Someone asked me what I got for the number of nickels needed to cover NY state. Let me add that the interviewee can ask Siri one question, in which I would ask her what the sq. mileage of NY would be, so we have a given of 54,446 sq. miles.
Presumably, it’s to cover the state at a minimum, without stacking them, along with not figuring in the topography of the state with mountains and valleys, trees and weeds, etc.; further, the land has been plowed over and we’ll have a tarp to cover the waterways internally to lay coins. Calc could have an application for simulating the coastline of the state and employing computers to best lay them also, but that would be way beyond my scope in how to even consider this.
Additionally, the area of a nickel would be less than area of a square with sides equaling the diameter of the nickel, but one cannot place them side by side any closer than a square with these same dimensions, so I can sub in the area of a square and get the same no. of nickels needed to cover the state.
I’m going to try to simulate being a mathematician despite it being another considerable stretch, and I guessed that the diameter of a nickel would be .75”. I’m going to let X algebraically equal the number of nickels needed to cover NY. I’ll let A equal the areas involved in the equation. C will be the conversion to like area measurements. “[]” means subscript; “*” means multiplication; “/” with space between numbers means division, “^2” means squared.
So we have, X(A) = a[ny]C/a[nickel]
………………….X(A) = a[ny](c[1]c[2]…c[n]) / a[nickel]
…………………………= a[ny](c[1]c[2]…c[inch]) / (a[nickel] c[inch-nickel])
…………………………= a[ny-mi^2](feet^2/sqmi^2)(inches^2/feet^2) / a[nickel-inches^2]
…………………………= 545565280^212^2 / .75^2
…………………………= 389,359,101,542,400 nickels; ~ 3.89359E+14 or ~ 389 trillion nickels
Hope everyone stays safe and well and takes considerable precaution; hopefully the pandemic will just be a temporary problem that’ll pass soon.