is, of course, 46656.

    The list is now no longer odd, but I don’t think that makes us even. 😉

Leave a Reply