While we wait for K-On! episode 2 – About Ritsu’s Face

Allow me to do stuff like this:

meant to be a teaser.

meant to be a teaser.

A poll in Sankaku Complex (nsfw) on the K-On! girls has Ritsu Tainaka in the last (!) place with only 7% of the voters considering her their favorite character.  Well, through mathematical analysis I have been able to prove the aesthetic quality of Ritsu’s face, and I want to share my results with you in this post.

Classical beauty relies on the Golden Ratio.  Look the Golden Ratio up in Google and you’ll get half a million hits, but just in case let me give a little explanation.  If you know what the Ratio is, then skip to the next Ritsu pic.

Say you grow worms.  Last year a plague wiped out most of them, so you decide to throw a party to encourage the hardy survivors.  The program for the evening includes line dancing, and you decide to pair up the worms yourself (they’re really shy).  Just in case the paparazzi show up, it’d be best to pair these babies up in the most aesthetically pleasing manner.  How do you achieve this?  Do you have the partners be exactly the same length?  Actually, no.  What you do is you make sure theres’s a longer worm and a shorter worm, and the longer worm is 1.618 times longer than the little worm.  That’s the Golden Ratio.

Why 1.618?  Well, look at this picture.

the worms

the worms

Warmy and Wirmy will be partners at the party.  Warmy is 1.618 times as long as Wirmy.  Imagine now there’s a longer worm that’s exactly as long as Warmy and Wirmy put together; call it Wurmy.  Wurmy is obviously longer than Warmy.  How much longer?  Exactly 1.618 times.  The Golden Ratio has this magical property! (if A golden ratio B, then A+B golden ratio A).  Somehow, the Greeks and others believe that this situation generates beauty.

So, look at Ritsu’s face.

vertical ratios

vertical ratios

Classically speaking, the distance between hairline and base of the nose (a) should be 1.618 times longer than the distance from the nose to the chin (b).  Also, the distance from the eyes to the mouth (c) should be in the same Golden Ratio to the distance from the mouth to the chin (d).

In this picture, Ritsu’s (c) is 1.62 times as long as (d).  So that’s pretty much classical perfection right there!  (a) is about 1.80 times longer than (b), so this one’s way off…but wait!  The trend in modern pop aesthetics is to be attracted to people with longer (a) distances.

I read a science article years ago and now I can’t find it, but I remember it analyzed a photo of Jennifer Love Hewitt and included speculation as to the meaning of this trend.  In the case of pop stars today, their forehead is unusually long (e.g. Hewitt, Rihanna), and obviously netizens are debating this issue (for example here and here).

In Ritsu’s case, and in the anime world as a whole, it’s the eyes that are so big, but the result is very similar: an (a) to (b) ratio of 1.80 is not classically beautiful, but it’s pop modern beautiful.

If you can bear with me, there’s another trait I want to go into: eyebrows.  I know Kotobuki Tsumugi’s the one generating all the eyebrow buzz, but I’ll stick to Ritsu here.

There’s an eyebrow guru in Beverly Hills by the name of Anastasia Soare.  She has developed a system for creating the perfect eyebrow based on the Golden Ratio (check out her page here).  Basically, she draws three lines on a person’s face: (a) from the nose straight up (b) from the nose through the center of each iris and (c) from the nose through the outer edge of the each eye.  (b) should be the high point of the eyebrow and divide the line ac into two segments in a Golden Ratio (so ab should be 1.618 times as long as bc).

OK, so here’s Ritsu.

eyebrow situation

eyebrow ratios

Well, if we went strictly by the Beverly Hills method then her eyebrows would have to be huge, which makes sense when you consider just how big her eyes are.  However, the surprising thing is that if you go ahead and measure the lines as I described above, it turns out the A segment is right around 1.59 times as long as the B segment!  So the Golden Ratio as Ms. Soare conceived it does hold here for Ritsu…

So to sum up, the eye-mouth-chin proportions are very classical (1.62) whereas the hairline-nose-chin proportions are too large (1.80), mostly because of the size of the eyes (but appropriately large for our modern appreciation).  However, the large eyes don’t look strange as the “eyebrow level” proportions (basically the balance between the nose and the eyes) are firmly classical at 1.59.

Don’t worry about Ritsu.  She’s fine.  Here:


~ by Haloed Bane on April 6, 2009.

44 Responses to “While we wait for K-On! episode 2 – About Ritsu’s Face”

  1. Brilliant post, and hey hey, Ritsu is my favorite!!! She hasn’t had time to shine yet and she’s not as moe as other girls, but sh’s the only one for me!!! Golden ratio fuck yeah!

