# What is the English word for the French "repère"?

I'm preparing a holiday class in computer graphics. The class will be held in English. I'm a French speaker and I'm fighting with some words which have lots of meanings to find the right one in the context of maths or physics.

The current one is "repère" (an origin, and in my case 2 or 3 basis vectors) in the context of "changement de repère". The translation for "repère" that sounds to be the best so far is "frame", but is that right? Can we then speak about "frame shift"?

• Not a French speaker, but are you referring to shifting the origin or possibly a change of basis (as in linear algebra)? Be careful with the term "frame" (en.wikipedia.org/wiki/Frame_(linear_algebra)) as that is a generalization of the concept of a basis of a vector space.
– J W
Jun 19 '21 at 10:02
• Did you look at WordReference? It has a bunch of translations related to math like «repère (Géométrie : système de coordonnées) coordinate system» ; «changement de repère (maths : passage d'un repère à un autre) change of basis» ; «repère cartésien (maths : repère normé affine) Cartesian system» ; «repère orthonormé, repère orthonormal (repère orthogonal normé à 1) orthonormal coordinate system» . (I'm not a math educator but I saw this question on HNQ and I know some French.) Jun 20 '21 at 2:53

Elie Cartan wrote a paper in 1935 that was foundational for differential geometry. It is titled

La Méthode de Repère Mobile, La Théorie des Groupes Continus, et Les Espaces Généralisés.

In English, we often refer to the "method of moving frames."

Here is a link to a review of the paper

The set of basis vectors is just called the basis in English, and so your topic is usually called change of basis. Google is telling me that "repère" is translated as "coordinates", which would be the family of scalar variables that are used to define each point in the space in terms of the basis vectors.

Bonne chance!

• I think "coordinate system" might be a better match for repère itself, since it refers more to the method for assigning numbers to points than to the numbers themselves. However, the difference is often elided; for example, changement de repère would probably translated as "change of coordinates" rather than "change of coordinate system". Jun 19 '21 at 12:45

Yes, (ignoring diacritical marks) Cartan's "repere mobile" is "moving frame", but that refers to a more complicated idea than I think will come up in basic linear algebra. In basic linear algebra, it would make sense to just say "frame", rather than "moving frame", but/and the plain "frame" is better translated to contemporary English as "coordinate system", I think

• I think in the linear algebra context a frame is best called an (ordered) basis. It determines a coordinate system, but I would not use the words as synonyms. A moving frame is a field of ordered bases (formally a section of a principal bundle usually called the frame bundle). Cartan's moving frames were sometimes sections of more general bundles with fibers comprising affine or projective bases. Jun 24 '21 at 8:37