I’m no mathematical expert, in fact, I’d say I’m just above the modern chimpanzee or maybe some sort of cute tiny monkey. However, I do have an imagination and right now I’m reading a book that has my imagination in overdrive (Playing With Infinity: Mathematical Explorations and Excursions by Rozsa Peter). I got to thinking about the number line, what if it was spiraled instead of flat? Let me explain…
Imagine taking the number line and spiraling it in both directions (positive and negative) so that each number rests directly and precisely 10 above and 10 below (i.e. 0 is below 10 is below 20, 1 below 11 below 21, 2 below 12 below 22,…n below n below n).
The laws of mathematics still applies, all of them but now there is new ways to measure a numbers proximal distance to or from another number on the number line, at least geometrically.
I imagined taking a cube and placing it inside the spiral and measuring at what precise points does each corner hit? Then I thought about rotating the cube so that the points hit new numbers and adding them all up to see if all 8 points will always add up to the same number no matter how you turn it between any set of 10 numbers (i.e. 0 thru 9).
The distance between 0 and 10 is precisely the same distance between 0 and 1, I can call each an increment. Let me say the cube is 2.5 x 2.5 x 2.5 increments.
This means absolutely nothing…but this is what happens when Christopher (Havens) gives me math books to read, my imagination goes berserk!!