Quarter Circles Inside Squares
Difficulty: Hard · Topics: Calculus, Series, Geometric Series
Kvadratlar ichidagi chorak doiralar
Inside a square of side 1 a quarter circle is drawn, with its centre at one vertex of the square and radius equal to the side, so that it is inscribed in the square. Inside that quarter circle the largest square having two sides along the two radii is drawn, and inside this new square a quarter circle is drawn in the same way, and so on without end.
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Tomoni 1 bo‘lgan kvadrat ichiga markazi kvadratning bir uchida, radiusi tomonga teng bo‘lgan chorak doira chizilgan, ya’ni u kvadratga ichki chizilgan. Bu chorak doira ichiga ikki tomoni ikkala radius bo‘ylab yotadigan eng katta kvadrat chizilgan, bu yangi kvadrat ichiga xuddi shunday chorak doira chizilgan va hokazo, cheksiz.
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