  2. You’re… you’re insane!

  3. I lol’d.

  4. i also lol’d.

    I KNEW this was going to use teh goruden ratio, but I was hoping it’d be on Yui =3

  5. and yeah, great post.

  6. This was great. Sucks that apparently not that many people seem to like Ritsu. Or rather, people who aren’t anime bloggers. 😛

  7. wtf is this lol

    you nuts :/

    Mio > Yui > Ritsu > Tsumugi let there be war!

  8. Too much tylenol…

  9. Inspired.

  10. Latest poll numbers: Mio 63%. Ritsu still 4th at 8%.

    BTW, my granny takes loads of tylenol and she can’t come up with this stuff!

    PS, @ ghostlightning: Join the Keion side of the force. You know you want to..

  11. You know, you’d really expect Tsumugi to come in last place…
    She’s a Miyuki, that ‘other’ character who’s just over there in the corner…. right? :<

    Ritsu has all the facial expressions in this episode, and Tsumugi’s got… brows. Phooey.

  12. The perfect classical woman had small breasts. And was pretty much just a really feminine guy. Coincidence much?

  13. I’m not dropping Keion yet. I just thought the 1st ep was boring, albeit the character designs are cute. Btw, you may want to reconsider the font colors you employ. Feed readers, particularly google reader imports posts in a white background, rendering parts of your post nigh unreadable.

  14. @fangzhao

    I like all of them, Tsumugi’s eyebrows included..


    I went to the Louvre. I took a look at the Venus de Milo: “wow it’s practically a guy!” Then I saw the Mona Lisa next door, even more obvious. Then there’s Michelangelo’s women: I think they’re gorgeous but really they’re just men with breasts (eg the decorations in the Medici Tombs, which I’ve only seen in books).

    Male domination of Culture throughout History is total, absolute. I honestly think it had been better for you to realize this later on in life, but they say what doesn’t kill you makes you stronger 🙂


    I’m not satisfied with your answer. when you’re ready please recite this auto-de-fe:

    “By the grace of Mio and the wealth of Tsumugi, by Yui’s mirth and Ritsu’s power, I hereby renounce my former doubts and embrace the faith with heart undivided, K-On Eleison!”

    BTW, I’ll try to keep my yellow font usage under control. That’s the source of the problem…

  15. Haha, this is great. But are you sure the other girls don’t follow the same ratio and proportions?

    By the way, I love all of them too, but my tastes seem to be rather mainstream. For me, it’s Mio > Mugi > Ritsu > Yui.

  16. @ Sasa

    I imagine they’re all fairly close, but I don’t have the time or the strength to run the appropriate tests. Did you get to watch Tomato Ketchup??

  17. No, I didn’t! Awhile ago, the torrent of the one version died on me, and then one computer died. Now that it is alive again, I haven’t continued my endeavour yet… And you, have you gotten to watch “M”?

    By the way, I think K-ON needs more gimmicky postings like these – that is what anime blogging is about!

  18. @Sasa

    Haven’t watched M yet. Will do, though. As to this sort of post, the more I’m blogging the less shy I’m getting so I imagine bolder and more challenging posts will be coming out in the future (the trouble is they will be too ridiculous for most people to take!).

    BTW, I’m now officially self-studying German. I bought the latest Der Spiegel yesterday and am slowly working through an article on NATO’s 60th anniversary. Der Weltpolizist baby!!

  19. lol, i learned about the golden ratio and fibonacci just 2 days ago and now im seeing this everywhere -,-“

  20. […] capture by K-ON! Some even when as far as “mathematical analysis Ritsu’s face” cough animekritik […]

  21. Don’t be ridiculous, Mio is the best. If it were possible I’d eat Mio 3 times a day, 5 to be healthier.

  22. @BKK

    It IS everywhere, even in Prison Break…


    I just read someone on animesuki claiming they were going to borrow Mio for a few hours, so i guess she’s really busy. Time will tell who’s the best, though..

  23. Self-studying, my my. That is impressive, but then again, you seem to be quite good with languages in general.

    I really think that there should be more of this kind of postings, because I enjoy them a lot, so you have no reason to be shy about it. I think people have enough humour to take these kinds of things, heh.

    By the way, are you on MAL at all? Or do you use IM or whatever?

