1. The fan is above the desk.

(Can we use 'above' any time when the fan is on the ceiling, for example, in each corner. When the fan is directly over the desk, can we use "over" as in the sentence? Can we use 'above' when the fan is in each corner of the ceiling.)

2. The fan is over the desk.
(Do we use 'over' when the fan is directly above the desk verticallty? When the fan is in each corner, can't we use 'over? If the desk is in the midder of the room, the fan is not directly above the desk.) •English - Writeacher, Tuesday, November 29, 2016 at 7:05am
If the fan is sitting on one corner of the desk or the other corner, you'd say the fan is ON the desk. ..............

To be ABOVE the desk or OVER the desk, it would have to be mounted on the wall and above the surface of the desk or suspended from the ceiling.
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Thank you for your kind explanation. At the center of a room, there is a small table. If a fan is atttached to the ceiling, can we use both 'above' and 'over' in the same way? Or we can use 'above' wherever the fan is attached on the ceiling, but we use 'over' when the fan is directly above the table. How about this explanation? (Situation: the fan is not on the table.)

At the center of a room, there is a small table. If a fan is attached to the ceiling, can we use both 'above' and 'over' in the same way? Or we can use 'above' wherever the fan is attached on the ceiling, but we use 'over' when the fan is directly above the table. How about this explanation?

In these examples, either "over" or "above" is fine. They mean approximately the same thing.

In the given situation where the fan is attached to the ceiling above a small table at the center of a room, both "above" and "over" can be used to describe the position of the fan depending on the context.

If you want to indicate that the fan is positioned higher than the table but not necessarily directly centered above it, you can use "above." For example, "The fan is positioned above the table" suggests that the fan is attached to the ceiling and located higher than the table, but not directly centered over it.

On the other hand, if you want to emphasize that the fan is directly centered above the table, you can use "over." For example, "The fan is directly over the table" indicates that the fan is positioned directly centered above the table.

So, in summary, you can use "above" to describe the fan's general position in relation to the table, and "over" to specifically indicate that the fan is directly centered above the table.

In the situation you described where there is a small table at the center of the room and a fan attached to the ceiling, you can use both "above" and "over" to describe the position of the fan relative to the table.

If the fan is attached to the ceiling anywhere in the room, you can say it is "above" the table because it is positioned higher than the table. The term "above" in this context refers to the vertical position of the fan relative to the table.

If the fan is directly positioned above the table, you can also use the word "over" to describe its position. In this case, "over" implies that the fan is directly vertically aligned with the table.

So, in summary, you can use "above" to describe the general position of the fan in relation to the table when it is attached to the ceiling, and you can use "over" to specifically describe the position when the fan is directly aligned with the table.