frustum
C2Technical/Formal
Definition
Meaning
The portion of a solid (typically a cone or pyramid) that remains after its top has been cut off by a plane parallel to its base.
In geometry and computing, a three-dimensional shape created by slicing a solid figure, often used in the context of 3D graphics (viewing frustum) and architecture.
Linguistics
Semantic Notes
Primarily used in mathematics, engineering, and computer graphics. Its plural is 'frusta' or 'frustums'. The term implies a truncation parallel to the base, distinguishing it from other cross-sections.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Pronunciation differs slightly.
Connotations
Purely technical with no regional connotative differences.
Frequency
Equally rare in general usage in both regions, confined to technical fields.
Vocabulary
Collocations
Grammar
Valency Patterns
frustum of [a cone/pyramid]frustum with [a given height/base]Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “None”
Usage
Context Usage
Business
Virtually never used.
Academic
Used in mathematics, geometry, and engineering textbooks and papers.
Everyday
Extremely rare; would only appear in highly specific educational contexts.
Technical
Core term in 3D computer graphics (defining the visible region in a 3D scene) and architectural/geometric modelling.
Examples
By CEFR Level
- The lamp shade had the shape of a frustum.
- To find the volume of a conical frustum, you need the radii of both bases and the height.
- The game engine culls objects outside the camera's viewing frustum to optimize performance.
Learning
Memory Aids
Mnemonic
Think: 'The frustum is the part that's left, after the top has been reft.' (reft = archaic for torn off).
Conceptual Metaphor
A FRUSTUM IS A REMNANT/CUT-OFF PIECE (from a larger whole).
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'фрустрация' (frustration). The Russian geometric term is 'усечённый конус/пирамида' (usechennyy konus/piramida).
Common Mistakes
- Misspelling as 'frustrum' or 'frustrum'.
- Incorrect plural 'frustums' (acceptable but 'frusta' is more technical).
- Using it to describe a non-parallel truncation.
Practice
Quiz
What is the plural of 'frustum' most commonly used in technical literature?
FAQ
Frequently Asked Questions
No, it is a specialised term used almost exclusively in geometry, engineering, and computer graphics.
No, by definition it is a three-dimensional solid. A 2D equivalent would be a trapezoid (from a truncated triangle).
They are largely synonymous, but 'frustum' specifically implies the cutting plane is parallel to the base. 'Truncated' can be more general.
The 'viewing frustum' is a pyramid-shaped volume that determines which objects are rendered on screen, crucial for efficiency and realism.