MHB Calculating the Number of Squares Inside a Circle in the 1st Quadrant

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A 10 by 10 square contains 100 1 by 1 squares, and a circle drawn inside is tangent to all sides. The discussion focuses on calculating how many of these squares are fully inside the circle, with an initial estimate of 60 squares. A proposed method involves programming a loop to count the squares in the first quadrant based on the circle's radius. The formula iterates through x values, calculates corresponding y values, and multiplies the count by four to account for all quadrants. The accuracy of this method and the need for a general case formula are key points of consideration.
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A 10by10 square contains 100 1by1 squares (of course!).
A circle is drawn inside above square, tangent to all 4 sides.
How many of the 1by1 squares are fully inside the circle?

I get 60...which I think is correct.
Trying to devise a general case formula...
 
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Couldn't come up with general case formula.

However, this simple program seems to work:

-center of circle at origin
-examine the 1/4 circle in 1st quadrant

r = radius
x,y = points on circumference

INPUT r
LOOP x FROM 1 TO r
y = FLOOR[SQRT(r^2 - x^2)]
count = count + y
ENDLOOP
PRINT count*4

See anything wrong?
 

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