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著名的几何作图三大难题是: 立方倍积问题:求作一立方体,使它的体积两倍于一已知立方体的体积。 三等分角问题:求作一任意角的三等分角。 化圆为方问题:求作一正方形,使它的面积等于一已知圆的面积。 这三个问题,早在两千多年前的希腊就盛传着,并规定仅仅借助于有限次使用没有刻度的直尺、闭开自如的圆规为工具作出。1 作图公法 (1)过两已知点可作一直线; (2)已知圆心和半径可作一圆; (3)已知两直线可求其交点; (4)已知一直线与一圆周相交,可求其交点; (5)已知两圆周相交,可求其交点。
The three major challenges of the famous geometric drawing are: Cubic product times: Find a cube and make it twice the volume of a known cube. Trisection angle problem: Seeking a trigonometric angle of an arbitrary angle. To solve the square problem: Find a square so that its area is equal to the area of a known circle. These three problems were prevalent in Greece as early as 2,000 years ago and were stipulated as a tool only with the help of a limited use of a ruler without a scale and a closed compass. 1 Draw public method (1) Use two known points to make a straight line; (2) Known circle center and radius can be made a circle; (3) Known two straight lines can find their intersections; (4) Known straight lines and A circle intersects, and the intersection can be found; (5) It is known that the two circles intersect and the intersection can be found.