Today was fun visiting Neocities again. It seems that I have surfed enough good websites today. If you have anything about me send me an email without hesitancy. See you again!
>Katawa_Shoujo I recommend you to finish other routes first before you write the analysis. Including our schizo Kenji Davis route too :). And yes. Emi route is way deeper than you might have expected. Also Emi is seemingly cute, but she is a literal Übermensch. She is the coolest one. I respect her the most as a human being.
>the_quintic_problem By the way historically the origin was the quintic problem. But that era has ended and Galois theory is used in number theory the most. I could even say that it is basically linear algebra for number theory. So study hard if you were interested in number theory.
>the_quintic_problem Therefore an equation of degree n has general solutions if and only if Sn is solvable. And since Sn is a finite group, it means whether Sn has a composition series in which all factor groups are Zp. This corresponds to that by adding the primitive p-th root of unity, you can extend the base field to the field that factorizes the polynomial. But for n>4, An is simple so that Sn is not solvable.
>the_quintic_problem I will not explain long. The solutions for a cubic equation depend on a+bw+gw^2 (Lagrange resolvent) and the permutations of {1,w,w^2}. Because in the end those permutations form the Galois group which fixes the base field. So it all depends on the structure of S3. Similarily for a quartic equation, {1,i,i^2,i^3} and its permutations S4. And so on.
>diary By the way, speaking of Katawa Shoujo I like Emi route the most. 幽玄. A singularity and its monodromy group. It's really insightful. Especially Mutou in that route is my favorite.
>diary Katawa Shoujo came as the first example. Interesting. Could you explain why? Besides Hanako route, I haven't thought that loneliness is a main theme of it.
>Analogy Analogy is just how a visual thinker tries to explain the image in own mind. If you have to "understand" or consider it a "tool", you are definitely not a visual thinker and analogy is not for you.
>mika.html After the long time, I came Neocities again and the first webpage I saw was this; Well Mika kawaii :). Though my oshi in blue archive is Noa.
I like your perspective on music as a way to experience numbers. It made a lot of sense to me.