Monogatari Series: Final Season
| I created an account to ask this question, so I hope that there will be someone to answer it! I shall add that English is not my native language, so feel free to correct my grammatical mistakes. First, I would like to say that I found incredible the mathematical part with Sodachi in episode 2. Especially, to compare Gauss and Euler by the formula with the exponential function (with i, 0, 1) and the Gauss integers was brilliant, as they also involve i - the square root of -1 - (I wonder by how many viewers this point was understood?). Also, as most people who studied a bit of history of mathematics know, there is a famous rivalry between aficionados to determine who was greatest between Euler and Gauss, and it was pleasant to see the reaction of Araragi. Here comes my real question : when they display the portraits of Euler and Gauss, Gauss is taken from a famous painting and looks very similar (just check the Wikipedia page if interested), but I must say that Euler felt extremely awkward to me. The proportions of his head were not correct and I did not feel at all that he looked like Euler from the paintings and drawings I know of him (for example, the famous one by Emanuel Handmann would have been a good pick). Would anyone have an explanation for this strange representation of Euler? Is it possible that the portrait represents another mathematician (say, a member of the Bernoulli family)? The second alternative may seem plausible if the creators of the series thought (for some reason elusive to me) that the true self of Euler was different from the representations that we have of him. But then why Gauss would remain unchanged, is he like Tsukihi? This seems like a bold statement. Finally, I would like to add that it would have been even more funny to see the portraits with reversed orientation from the real paintings.  |
MeusnierJun 23, 2019 6:28 AM
Nunnaly1 said: Can you explain more about the relationship between the 2 formulas Sure, they are both on the following picture :  Now take a mirror to get the right identities. The first one is the famous identity of Euler relating 0,1, e, and i (the square root of -1). Why is this so famous? Well, it is linking the ubiquitous 0, 1, with the basis of the exponential function e and the "first" complex number i, and this is somewhat remarkable (one may argue that &pi is missing). There are more sophisticated explanations, but I think that its main interest comes from its aesthetic appeal. On the other hand, the second formula is giving the Gauss integers, of the form a+ib, where a and b are integer. Equivalently they correspond to the vertices of the standard integer grid (lattice) on the plane. From a trivial perspective, the relationship between these two formulas is that they both involve i (the square root of -1). They are otherwise unrelated, but they suggest an argument to explain why Sodachi considered Gauss superior to Euler (this is where the humour is to me, since one cannot compare these two giants by looking at two very specific contributions...). Indeed, the introduction of Gauss integers is not just a formula, but a new space (a ring actually) used in number theory to prove many theorems, including quadratic reciprocity, that Gauss proved when he was 18. They constitute a milestone in the history of modular arithmetic, and I think one of the first example of the general study of a ring of integers (of the field of Gaussian rational numbers). I do not think that the topic of fields extensions was seriously considered at the time (1795-1796), and one may argue that Gauss is one of the precursors of Galois theory, which is of lasting importance up to this day (although Gauss's motivations were quite different from the ones of Abel and Galois 30 years later). Compared to this, Euler's formula becomes a mere curiosity. |
MeusnierAug 18, 2019 7:45 AM
| Interesting explanation. Also question, when Araragi finally got the "truth" behind the mirror, was that an Archimedes "Eureka" reference? I feel that the greek letters behind the statue would be Eureka but I don't read greek. Meusnier said: I created an account to ask this question, so I hope that there will be someone to answer it! I shall add that English is not my native language, so feel free to correct my grammatical mistakes. First, I would like to say that I found incredible the mathematical part with Sodachi in episode 2. Especially, to compare Gauss and Euler by the formula with the exponential function (with i, 0, 1) and the Gauss integers was brilliant, as they also involve i - the square root of -1 - (I wonder by how many viewers this point was understood?). Also, as most people who studied a bit of history of mathematics know, there is a famous rivalry between aficionados to determine who was greatest between Euler and Gauss, and it was pleasant to see the reaction of Araragi. Here comes my real question : when they display the portraits of Euler and Gauss, Gauss is taken from a famous painting and looks very similar (just check the Wikipedia page if interested), but I must say that Euler felt extremely awkward to me. The proportions of his head were not correct and I did not feel at all that he looked like Euler from the paintings and drawings I know of him (for example, the famous one by Emanuel Handmann would have been a good pick). Would anyone have an explanation for this strange representation of Euler? Is it possible that the portrait represents another mathematician (say, a member of the Bernoulli family)? The second alternative may seem plausible if the creators of the series thought (for some reason elusive to me) that the true self of Euler was different from the representations that we have of him. But then why Gauss would remain unchanged, is he like Tsukihi? This seems like a bold statement. Finally, I would like to add that it would have been even more funny to see the portraits with reversed orientation from the real paintings. |