  24. I must say, for some reason, I want to see more of Warmy, Wurmy and Wirmy in the future. And Ritsu, of course, but that’s a given.

    re:something else namely M which induces me into fanboy mode

    You’re in for a treat. ‘Tis marvelous. Lorre’s speech, as hyped (if that’s at all the correct word for it) as it is, is truly magnificent, and the directing is awe-inducing.

  25. @Sasa

    gaguri asked me about this MAL thing, too. i just signed up as animekritik.


    M M M. Next week is new year here so i might have time to squeeze it in then..

  26. @animekritik: Yay, I hope that you will be filling out the other shows you have seen so far. I know it’s a dreadful and long job, but for me, it ended up being pretty convenient.

    About “M”: Kaiserpingvin speaks the truth. Awhile ago, when I was at one of those gathering at which my parents invite their friends to dinner, we had a discussion about the “best german movie” question. Suddenly, some older guy I never talked to bursted into the conversation and said he agrees with us that it must be “M”. Although I know that “M” is a classic, I never expected anyone under the age of 60 to have actually seen it… So yeah, the film really seems to be very hyped.
    But when I saw it (and unfortunately I only saw it once), everyone was glued to the screen in awe and the movie became an instant 10/10 on Imdb. For contemporary tastes, the film might come off a little weird, especially at the beginning, but throughout its course, the drama picks up and shows the depth of the psychology of masses. Then the film turns into a marvelous illustration of the politics and society in Germany of the 1920s, but not without becoming slightly absurd and satirical. Finally, Peter Lorre is a genius actor indeed, and I can’t think of any more epic monologue than perhaps Hamlet’s. You have to see it!

  27. @Sasa

    alright then, this will be watched in the following week (and by none other than me!)

  28. I sign up for MAL while ago but only recently updated cuz my friend who first told me about MAL kept bugging me to update lol

    its annoying at first because you have to find your old anime, manga you watch/read.. but once you’re past that MAL is very useful! I have many times lost the manga/anime txt file I kept for which episode/chapter I am on

    today I started to use MAL Updater http://myanimelist.net/clubs.php?cid=907 because saw someone on mIRC use it and it seemed pretty neat. The program keeps track of the videos you watch and it updates your MAL status for you. Not sure how manga works…. but probably the same way…

    btw added you on MAL ak 😛

  29. @Sasa and Kaiser

    Finished M, it was excellent except for the end (what’s up with that last line: “We’d better watch the children more”. Huh? Should have finished it before that scene)
    Now I realize who Lorre is, he used to be in the Warner Bros. cartoons along with Bogart and others. Interesting that he actually studied with Freud, as this movie has a bunch of Freudian issues.


    I’m usually very bad at stuff like MAL, Facebook, etc. Maybe it’s my hermit tendencies.

  30. IIRC this last line has garnered quite a bit of attention in the analysis of the film. I am not even sure what the common interpretation is, the German Wikipedia says it is a metaphor in which Lang warns Germany to protect their child (the Weimar Republic) against the upcoming Nazism. In the context of Lang’s other works, it is very likely that the whole film is a reference to Nazi Germany.

  31. […] I’m no expert like animekritik (and that’s obviously why I’m linking to his incredibly detailed post instead of making […]

  32. Finally…somebody else who is willing and able to apply mathematic to prove a point! You’re in my list now. ^_^

  33. @7

    Music of the spheres and all that, math rulz.

  34. […] is. Ritsu however, has fans who know what they like and why they like it: invoking the freaking Golden Ratio as a cause/justification for their appreciation. ‘They’ is perhaps hyperbole, only 1 […]

  35. […] She doesn’t look bad either, a claim justified by her design’s consistency with the golden ratio. But between discontent about her not being in a silly video and joy for finding Macross love […]

  36. […] popular one wasn’t even an episode review at all, but a post I did between episodes 1 and 2 (“While we wait for K-On! episode 2″).  That’s in second place (I’ll get to first place below) and over 400 hits ahead of […]

  37. Absolutely perfect.
    Also, Ritsu IS my favorite.

  38. @Nikki

    Yup, Ritsu’s the bomb. And then the show kinda bombed…

  39. I’ve always found Ritsu to be pretty

  40. That’s why she’s my waifu.

  41. […] I picking on Ritsu? I think not, though I don’t share some people’s appreciation for Ritsu’s beauty (animekritik 2009/04/06) Possibly related posts: (automatically generated)The Mynah Bird – […]

  42. Im stupid in maths so dont think i can get what you want to say XD

  43. […] While We Wait For K-On! Episode 2, About Ritsu’s Face […]

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