Owarimonogatari Episode 1

*Warning Potential Spoilers Below*

We start with Euler's Identity and a monologue of it's beauty. Near the end of Araragi's talk turned dialogue by Ougi Oshino, he mentions this story is about the ugliest formula in history which we must believe is a reference to Ougi hence the title "Ougi Formula". Ougi and Araragi are stuck in a classroom. Windows and doors will not budge. There is no escape. The supernatural is nothing new to this series. Supposedly Kanbaru is the one who introduces Ougi to him. Part of this was briefly shown in a previous installment I believe. Ougi is an anomaly. Ougi has mentioned the term apparition. The timeline really makes this all the more confusing. As I recall, in the Nadeko snake saga Ougi took part in pushing her on to become the white snake deity. At another instance, Araragi was riding his bike and questioning if he had met Ougi before. Now we have seen a formal introduction between the two. Somewhere on this timeline before he graduated and was driving Kanbaru around, he has met Ougi Oshino. In this room that seems like a trap by Ougi, Araragi has confused himself on what time is. He can't tell how many years its been since he started High School and the time on the clock has also stopped. Mind games are happening. The psyche of Araragi has been penetrated by Ougi. 

We go back to two years to a case where Oikura, a classmate of Araragi and dubbed herself as Euler's Formula. Back then she held everyone there until they found a culprit for the 20 point differential in their math test. We take this long dive into this past and explore what Araragi's feelings are; what his sense of right is. Ougi has held him there, trapped in the same classroom until the solution was proved. Ougi explained that the culprit was actually the teacher. Araragi faces the reality that when it came down to Oikura suggesting that majority votes on the culprit to end the trial, the teacher participated in the vote as well. Upon the lesson ending and Ougi releasing Araragi from the classroom, they both realized, or perhaps learned, something. The next day Araragi sees if that very classroom is still there; it isn't. 

At the point in the story that is Monogatari, Araragi returns to his classroom to find Hanekawa coming out prohibiting him from entering. She says that the seat that has been empty all this time (who we learn belongs to Oikura) is now filled. Oikura has returned to school despite being homeschooled the last few years after the incident. 

It seems familiar. It feels like this empty seat has been mentioned before in the first story: Bakemonogatari. We get a brief view of Senjougahara in the vision of the past which reminds us of the accuracy in the story since they've been in the same class for a couple of years to graduation. Then we also see Hanekawa with short hair, no glasses, and no tiger stripes. It should be fair to say that Araragi is now very aware and suspicious of the existence we acknowledge as Ougi Oshino. After this episode, almost magically, Oikura suddenly returns to school. Araragi has a reaction of disbelief when he heard the news as if he desperately wishes to know what's going on. Can you blame him? I'm still very curious of what is the definition of Ougi's role. Nobody has verification to whether or not Ougi is even related to Meme, but Ougi knows that Koyomi is a vampire and Shinobu is with him.

Thanks for reading!