Formulas 数学公式 1948-1994

1948 $H(S) \leqslant m(S) \leqslant H(S) + 1$ The mathematician Claude Shannon introduced the entropy in information theory in 1948. Entropy in information theory can be defined as the expected number of bits of information contained in an event. For instance, tossing a fair coin has the entropy of 1. It is because of the probability of havi...

Formulas 数学公式 1901-1927

1901 $\begin{array}{c} P\left(\frac{X_{1}+X_{2}+\cdots+X_{n}-n_{\mu}}{\sigma \sqrt{n}} \leq x\right) \\ \rightarrow \\ \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{x} e^{-t^{2} / 2} d t \end{array}$ Lyapunov’s theorem in probability theory is a theorem that establishes very general sufficient conditions for the convergence of the distributions of ...

Formulas 数学公式 1825-1896

1825 $\oint_{\gamma} f(z) d z=0$ Cauchy’s integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorph...

Formulas 数学公式 1500-1799

1500 \begin{aligned} &x^{3} + mx = n\\ &\Rightarrow\\ &x=\sqrt{\sqrt{\frac{n^{2}}{4}+\frac{m^{3}}{27}}+\frac{n}{2}}-\sqrt{\sqrt{\frac{n^{2}}{4}+\frac{m^{3}}{27}}-\frac{n}{2}} \end{aligned} At some point in the early 1500’s, an Italian mathematician named Scipione del Ferro determined a general solution for what is known a...

Frozen 2 冰雪奇缘 2

In this sequel to ‘Frozen,’ Queen Elsa has lifted the spell that left her kingdom in an eternal winter. When Elsa is drawn to the enchanted forest by a mysterious siren, her powers return, putting the kingdom at risk. Her sister Anna sets off with Olaf, Kristoff, and Sven to find the origin of Elsa’s powers. Release date: Nov 22, 2019 (United S...

IELTS 雅思考试

The International English Language Testing System, or IELTS, is an international standardized test of English language proficiency for non-native English language speakers. It is jointly managed by the British Council, IDP: IELTS Australia and Cambridge Assessment English, and was established in 1989. IELTS is one of the major English-language t...