Abstract
Let P n be an arbitrary regular polygon with n sides. What is the maximum number k( P n ) of congruent regular polygons (copies of P n ) that can be arranged so that each touches P n but no two of them overlap? Youngs (1939), Klamkin (1995) and others established that k( P 3) = 12, k( P 4) = 8 and k( P 6) = 6. In this paper, we will establish the general and nice result k( P n ) = 6. where n > 6.
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