| 1. | Why not poincare
为什么不是庞加莱总统 |
| 2. | To understand the poincar conjecture , start by thinking of any object existing in a three - dimensional world
要理解庞加莱猜想，当始于对三维世界存在的一切物体的认识。 |
| 3. | Proving the conjecture false would have cast doubt on much of modern mathematics ? and everything that depends on it
一旦证明猜想是伪命题，那将使人们对现代数学的许多部分产生质疑? ?当然也包括基于庞加莱猜想的一切。 |
| 4. | Pioncare says : if we should predict the future of math , the proper way is to know the history and development of the subject
庞加莱认为： “如果我们希望预知数学的将来，适当的途径是研究这门学科的历史和现状” 。 |
| 5. | Poincar ' s conjecture is important not for its practical applications , but because a vast quantity of mathematical work assumes that it is true
庞加莱猜想的重要不仅在于它的实际应用性，还因为巨量的数学工作是基于假定庞加莱猜想是正确的。 |
| 6. | General topology has gone through over one hundred years ' development since it was initiated to become a independent science branch by poincare from the end of the 19th century to now
一般拓扑学从19世纪由庞加莱开创为一个独立的科学分支至现在已经历了一百多年的发展历史。 |
| 7. | The most important property for hamiltonian systems is the poincare and liuville ' s conservation law of phase areas , i . e . , the phase flow is a one - parameter symplectic transformation
哈氏系统最重要的性质是庞加莱-刘维尔的一系列相面积的守恒律，即系统的相流是一个单参数的保辛变换。 |
| 8. | Based on comprehending the definition of chaos and its concepts , several description methods of chaos are discussed , including poicare mapping , power spectrum and lyapunov exponent , and so on
在理解混沌的含义和几个概念基础上，重点讨论了混沌运动的几种刻划方法，包括庞加莱映射、功率谱与lyapunov指数等。 |
| 9. | Grigory perelman , a reclusive russian mathematician who solved a key piece in a century - old puzzle known as the poincar conjecture , was one of four mathematicians awarded the fields medal today
格雷高利、佩雷尔曼，一位解决了一个被称为庞加莱猜想的世纪性难题的关键部分的俄罗斯数学隐士，是今天四位菲尔兹奖得主之一。 |
| 10. | But because there is the uncertainty principle in quantum mechanics , the particle ' s momenta and coordinates ca n ' t be determined at the same time , we ca n ' t use the orbits in phase space to describe quantum chaos
但是在量子力学中，由于不确定关系，粒子的动量和坐标不能同时被确定，所以经典庞加莱截面取法就不适用了。 |
