Mon 29 Jun 2009
A Mathematical Analysis and Alternative of the Zettai Ryouiki Ratio
Posted by kevo' under Essays
[7] Comments
The zettai ryouiki is the widely accepted terminology to describe the slit of visible skin between a girl’s miniskirt and her thighhighs. The phrase means “absolute territory” in Japanese, and its usage is an homage to the Eva units in Neon Genesis Evangelion (DarkMirage, 2006). Very common in tsundere-type characters, the zettai ryouiki is a popular, increasingly present aspect of character design in modern anime. It combines the elegance of thighhigh stockings with the raciness of the short skirt, and it’s one of the only instances (well, outside of nudity) people get to see the top of thighhighs. Interestingly, the attractiveness of the zettai ryouiki generally increases as the slit becomes narrower, one of the only instances when less skin revealed is preferred. All of these attributes and many more add to the mystique of the zettai ryouiki.

This post will soon contain math. Enjoy it while you still can.
Because internet and anime are both serious business, there has been tons of discussion about zettai ryouiki. Zettai ryouiki can’t just get thinner and thinner without any kind of rhyme or rhythm, there has to be ORDER to the madness! Some of my more experienced readers are already smugly smiling, knowing what is coming up next. Yes. 4 : 1: 2.5 with 4 being the length of the skirt, 1 being the zettai ryouiki,
and 2.5 being the length of the sock above the knee. Junkies will also not that this ratio is rarely found precisely in nature, because it would be so moe that the world would explode. I, however, attribute its rarity because it’s kinda bullshit. In my epic search for zettai ryouiki and measuring everything, I have seldom found zettai ryouiki even close to the prescribed ratio. However, I have found something else interesting that is much more prevalent. So here I offer my alternative zettai ryouiki ratio, of which the old 4:1:2.5 ratio is actually included. I do not claim that this is the optimum zettai ryouiki, but it is the property found in the most zettai ryouiki. My conjecture is that the ratio of the distance from the top of the skirt to the beginning of the sock to the distance from the bottom of the skirt to the beginning of the knee is usually around 1.618, the golden ratio, but it can get as low as 1.4. As seen in the image on the right, the green line represents to zettai ryouiki itself. The orange line divided by the blue line should yield a number close to 1.618, which it does. 291/180=1.61667
The commonly accepted optimum ratio of zettai ryouiki, 4:1:2.5 serves as the lower bound of this new rule. The length of the skirt is 4 times the zettai ryouiki, so the numerator is 4x+x = 5x, while the thighhigh above the knee is 2.5x, so the denominator is 2.5x+x=3.5x. The ratio of the two is thus 5:3.5= 1.428, close enough. Of the several images I have measured, 90% of aesthetic images have zettai ryouiki within this range, with the distribution skewing in favor of the upper bound.
Note how my conjecture does not address the actual size of the zettai ryouiki itself. The ratio is determined instead by the length of the skirt and sock. Because many different artists draw differently, a “universal” rule for zettai ryouiki is perhaps impossible. My conjecture, however, is much more general and prevalent. It also shows how I probably need another hobby. Lets see some more examples.

108:74=1.459 Most zettai ryouiki ratios I have found lie between 1.4 and 1.62, about the ratios defined by the "optimum" zettai ryouiki of 4:1:2.5 and the golden ratio.
Let’s take another look at Louise’s lower body. Crappy zettai ryouiki turn out ratios that are well outside the range. Note.

181:100 = 1.81, too much. Note how the slit is way too wide and how the skirt and sock just don't look right.
Obviously, this is far from perfect. There has to be something to govern the zettai ryouiki slit itself, as it’s quite possible to have a terrible looking zettai ryouiki but a perfect ratio. The more obvious factor, however, is measuring
accuracy. Are you supposed to measure from the inner thigh? The outer thigh? The middle? And when characters are sitting down it’s a nightmare to guess how long the skirt is supposed to be. The location when the knee is also questionable, because it’s tempting to measure from the bend in the knee when you really should measure a hair above it, at the knee’s “start”. Look at the second picture of Louise, if I measured from the “start” of the knee, the ratio would be even worse.
Now I’m off to my underground laboratory to study more of the mystical properties of the zettai ryouiki. Your comments about my ground-breaking research is much appreciated. Please place all Nobel Prizes for me on that table over there.
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medy anime at its absolute finest. The show and its premise simply does not get old. Kohji Kumeta does such a great job with the manga, while SHAFT and Akiyuki Shinbo create an absolutely superb animated product. Sayonara Zetsubou Sensei is what everyone who loves comedy should watch- it’s a near perfect balance of dark humor, pure fun, and anime references, all put together with near flawless technical execution. The art is original, unique, and eyecatching. If you’ve seen Shinbo’s other works you know exactly what I’m talking about.
J.C. Staff, which is the only reason I’m even considering it. Lovey drama shoujo suki suki rabu is what I’m expecting. Doesn’t mean it can’t be good, it means it would have to be extra good to get me to care. Umineko no Naku Koro Ni will be watched on a short leash. “But kevo! You loved Higurashi!” Aha! That’s the trap there. The difference between Umineko and Higurashi is not simply the difference between Kanon and Clannad.Umineko is turning out to be a totally different breed than Higurashi. It probably won’t be certifiably bad, but holding Umineko to expectations from Higurashi will probably leave you dissapointed. I don’t like how Umineko looks, but I’ll swallow these words right here if I enjoy the first few episodes.
But I’ll probably give this anime a watch for voice actors and discussion and do a quick drop if I’m not impressed. In order to instill maximum confusion to us, however, there is an anime similarly named Bakemonogatari, which looks awesome. I didn’t put it in the definitely watching section because I wanted to instill some suspense and mystery into the blog post. Moreso that I forgot before and when I remembered I already thought of the neat segue from Umi Monogatari. Akiyuki Shinbo is making this one again, so that’s already enough reason to watch the anime. From what I’ve seen, the character design and art look great. This anime will be hyped regardless so I might as well jump in and see what it’s all about.
Episode 11 thankfully returns to being funny. I think overall, the major flaw with K-ON! is that it’s trying to be something else than a fun, moe comedy show with music. Quite honestly, I expected more music from this show. So in this episode we find out that Yui has neglected to maintain her $3,700 Gibson Les Paul Sunburst and the gang goes to a music store to get it cleaned up, restrung, and whatever else they do to guitars that you can buy a used car with.





so my thought process concerning anime premises are probably not normal. I expected an anime about real streetball style basketball, with you know… a hoop and awesome basketball moves that happen to involve mechs. I basically expected a sports anime. Wrong. Basquash! is mecha first, basketball second. That is, if you can even call it basketball. Most of the “basketball” in the first few episodes of Basquach is simply defined as “having a basketball in the scene”. If you were expecting awesome ballin’ moves straight away like I was, I’m afraid you will be disappointed, yo!