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# Surface

In mathematics, specifically in topology, a surface is a two-dimensional manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space, E³. On the other hand, there are also more exotic surfaces, that are so "contorted" that they cannot be embedded in three-dimensional space at all.

To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide coordinates on it — except at the International Date Line and the poles, where longitude is undefined. This example illustrates that in general it is not possible to extend any one coordinate patch to the entire surface; surfaces, like manifolds of all dimensions, are usually constructed by patching together multiple coordinate systems.

Surfaces find application in physics, engineering, computer graphics, and many other disciplines, primarily when they represent the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.

Best Surface: A Nice Time for Loving

2nd Wave

Perfect 10

Best Surface: A Nice Time for Loving

Perfect 10

First Time: The Best of Surface

Surface

Our World

Surface

Best Surface: A Nice Time for Loving

3 Deep

Perfect 10

Surface

Best Surface: A Nice Time for Loving

Perfect 10

Best Surface: A Nice Time for Loving

Surface

2nd Wave

3 Deep

3 Deep

Perfect 10

I'm Fine Thank You & You

Our World

Surface

Breaking the Surface

Breaking the Surface

Re:start (Yakitate!! Japan Ending Theme)

Re:start (Yakitate!! Japan Ending Theme)

Surface

Surface

I'm Fine Thank You & You

Surface

Surface

I'm Fine Thank You & You

First Time: The Best of Surface

Surface

Surface

Surface

Our World

Surface

3 Deep

Surface

Surface

First Time: The Best of Surface

Surface

Surface

Surface

Our World

Surface

Surface

Seventimesoverfold

Jumpstart

Seventimesoverfold

Surface

Surface

Jumpstart

Seventimesoverfold

Seventimesoverfold

3 Deep

Jumpstart

Seventimesoverfold

Breaking the Surface

Surface

Jumpstart

3 Deep

Breaking the Surface

Surface

Jumpstart

Seventimesoverfold

Breaking the Surface

Jumpstart

Seventimesoverfold

Surface: On Target

Jumpstart

Seventimesoverfold

Breaking the Surface

Surface: On Target

Seventimesoverfold

Breaking the Surface

Surface: On Target

Jumpstart

Seventimesoverfold

Breaking the Surface

Surface: On Target

Jumpstart

Breaking the Surface

Surface: On Target

Jumpstart

Breaking the Surface

Surface: On Target

Jumpstart

Surface: On Target

Jumpstart

Phase

Breaking the Surface

Surface: On Target

Breaking the Surface

Surface: On Target

Best Surface: A Nice Time for Loving

2nd Wave

Breaking the Surface

Surface: On Target

2nd Wave

Breaking the Surface

Re:start (Yakitate!! Japan Ending Theme)

Re:start (Yakitate!! Japan Ending Theme)

Surface

I'm Fine Thank You & You