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The following is a method to estimate value of ( §ÚøÃÑ¥´,,¤£¹LÊ\«Yµ¥¦p3.14....or 22/7 ):
In a circle, draw a regular n-gon. As the value of n increases, its perimeter gerts to the circumterence
of the circle. The figure shows a circle with radius 1cm and centre at O. A regular n-gon P1P2...Pn-1 is drawn in
the circle. Given that if ¡çP1P2= (Ãþ¦üx嘅ª«Åé), then P1P2=2sin x/2 ( ©OÓø«Yx,,¤£¹LÃþ¦ü°Õ,¦P«e±¤@¼Ë )
ai.If n=10, find the perimeter of the regular 10-gon, correct to the nearest 0.00001cm.
ii. Using the result in (ai), find the approximate value of ( §ÚøÃÑ¥´,,¤£¹LÊ\«Yµ¥¦p3.14....or 22/7 ), correct to 5
significant figures.
bi. If n=20, find the perimeter of the regular 20-gon, correct to the nearest 0.00001cm.
ii.Using to result in (bi), find the approximate value ( §ÚøÃÑ¥´,,¤£¹LÊ\«Yµ¥¦p3.14....or 22/7 ), correct to the nearest 0.00001cm,
ci. If n=100, find the perimeter of the regular 100-gon, correct to the nearest 0.00001cm.
ii. Using the result in (ci), find the approximate value ( §ÚøÃÑ¥´,,¤£¹LÊ\«Yµ¥¦p3.14....or 22/7 ), correct to 5
significant figures.
di. If n=200,find the perimeter of the regular 200-gon , correct to the nearest 0.00001cm.
ii. Using the result in (di)m find the approximate value of ( §ÚøÃÑ¥´,,¤£¹LÊ\«Yµ¥¦p3.14....or 22/7 ), correct to 5
significant figures.
[ ¥»©«³Ì«á¥Ñ vs17 ©ó 2008-8-23 03:43 PM ½s¿è ]
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