R Hansen says: >The original point, my point, was the myth of "visual thinking". I asked you to justify your picture because you are one move from losing your king. I was proving that it doesn't matter if the construction is visual, symbolic or just verbose sentences. Those are just the props. To be mathematics, whatever you are doing has to be justified by a reasonable mathematical argument. The plot if you will. That is the thinking. That is not visual. It is logical.
No myth! I simply *sought* the picture that illuminated the relationship among e, pi, and log(pi)*. That's visualization. That's was the "strategy" to use a overly grand word.
I didn't seek a "proof", or chain of reasoning, or logic, or "argument". I knew the picture would contain all those things, and it absolutely does, if you know how to read it. It answers other questions as well.
Cheers, Joe N
* I took a leisurely path, actually. At first I entertained thoughts of visualizing the original problem directly (without taking logs,) but I was just amusing myself. I knew that taking logs would be more or less required.