Orthogonal vs. perpendiculaire

The French words 'orthogonal' and 'perpendiculaire' both relate to the concept of angles meeting at right angles, but they are often used in slightly different contexts. In this overview, we will explore the nuances that distinguish these terms.

Orthogonal

'Orthogonal' is a term used primarily in mathematics and geometry to describe a situation where two lines or planes meet at a right angle (90 degrees). It can also be used more broadly in other fields such as computer science or art to describe concepts or objects that are figuratively 'at right angles' to each other, implying independence or non-interference.
Deux droites sont orthogonales si elles forment un angle de 90 degrés.
(Two lines are orthogonal if they form a 90-degree angle.)
Dans un espace vectoriel, deux vecteurs sont orthogonaux si leur produit scalaire est nul.
(In a vector space, two vectors are orthogonal if their dot product is zero.)
En traitement du signal, les fonctions orthogonales permettent la décomposition d'un signal en composantes indépendantes.
(In signal processing, orthogonal functions allow the decomposition of a signal into independent components.)

Perpendiculaire

'Perpendiculaire' is also used in mathematics and everyday language to describe two lines or surfaces meeting at a right angle, similar to the English term 'perpendicular'. It is usually used when discussing physical objects and tangible situations rather than abstract concepts.
La table est perpendiculaire au mur.
(The table is perpendicular to the wall.)
Un escalier perpendiculaire relie les deux étages du bâtiment.
(A perpendicular staircase connects the two floors of the building.)
Pour mesurer un angle perpendiculaire, un équerre est souvent utilisée en dessin technique.
(To measure a perpendicular angle, a square is often used in technical drawing.)

Summary

In summary, while both 'orthogonal' and 'perpendiculaire' can be translated as 'perpendicular', 'orthogonal' tends to be favored in more abstract and mathematical contexts, while 'perpendiculaire' is commonly used for physical instances of right angles in day-to-day life as well as geometry. Understanding the subtle differences between these words is essential for using them correctly in various disciplines.