论文部分内容阅读
学生在求边数倍增的圓內接正多边形的边长时,宁可采取別的方法,却很少运用現成的倍边公式。高中平面几何課本中关于圓的內接正多边形的倍边公式是这样給出的: a_(2n)=(2R~2-R(4R~2-a_n~2)~(1/2))~(1/2) (1)如果将(1)式根据代数上所讲的公式(a-b~(1/2))~(1/2)== ((a+(a~2-b)~(1/2))/2)~(1/2)-((a+(a~2-b)~(1/2))/2)~(1/2)进行变换,可变成a_(2n)=R((1+((a_n)/2R))~(1/2)-(1-((a_n)/2R))~(1/2)) (2) (2)式和(1)式比較起来,不但形式簡单,便于記忆;而且由于(2)式比(1)式少了一层开方运算,也容
Students in the search for multiplication of the number of sides of the regular polygon, it would rather take other methods, but rarely use the ready-made fold edge formula. The formula of the doubling edge of the inscribed regular polygon of the circle in the high school plane geometry textbook is given by: a_(2n)=(2R~2-R(4R~2-a_n~2)~(1/2))~ (1/2) (1) If formula (1) is based on algebraic equation (ab~(1/2))~(1/2)==((a+(a~2-b)~( 1/2))/2)~(1/2)-((a+(a~2-b)~(1/2))/2)~(1/2) transforms to become a_(2n ) = R((1+((a_n)/2R))~(1/2)-(1-((a_n)/2R))~(1/2)) (2) (2) and (1) Compared with formulas, not only is the form simple and easy to remember, but also because formula (2) has less than one layer of square operations than formula (1).