古堡朝圣尺规作图的一个反例

Counterexample of construction with straightedge and compass to solve pilgrmage to castrum

针对古堡朝圣问题,从未知量θ入手,用万能公式将含有sinθ和cosθ的三角方程转化为关于tanθ2的一元四次方程,在构造反例中再将其转化成一个一次方程和另一个不可约的三次方程,进而证明,就普遍意义而言,古堡朝圣问题尺规作图法不可能.

For the end ofsolving the pilgrimage to castrum,proceed from variate θthe trigonometric equation with sinθ and conθ was changed into a variant equation of 4th order of tanθ2 by universal formula,then,when making up a counterexample it was changed into an equation of 1st order and an equation of 3rd order.Finally,it was proved that constructin method with straightedage and compass for solving pilgrimage to castrum is impossible in universality.