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# Squares in a circle, which is in a square

Let $$n$$ be a positive integer. Consider a square $$S$$ of side $$2n$$ units. Divide $$S$$ into $$4n^2$$ unit squares by drawing $$2n-1$$ horizontal & $$2n-1$$ vertical lines one unit apart. A circle of diameter $$2n-1$$ is drawn with it's centre at the intersection of the two diagonals of the square $$S$$. Prove that the number of unit squares which contain a portion of the circumference of the circle is $$8n-2$$.

Note by Paramjit Singh
2 years, 11 months ago