John L's Formulas – Chapter One

Page 3 – updated January 15, 2013.

In these pages, we intend to find numbers which – when added to or multiplied by themselves the same number of times – result in the sum equaling the product. The development of the formula through Page 2 can be summarized as follows.
(Click on the image for a larger view.)

Note that we must present this discussion as clearly as possible. For example, if we were to casually define n as "the number of times a number is added to or multiplied by itself" (rather than as put forth so far), then (technically) the sum of 2 added to itself twice would be 6, and the product of 2 multiplied by itself twice would be 8.

Continuation of the graphing discussion begun on Page 2 continues on Page 4 where we find a "hole" (discontinuity) in our graph (!) and perhaps realize more the importance of the mathematical constant e.