The author's results and auto-ratio-maker are based on an assumption ("educated guess") he makes in the middle about the ratio between line-height and line-width:
"With the help of basic mathematical modeling, you can make an educated guess that the relationship between the optimal line height and line width is exponential. Here’s the simplest equation to express that:"
The author chooses to square height to determine the "optimal" width, as the "simplest equation to express" the exponential.
But obviously the best educated guess would be W = Lh^GOLDEN RATIO
"With the help of basic mathematical modeling, you can make an educated guess that the relationship between the optimal line height and line width is exponential. Here’s the simplest equation to express that:"
The author chooses to square height to determine the "optimal" width, as the "simplest equation to express" the exponential.
But obviously the best educated guess would be W = Lh^GOLDEN RATIO