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Here's what I think I know, but I'm a geography newbie, so please correct any misconceptions I have, especially with regard to the term graticule.

A graticule is a specialized grid where the lines represent parallels and meridians. If those lines are latitude and longitude, then this kind of graticule is called a "conjugate graticule".

This is what I think is the most common usage of the term "graticule". However, I think it's just a common usage (and not a necessity) for the graticule's lines to be latitudes and longitudes.

My question is, if you have a UTM based map, isn't it possible (and more useful) to have a graticule in UTM coordinates (meters)?

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An enthusiastic contributor to Wikipedia started using the term "conjugate graticule" several years ago. But the use of "conjugate" is this context is a real stretch (it's borrowed from the terminology for ellipses). I recommend not using the "conjugate" modifier. (The term "conjugate graticule" no longer appears in Wikipedia.) –  cffk Mar 7 at 20:15
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Your definition of a graticule seems to be in line with that of Dictionary.com i.e. usually (not exclusively) applied to latitude and longitude.

However, at least amongst Esri users, the term used to describe a "graticule in UTM coordinates" is measured grid.

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I've never heard it called graticule in GIS - I've only seen that terminology in optics. I know it as "coordinate grid", and it is intended to help you find something on the map (or to read off coordinates for paper maps).

I think the sensible approach is to draw the lines / tic-marks / labels (whatever you decide to call it) in the way that makes the most sense to the viewer. You probably don't know that in advance, but if you can, then a user-selectable option for the software would be useful. So if the map is in UTM and the reader needs degrees / minutes / seconds, you can draw it in degrees / minutes / seconds. If the map is in lat / long and the reader needs GARS, then draw GARS keypads.

As a default, draw it in whatever the map is projected in.

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