booyah10 said: Interesting explanation. Also question, when Araragi finally got the "truth" behind the mirror, was that an Archimedes "Eureka" reference? I feel that the greek letters behind the statue would be Eureka but I don't read greek. Meusnier said: I created an account to ask this question, so I hope that there will be someone to answer it! I shall add that English is not my native language, so feel free to correct my grammatical mistakes. First, I would like to say that I found incredible the mathematical part with Sodachi in episode 2. Especially, to compare Gauss and Euler by the formula with the exponential function (with i, 0, 1) and the Gauss integers was brilliant, as they also involve i - the square root of -1 - (I wonder by how many viewers this point was understood?). Also, as most people who studied a bit of history of mathematics know, there is a famous rivalry between aficionados to determine who was greatest between Euler and Gauss, and it was pleasant to see the reaction of Araragi. Here comes my real question : when they display the portraits of Euler and Gauss, Gauss is taken from a famous painting and looks very similar (just check the Wikipedia page if interested), but I must say that Euler felt extremely awkward to me. The proportions of his head were not correct and I did not feel at all that he looked like Euler from the paintings and drawings I know of him (for example, the famous one by Emanuel Handmann would have been a good pick). Would anyone have an explanation for this strange representation of Euler? Is it possible that the portrait represents another mathematician (say, a member of the Bernoulli family)? The second alternative may seem plausible if the creators of the series thought (for some reason elusive to me) that the true self of Euler was different from the representations that we have of him. But then why Gauss would remain unchanged, is he like Tsukihi? This seems like a bold statement. Finally, I would like to add that it would have been even more funny to see the portraits with reversed orientation from the real paintings. Thank you for your kind words! Yes, I think so, but I would have to see the movie again to be sure. I checked the episode 5 and only saw written on his back "Naoestu Koukou" (see the image below). Could you please tell me to which scene you were referring to? https://rabujoi.files.wordpress.com/2019/06/zowa52.jpg |
Meusnier said: booyah10 said: Interesting explanation. Also question, when Araragi finally got the "truth" behind the mirror, was that an Archimedes "Eureka" reference? I feel that the greek letters behind the statue would be Eureka but I don't read greek. Thank you for your kind words! Yes, I think so, but I would have to see the movie again to be sure. I checked the episode 5 and only saw written on his back "Naoestu Koukou" (see the image below). Could you please tell me to which scene you were referring to? https://rabujoi.files.wordpress.com/2019/06/zowa52.jpg I saw it in Episode 2. I have yet to watch the remaining episodes |
Meusnier said: booyah10 said: Interesting explanation. Also question, when Araragi finally got the "truth" behind the mirror, was that an Archimedes "Eureka" reference? I feel that the greek letters behind the statue would be Eureka but I don't read greek. Thank you for your kind words! Yes, I think so, but I would have to see the movie again to be sure. I checked the episode 5 and only saw written on his back "Naoestu Koukou" (see the image below). Could you please tell me to which scene you were referring to? https://rabujoi.files.wordpress.com/2019/06/zowa52.jpg I saw it in Episode 2. I have yet to watch the remaining episodes |
booyah10 said: Meusnier said: Thank you for your kind words! Yes, I think so, but I would have to see the movie again to be sure. I checked the episode 5 and only saw written on his back "Naoestu Koukou" (see the image below). Could you please tell me to which scene you were referring to? https://rabujoi.files.wordpress.com/2019/06/zowa52.jpg I saw it in Episode 2. I have yet to watch the remaining episodes booyah10 said: Meusnier said: Thank you for your kind words! Yes, I think so, but I would have to see the movie again to be sure. I checked the episode 5 and only saw written on his back "Naoestu Koukou" (see the image below). Could you please tell me to which scene you were referring to? https://rabujoi.files.wordpress.com/2019/06/zowa52.jpg I saw it in Episode 2. I have yet to watch the remaining episodes I have found it! It was indeed Eureka.  |
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