path-invariant
|path-in-var-i-ant|
🇺🇸
/ˌpæθ-ɪnˈvɛəriənt/
🇬🇧
/ˌpɑːθ-ɪnˈveəriənt/
unchanged by route
Etymology
'path-invariant' is a compound formed from 'path' and 'invariant'. 'path' originates from Old English 'pæþ' (meaning 'way, track'), and 'invariant' originates from French 'invariant', ultimately from Latin roots 'in-' (meaning 'not') and 'variare' (meaning 'to change').
'path' evolved from Old English 'pæþ' to Middle English 'path' and retained the meaning 'way, route'. 'invariant' passed from Latin (via French 'invariant') into modern English; the component 'in-' (not) combined with the root related to 'vary/change' to make 'invariant'. The compound 'path-invariant' is a modern technical formation combining these elements.
The components originally meant 'way/route' and 'not changing'; combined in modern technical usage they express 'not changing with the route taken' (the compound's current technical meaning).
Meanings by Part of Speech
Noun 1
the property or condition of being path-invariant; path-independence.
Path-invariance is an important property in potential theory and conservative systems.
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Antonyms
Adjective 1
not changing with respect to the route taken; independent of the particular path (e.g., a quantity or property whose value depends only on endpoints, not on the path between them).
In a conservative vector field, the line integral is path-invariant: it has the same value for any path between two points.
Synonyms
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Last updated: 2025/11/19 11:16