family of curves
C1Academic/Technical
Definition
Meaning
A set of curves defined by a common equation or principle, differing only in the value of one or more parameters.
A grouping of similar mathematical or graphical relationships, often used to illustrate how a system behaves under different conditions. Can be extended metaphorically to describe any set of related trends, patterns, or possibilities sharing a common origin or structure.
Linguistics
Semantic Notes
A technical term from mathematics (especially calculus, differential equations, and statistics) with potential metaphorical use in data analysis, economics, and engineering. Implicitly conveys a relationship, lineage, or shared underlying structure among distinct entities.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or semantic differences. Spelling conventions may apply to surrounding text (e.g., 'parameterise' vs. 'parameterize').
Connotations
Identical in both varieties; purely technical.
Frequency
Similar frequency within equivalent technical and academic contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
[Verb] a family of curves (e.g., 'plot', 'describe', 'analyse')[Adjective] family of curves (e.g., 'related', 'differential')family of curves [Verb-ing] (e.g., 'family of curves representing...')Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “A whole family of possibilities (metaphorical extension)”
Usage
Context Usage
Business
Rare; potentially in data analytics or forecasting to describe related trend lines (e.g., 'We modelled a family of revenue curves under different market conditions.').
Academic
Common in mathematics, physics, engineering, and economics to describe solutions to equations or related graphical data.
Everyday
Extremely rare; would likely be misunderstood or require explanation.
Technical
Core usage. Found in textbooks, research papers, and technical documentation related to modelling, statistics, and system analysis.
Examples
By Part of Speech
verb
British English
- The equation can be parameterised to generate a family of curves.
- We need to analyse how the family of curves behaves as C varies.
American English
- The equation can be parameterized to generate a family of curves.
- We need to analyze how the family of curves behaves as C varies.
adjective
British English
- The family-of-curves analysis revealed the underlying trend.
- This is a classic family-of-curves problem in the textbook.
American English
- The family-of-curves analysis revealed the underlying trend.
- This is a classic family-of-curves problem in the textbook.
Examples
By CEFR Level
- The graph shows a family of curves, each representing a different temperature.
- By changing the constant, you can produce a whole family of curves from one equation.
- The differential equation's general solution defines an infinite family of curves, each corresponding to a specific initial condition.
- Economists presented a family of Lorenz curves to illustrate the range of possible income distributions under the proposed policy.
Learning
Memory Aids
Mnemonic
Think of a literal family tree, but instead of people, it's a tree of different curved lines, all descended from the same 'parent' equation.
Conceptual Metaphor
LINEAGE/RELATIONSHIP IS A FAMILY (applied to abstract mathematical objects).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Avoid translating 'family' literally as 'семья' in this context; use 'семейство кривых' or 'набор кривых'.
- Do not confuse with 'group of curves' which might imply a less formal or non-parametric collection.
Common Mistakes
- Using 'family' without the necessary technical context, leading to confusion (e.g., 'the family of curves went on a picnic').
- Treating it as a plural noun (e.g., 'The families of curves are...' when referring to one set). It is a singular collective noun: 'The family of curves is...'.
Practice
Quiz
In which context is the term 'family of curves' MOST appropriately used?
FAQ
Frequently Asked Questions
No, it is not common in everyday English. It is a specialised term used almost exclusively in academic, scientific, and technical fields such as mathematics, physics, engineering, and economics.
Yes, but carefully. In technical or analytical writing, one might metaphorically refer to a 'family of scenarios' or a 'family of data trends' to imply a set of related outcomes derived from a common model. This usage should be clearly understood by the intended audience.
It is treated as a singular collective noun. Use singular verbs: 'This family of curves is fascinating,' not 'are fascinating'.
It is like having one recipe (an equation) where you can change one ingredient (a parameter) to get many similar but slightly different dishes (the curves). All the dishes belong to the same 'family' because they come from the same basic recipe.