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Kekule's Dream

Friedrich August Kekule von Stradonitz (1829-1896) was born in Germany. He entered the University of Giessen to study architecture but switched to chemistry after taking a chemistry course. He was a professor of chemistry at the University of Heidelberg, at the University of Ghent in Belgium, and then at the University of Bonn. In 1890, he gave an extemporaneous speech at the twenty-fifth anniversary cele­bration of his first paper on the cyclic structure of benzene. In this speech he claimed that he had arrived at the Kekule structure as a result of dozing off in front of a fire while working on a textbook. He dreamed of chains of carbon atoms twisting and turning in a snakelike motion, when suddenly the head of one snake seized hold of its own tail and formed a spinning ring. Recently, the veracity of his snake story has been questioned by those who point out that there is no written record of the dream from the time he experienced it in 1861 until the time he related it in 1890. Others counter that dreams are not the kind of evidence one publishes in scientific papers. But it is not uncommon for scientists to report moments of creativity through the unconscious, when they were not thinking about sci­ence. After relating his dream, Kekule said, "Let us learn to dream, and per­haps then we shall learn the truth. But let us also beware not to publish our dreams until they have been examined by the wakened mind." In 1895, he was made a nobleman by Emperor William II. This allowed him to add "von Stradonitz" to his name. Kekule's students received three of the first five Nobel Prizes in chemistry: van't Hoff in 1901, Fischer in 1902, and Baeyer in 1905.

Contributed by Mr S. Devender Singh, .

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Let $f(x)=x^6+2x^4+x^3+2x+3,x \in R $. Then the natural number n for which $\mathop {\lim }\limits_{x \to 1} \frac{{{x^n}f(1) - f(x)}}{{x - 1}} = 44$ is _ _ _ _ . Solution Since the limit has $\left[ {\frac{0}{0}} \right]$ form, L.H. Rule is applicable. Thus, $\mathop {\lim }\limits_{x \to 1} n{x^{n - 1}}f(1) - f'(x) = 44$ $\therefore nf(1) - f'(1) = 44$ $\therefore n.9 - ({6.1^5} + {8.1^3} + {3.1^2} + 2.1) = 44$ $ \Rightarrow 9n - 19 = 44$ $\Rightarrow n=7$