Quotations & equations of the month

Here you can find citations and equations already displayed in the widget in the right column.


October 2018 :

“A mathematician is a machine that turns coffee into theorems.” – P. Erdös

Ramanujan’s Pi Serie : \(\frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^{\infty}{\frac{(4k)!(1103+26390k)}{(k!)^{4} 396^{4k}}}\)

 

November 2018 :

“A problem can be solved by thinking about how it was created.” – A. Einstein

Eulerian product : \(\zeta (s) = \prod_{p \in \mathcal{P}}^{+\infty}{\frac{1}{1-p^{-s}}}\)

 

December 2018 :

“It is better to aim the perfection and miss it rather than aim the imperfection and reach it.” – B. Russell

Newton’s binomial formula: \( (a+b)^{n} = \sum_{k=0}^{n}{{n\choose{k}}a^{k}b^{n-k}}\)

 

January 2019 :

“Mathematics consists to prove obvious things with complex means.” – G. Polya

Hilbert inequality: \(a_i,b_i (0 \leq i\leq n)\in \mathbb{C}, \Bigg | \sum_{k,j=0}^n \frac{a_k \overline{b_j}}{1+j+k} \Bigg | \leq \pi \sqrt{\sum_{p=0}^n |a_p|^2} \sqrt{\sum_{p=0}^n |b_p|^2}\)

February 2019 :

“Doing mathematics, it’s often getting lost into a jungle and try to gather all information to find new ways. With luck, we get out of this.” – M. Mirzakhani

Arc length in Riemannian metric:

\(\ell=\int_a^b\|\gamma'(t)\| {\mathrm d} t=\int_a^b\sqrt{g(\gamma'(t),\gamma'(t))} {\mathrm d} t\)

March 2019 :

“Mathematicians do not study objects, but relations between these objects.” – H. Poincaré

Cauchy’s repeated integral formula (\(f\) is a real continuous function):

\(f^{[n]}(x) = \frac{1}{(n-1)!}\int_{a}^{x}{(x-y)^{n-1}f(t)\mathrm{d}t}\)

April 2019 :

“The art to ask right questions, in mathematics, is more important than the art to solve them.” – G. Cantor

Gauss’ integral:

\( \int_{\mathbb{R}}{\mathrm{e}^{-\alpha x^2}}\mathrm{d}x = \sqrt{\frac{\pi}{\alpha}} \)

May 2019 :

“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” – J. Von Neumann

Poisson’s probability law (\(k \in \mathbb{N}, \lambda > 0\)) :

\( p(k) = P(X = k) = \frac{\lambda^{k}}{k!}\mathrm{e}^{-\lambda} \)

June 2019 :

“Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” – W.P.Thurston

Volume of a \(n\)-dimension euclidian ball (\(k = \frac{n}{2}\)):

\(V_n = \frac{\pi^{k}R^n}{\Gamma(k + 1)} \)

January 2020 :

“No great discovery was ever made without a bold guess.” – I. Newton

Stirling equivalent :

\( n! \underset{+\infty}{\sim} \sqrt{2\pi n}(\frac{n}{e})^n \)

April 2020 :

“In mathematics, we don’t understand things, we’re settling into.” – J.von Neumann 

Rank-Nullity Theorem (\( u \in \mathcal{L}(E,F) \) ) :

\( \mathrm{rg}(u) = \mathrm{dim}\ E \ – \ \mathrm{dim}\ \mathrm{Ker}(u)\)

61 comments

  1. zmozero teriloren Reply

    Hey there! Do you know if they make any plugins to protect against hackers? I’m kinda paranoid about losing everything I’ve worked hard on. Any suggestions?

  2. Content Generator Reply

    👉 $5,000 FREE EXCHANGE BONUSES BELOW 📈 👉 PlaseFuture FREE $3,000 BONUS + 0% Maker Fees 📈 + PROMOCODE FOR NEWS USERS OF THE EXCHANGE 👉 [M0345IHZFN] — 0.01 BTC 👉 site: https://buycrypto.in.net Our site is a secure platform that makes it easy to buy, sell, and store cryptocurrency like Bitcoin, Ethereum, and More. We are available in over 30 countries worldwide.

  3. Content Generator Reply

    A secret weapon for anyone who needs content. I dont need to tell you how important it is to optimize every step in your SEO pipeline. But unfortunately, its nearly impossible to cut out time or money when it comes to getting good content. At least thats what I thought until I came across Article Forge. Built by a team of AI researchers from Stanford, MIT, Carnegie Mellon, Harvard, Article Forge is an AI content writer that uses deep learning models to research, plan out, and write entire articles about any topic with the click of a button. Their team trained AI models on millions of articles to teach Article Forge how to draw connections between topics so that each article it writes is relevant, interesting and useful. All their hard work means you just enter a few keywords and Article Forge will write a complete article from scratch making sure every thought flows naturally into the next, resulting in readable, high quality, and unique content. Put simply, this is a secret weapon for anyone who needs content. I get how impossible that sounds so you need to see how Article Forge writes a complete article with the Click Here:👉 https://stanford.io/3FXszd0

  4. best cryptocurrency Reply

    Its like you read my mind! You appear to know a lot about this, like you wrote the book in it or something. I think that you could do with a few pics to drive the message home a bit, but other than that, this is great blog. A fantastic read. I’ll certainly be back.

  5. zorivareworilon Reply

    Hello! I’m at work surfing around your blog from my new iphone 4! Just wanted to say I love reading your blog and look forward to all your posts! Carry on the fantastic work!

  6. zorivare worilon Reply

    Hello! I just wish to give an enormous thumbs up for the nice data you’ve got here on this post. I might be coming back to your blog for more soon.

  7. hackers for hire Reply

    Hi, Neat post. There’s a problem with your web site in internet explorer, would test this… IE still is the market leader and a good portion of people will miss your wonderful writing because of this problem.

  8. hire a hacker for social media Reply

    I have been browsing online more than three hours as of late, yet I by no means found any fascinating article like yours. It is pretty worth enough for me. Personally, if all site owners and bloggers made just right content material as you probably did, the web will be much more useful than ever before.

  9. trusted hackers for hire Reply

    The very core of your writing whilst appearing agreeable originally, did not work perfectly with me after some time. Somewhere within the paragraphs you actually were able to make me a believer unfortunately only for a very short while. I nevertheless have a problem with your jumps in logic and you would do well to fill in those gaps. When you actually can accomplish that, I could undoubtedly end up being amazed.

  10. נערות ליווי Reply

    I was extremely pleased to discover this page. I want to to thank you for ones time due to this wonderful read!! I definitely appreciated every part of it and I have you bookmarked to look at new information on your web site.

  11. https://www.israelxclub.co.il/---/ Reply

    Im excited to discover this web site. I need to to thank you for ones time for this wonderful read!! I definitely savored every bit of it and I have you bookmarked to look at new information in your web site.

  12. upper abs workout Reply

    I’ve learn several excellent stuff here. Definitely price bookmarking for revisiting. I surprise how a lot effort you put to create any such wonderful informative site.

  13. zomeno feridov Reply

    It?¦s really a nice and helpful piece of info. I?¦m glad that you shared this helpful info with us. Please keep us up to date like this. Thank you for sharing.

  14. zomeno feridov Reply

    Have you ever thought about adding a little bit more than just your articles? I mean, what you say is fundamental and all. Nevertheless think about if you added some great graphics or video clips to give your posts more, “pop”! Your content is excellent but with images and clips, this website could undeniably be one of the greatest in its field. Amazing blog!

Leave a Reply

Your email address will not be published.