Allow me to do stuff like this:

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.

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.

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.

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:

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Posted in K-On!

Tags: Aesthetics, K-On!, Mathematics