I have been struggling with the notion of an alternate arithmetic for a while now, but once again, I am stumped.
Let me start simple and try to not confuse myself:
One and zero are just conventions, starting from the on/off principle.
There are other ways of looking at nature.
How about the power of three? As in colour(of light) theory: red, green and blue.
Take an even-sided triangle, with the angles being one of these three colours.
You can divide up each side of the triangle in as many parts as you like, but the middle of each side will come out as one of three secondary colors and form a new smaller triangle, and you can repeat this process ad infinitum.
I’m certain that, starting from this premiss, one could create a viable construct for doing calculus with, but I am too thick to see it! Can anybody help?
- Millions of Colours! Senior Infants/ First Class, Holy Family N.S, Monkstown (dlrcreativityintheclassroom.wordpress.com)
- Rational right triangles (johndcook.com)
- Can a triangle be both isosceles and obtuse (wiki.answers.com)
- Tangrams (education.com)
- A Geometry Challenge (mrhonner.com)