Dual is an anime with robotic wars and parallel worlds(like Lain). Kazuki Yotsuga is the main character and he is just an ordinary high school boy. But there is one thing that separates him from his peers. He has visions of a parallel world. Kazuki sees visions that other people can't. He sees robots fighting battles in front of him. But there is one that appears to the young boy often - a giant white robot that might actually be a reflection of him.
But Kazuki is not all isolated from the real world. He is still a teenage boy, and is fascinated by Mitsuki Sanada, the most beautiful girl in school. When Mitsuki invites Kazuki to her home to be part of her father's experiment, Kazuki gets transported to another world...

The rest of the series deals with Kazuki trying to return to his original world.
The dual of a planar graph is the planar graph you get by interpreting the graph edges as the borders of areas (including the one 'outer space area', if the graph is finite), using the areas as nodes and connecting the neighbouring nodes with edges.

The Pythagorean solids are examples of such graphs:

For finite graphs, if the graph is connected and only has node of degree at least 3, and the same holds for the dual, then the dual of the dual graph is the original graph. If not, taking the dual (repeatedly) will lead to this situation.

A planar graph may have multiple different (i.e. non-isomorphic) duals; a given embedding into the plane (i.e. a way to draw it without any crossing lines) the dual is uniquely determined (up to isomorphism).

Grammatically, dual refers to a sense of number between singular and plural. Examples are the English word both, the Latin words duo and ambo (two and both), the familiar plural form in Icelandic, and various elements in Ancient Greek. Most languages have phased dual number out as it tends to be a confusing element in grammatical structure. Certain disappearing languages on the Pacific Rim are known to have a separate grammatical number for threes of things, too.

Du"al (?), a. [L. dualis, fr. duo two. See Two.]

Expressing, or consisting of, the number two; belonging to two; as, the dual number of nouns, etc. , in Greek.

Here you have one half of our dual truth. Tyndall.

 

© Webster 1913.

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