三等分

The ancient Greek mathematicians attempted to trisect an angle using only a compass and straightedge.
古代希腊数学家试图只用圆规和直尺将角度三等分。
The problem of trisecting an angle is one of the famous problems that cannot be solved by using a compass and straightedge alone.
将角度三等分的问题是著名的仅使用圆规和直尺无法解决的问题之一。
The trisection of an angle can be achieved using a neusis, which involves sliding a marked ruler along a line.
通过使用neusis（一种沿直线滑动标记尺的方法）可以实现角度的三等分。
Despite many attempts, no one has found a method for trisecting an arbitrary angle with just a compass and straightedge.
尽管尝试了很多次，但没有人找到仅使用圆规和直尺三等分任意角度的方法。
The impossibility of trisecting an angle with just a compass and straightedge was first proven by Pierre Wantzel in 1837.
仅使用圆规和直尺三等分角度是不可能的，这一事实最早由皮埃尔·旺策尔于1837年证明。
In mathematics, the trisection of an angle refers to dividing it into three equal parts.
在数学中，角度的三等分是指将其分为三个相等的部分。
Trisecting an angle is a classic problem in geometry that has fascinated mathematicians for centuries.
将角度三等分是几何学中的一个经典问题，几个世纪以来一直吸引着数学家们的兴趣。
While it is impossible to trisect an angle with just a compass and straightedge, there are other methods that can achieve the same result.
虽然仅使用圆规和直尺不可能将角度三等分，但还有其他方法可以达到相同的结果。
The trisection of an angle is closely related to the problem of doubling the cube and squaring the circle.
角度的三等分与立方体加倍和圆面积方问题密切相关。
In modern times, the concept of trisecting an angle is still used in various fields, including engineering and architecture.
在现代，将角度三等分的概念仍被用于工程、建筑等多个领域。