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The phrase "a planar surface" is correct and usable in written English.
It can be used in contexts related to geometry, physics, or engineering when describing a flat, two-dimensional surface.
Example: "In this experiment, we will analyze the reflection of light on a planar surface."
Alternatives: "a flat surface" or "a two-dimensional surface".
Exact(60)
An automotive component has been selected as a case study: the aim was to improve the planarity tolerance of a planar surface of the casted product.
Doing stuff on a planar surface is easy.
Another common method of illustration involves projecting the crystal structure onto a planar surface.
Consider a cylindrical hole (a pit) in a planar surface.
"Before, we would prefabricate all this on a planar surface," says Yonggang Huang, a mechanical engineer at Northwestern University in Evanston, Illinois, who's helping design the stretchy electronics.
As shown in Fig. 2, a planar surface is necessary for microwave generation at least with a size of ball lightning, which can be easily fulfilled in reality.
A planar surface with the desired dimension could not be achieved by using rods of squared section, because the etching introduced concavity of the surface.
In the paper, equation (12) is derived for a planar surface, and it is stated without proof that this is valid for arbitrary surfaces.
Tests showed three basic failure modes: failure through a planar surface, stepped failure, and failure by rotation of new blocks.
The fibrillar structure on NG/UFG substrate is expected to be more favorable for cellular response than a planar surface.
By contrast, rivers that drain surfaces capped by the Ogallala Group fan sediments show curved, divergent channel profiles (red lines), consistent with single-channel, non-branching rivers flowing directly down a planar surface.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com