Trying to find a formula. | Mathematics | Page 1

novel oriole Sep 30, 2023, 8:34 PM

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Consider a circle with radius R (R ∈ ℕ) placed on a grid of 1x1 cells. A circle can cover a different amount of cells at once depending on it's position on the grid. For example, a circle of R=1 can cover 1, 2, 3 or 4 cells at the time - giving a total of 4 different scenarios.

What is a formula that expresses the number of possible scenarios as explained above?

ebon pumiceBOT Sep 30, 2023, 8:34 PM

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novel oriole Sep 30, 2023, 8:39 PM

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Also, how would one prove such formula is true for any R?

white hazel Sep 30, 2023, 8:44 PM

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https://en.wikipedia.org/wiki/Gauss_circle_problem?wprov=sfti1

Gauss circle problem

In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius

    r
  

{\displaystyle r}

. This number is approximated by the area of the circle, so the real problem is to accurately bound the error term descr...

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Read about this!

#Trying to find a formula.