Today is Bach's 325th birthday, if you take the Julian calender date. What are you doing to celebrate? I'd recommend listening to the St. Matthew Passion or a cantata. Maybe play some yourself, if you're so inclined.
Christianity applied to all of life.
Such cases are exceptional, however, and when the form of $U(r)$ is arbitrary the angle $\Delta\phi$ is not a rational fraction of $2\pi$. In general, therefore, the path of a particle executing a finite motion is not closed. It passes through the minimum and maximum distances an infinity of times, and after infinite time it covers the entire annulus between the two bounding circles. The path shown in Fig. 9 is an example.
Biologist Paul R. Ehrlich wrote in his 1968 bestseller The Population Bomb, "The battle to feed all of humanity is over ... In the 1970s and 1980s hundreds of millions of people will starve to death in spite of any crash programs embarked upon now." Ehrlich said, "I have yet to meet anyone familiar with the situation who thinks India will be self-sufficient in food by 1971," and "India couldn't possibly feed two hundred million more people by 1980." - Ehrlich, Paul: The Population Bomb, 1968.