jordan arc
LowTechnical / Academic (Mathematics)
Definition
Meaning
A simple, continuous, non-self-intersecting curve in a plane or space that is homeomorphic to the interval [0,1].
A fundamental concept in topology and mathematical analysis representing a curve with no breaks or crossings, which, together with the Jordan curve theorem, helps define the notion of inside and outside of simple closed curves.
Linguistics
Semantic Notes
The term is strictly mathematical. Named after French mathematician Camille Jordan. In general discourse, the 'Jordan' component is unrelated to the country or the name.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling and pronunciation are consistent across varieties.
Connotations
Exclusively mathematical; no cultural or regional connotations.
Frequency
Extremely low frequency in general language, used almost exclusively in advanced mathematics contexts in both regions.
Vocabulary
Collocations
Grammar
Valency Patterns
The [ADJECTIVE] Jordan arcJordan arc defined by [FUNCTION/RELATION]Jordan arc in [SPACE/DIMENSION]Vocabulary
Synonyms
Neutral
Weak
Vocabulary
Antonyms
Usage
Context Usage
Business
Not used.
Academic
Used in pure mathematics, particularly in topology, complex analysis, and geometry. Example: 'The proof relies on decomposing the boundary into a finite union of Jordan arcs.'
Everyday
Not used.
Technical
Used in mathematical proofs, definitions, and theoretical discussions about continuity and spatial properties.
Examples
By Part of Speech
adjective
British English
- The Jordan-arc property is essential.
- We need a Jordan-arc connectivity.
American English
- The Jordan-arc property is essential.
- We need a Jordan-arc connectivity.
Examples
By CEFR Level
- This term is not used at the A2 level.
- This term is not used at the B1 level.
- A Jordan arc is a basic idea in higher mathematics.
- The contour was approximated by a sequence of polygonal Jordan arcs.
- A key lemma shows that any two points in the region can be joined by a Jordan arc lying entirely within it.
Learning
Memory Aids
Mnemonic
Think of drawing a line from point A to point B without lifting your pen and without crossing over your own line. That's a Jordan Arc.
Conceptual Metaphor
A 'path' or 'journey' that is simple and straightforward, with no doubling back or intersections.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating 'Jordan' as 'Иордания' (the country). It is a proper name. A transliteration 'жорданова дуга' or 'дуга Жордана' is standard.
- The word 'arc' here is a precise mathematical term ('дуга'), not the more general 'арка' (arch).
Common Mistakes
- Misspelling as 'Jordan Ark'.
- Confusing it with a 'Jordan curve' (which is closed).
- Assuming it has any connection to geography or sport.
Practice
Quiz
What is a defining property of a Jordan arc?
FAQ
Frequently Asked Questions
No. A Jordan arc is an open curve with two distinct endpoints. A Jordan curve is a simple closed curve, meaning it is a loop with no self-intersections.
It is used almost exclusively in pure mathematics, specifically in branches like topology, complex analysis, and plane geometry.
It is named after the French mathematician Marie Ennemond Camille Jordan (1838–1922).
Any smooth, non-crossing path you can draw on paper, like a segment of a circle or a wavy line from one point to another, conceptually models a Jordan arc, provided it has no thickness.