Episode 3

Episode 3 ("Big Sister, do I have to go to school?") is the third episode of the Null & Peta anime series.

Summary
The episode starts with Peta waking up Null for school. She has prepared a dish of Dark Fried Rice, as well as a funnel-shaped tower of school backpacks, one of which apparently has a jet engine installed. Null is fairly unhappy about all of this. When she reluctantly tries to eat a spoonful of rice, the smell kills her before she can even try it.

After the title card, Null is seen working on her contraptions. On Peta's request she asserts that she's not going to school. Peta accepts this, however in turn drags Null with her to take a bath. Null tries to distract again, but ultimately enters the bathtub as well.

When washing her hair later, Peta gives Null a Head Spa treatment, using awful-looking spikes which turn out to be quite harmless here. Despite this treatment actually being pleasurable, even making Null forget the horrors of the fried rice, she instinctively declines going to school the next day.

Next is a backflash showing a reason for Null's reluctance to go: a scene of her explaining a high-level physics problem, with all classmates and the teacher being so overwhelmed their expressions are all blacked out. This frustrating experience leaves Null alone in her class, while giving her a reason that school is unnecessary for her.

Null cheers Peta up by taking her shampoo hat and a cup, and topologically relating both to a torus. This brings Null back into her element, prompting her to discuss the Poincaré Conjecture with Peta. Staying on topic, Null's goodnight story is a math theorem from a book about Topology.

The last shot is a joke image displaying Peta having turned flat due to staying in the tub too long, and having hung herself up as a flag saying "Hey Null! Go to School!!"

Trivia

 * The formulas on the blackboard indicate a problem from Quantum Mechanics, since the bracket notation like "|0>" is often used to describe superpositions of quantum states. (Can anyone confirm the correctness of the formulas?)
 * The goodnight theorem might be a common result in Topology, about continuous mappings between topological spaces. It is usually encountered in the first year of college math, while a special case for the real numbers may be proven before topological spaces are properly defined. If this isn't indicative of Null's genius, I don't know what is.