User:Phenolla/Favorites

I create this subpage for collecting my favorite pages or interesting things in Wikipedia. Contents in this page was previously a section of my main userpage.

Favorite number




I've heard that the sum of the reciprocals of the square numbers is a constant number since childhood, but I cannot prove it completely at that young. After learning Advanced Mathematics in university, I know how to calculate this number by using Fourier series. Later I read this article and know 10 more methods about the proof, further know the concepts of Riemann hypothesis. It is my favorite maths problem.
 * }
 * $$\sum_{n=1}^\infty \frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \cdots = \frac{\pi^2}{6}$$.

My Birthday Town?
Veintiocho de Noviembre is a small town in Argentina, the name Veintiocho de Noviembre means 28th of November, which happens to be my birthday. I think if I have a chance to take a trip to Argentina one day, I must see this "birthday town" on my own.

Casablanca

 * See: "The White House" en español

The White House and Casablanca shares the same name in Spanish. The article even offers a disambiguation page on this issue. This is because in Spanish language, "casa" = "house", and "blanca" = "white". But in Chinese, the US President's residence and work place is translated into "白宫", and the Moroccan city is transliterated into "卡萨布兰卡" , which sounds like totally two unrelated things. Actually they sound like unrelated things in English too.

Flag of Nepal


Nepal is a country adjacent to China in Himalayas. The flag of Nepal is the world's only non-quadrilateral national flag, like it illustrated in the picture. Imagine that there's a circumscribed rectangle around this flag, then what is the aspect ratio of this rectangle?

To my surprise, the ratio is an irrational number. It is written as below.
 * $$1:\frac{6136891429688 - 306253616715\sqrt{2} - \sqrt{118-48 \sqrt{2}} \left( 934861968 + 20332617192 \sqrt{2} \right) }{4506606337686}$$

According to a precise description of the Constitution of the Kingdom of Nepal, this ratio is the least root of the quartic polynomial,
 * $$243356742235044 r^4 - 1325568548812608 r^3 + 2700899847521244 r^2 - 2439951444086880 r + 824634725389225,$$

Approximate value of this ratio is 1:1.21901033….

Fenoglia
There's a Frazione called "Fenoglia" in Ingria, Piedmont, Italy, which is a homophone of my username "Phenolla".