Ruler construction cannot issue
  Ruler and compasses can not be completed with the mapping problem. The most famous is known as the classical geometric problems three major issues: (1) Angle trisection problem - an arbitrary angle trisection; (2) times the cubic problem - to make a cube, so that its volume is known volume of a cube twice; (3) Squaring the circle problem - to make a square, it's an area equal to the known area of a circle. 2400 years ago in ancient Greece have been asking these questions until 1837, French mathematician million Chicago Fire before it is proved that, "Angle trisection" and "Doubling the cube" as the ruler and compasses can not be the problem. In 1882 the German mathematician Lindemann proved that π is beyond the numbers, "Squaring the circle" is also ruler and compasses can not be proved to the problem.
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