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No. A point has no dimensions and no area.
The classic point has only position, and no area. Therefore, an arbitrary large number (towards infinity) of points may occupy the same position.
The ticketing area is more secure than the area beyond the security check point
A curved surface area can be described as one where the gradient of the normal to the surface changes smoothly from point to point.
A point has zero dimensions; a line has only one direction, which is length. Two-dimensional objects have length and width, and therefore area.