This question is taken from a similar one inside the mathematics stack exchange. I followed the suggestion given in the comment by Jyrki Lahtonen and posted said question here.
Recently, on a flight back from Charlottesville, NC to Logan Airport, MA, the Pilot stated this to his passengers over the intercom, I paraphrase:
As you can see out the window, we just saw some lightning strike within 3 miles of our plane. Because of this, they closed the ramp gates. Every time lightning strikes within three miles of our plane, we have to reset the wait timer to ten minutes.
This made me wonder if there was a mathematical connection between the distance of a lightning strike and the amount of time needed to wait for take-off to ensure another strike will not occur on the ramp.
Let the "area that causes a delay" when lightning strikes be represented by a circle of radius 3 miles. In addition, let us envision a scenario where lightning strikes on the circumference of the circle, i.e. 3 miles away from the plane, which is the farthest distance from the place that will trigger a 10 minute wait.
The intersection of these circles is a clean venn-diagram shape, and results in an area of (9π)/3 sq.mi. or 3π sq. mi., which is about 9.42 sq. mi, and the ceiling of which would be 10.
Given that the pilot stated that a wait time of 10 min would be triggered if lightning struck within 3 miles of the plane, and the area in between a strike on the circumference of 3 miles and the plane results in a ceiling of 10, is there any mathematical basis for a lightning strike wait time of 10 if given a "danger zone" of 3 miles?