circumradius: meaning, definition, pronunciation and examples
Rare (Specialist)Formal / Technical / Academic
Quick answer
What does “circumradius” mean?
The radius of a circle that passes through all the vertices of a given polygon or polyhedron (its circumscribed circle or sphere).
Audio
Pronunciation
Definition
Meaning and Definition
The radius of a circle that passes through all the vertices of a given polygon or polyhedron (its circumscribed circle or sphere).
In geometry, it is a specific measure of the size of a regular polygon or polyhedron, relating the figure to its enclosing circle or sphere. It can also refer to the distance from the circumcenter of a triangle to any of its vertices.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or definitional differences. Potential minor spelling variations in surrounding text (e.g., centre/center).
Connotations
None; purely technical term with identical mathematical meaning.
Frequency
Identically rare and specialised in both dialects, used only in mathematical contexts.
Grammar
How to Use “circumradius” in a Sentence
[the] circumradius of [NP (polygon/triangle)][possessive] circumradius [is/equals] [value]Vocabulary
Collocations
Usage
Meaning in Context
Business
Virtually never used.
Academic
Used in mathematics, geometry, trigonometry, and computer science (e.g., computational geometry, mesh analysis).
Everyday
Not used in everyday conversation.
Technical
The primary domain. Used in engineering (e.g., structural analysis involving triangles), physics, and game development for spatial calculations.
Watch out
Common Mistakes When Using “circumradius”
- Mispronouncing as 'circum-radious' (/ˈreɪ.di.əs/). Correct stress is on 'ra' of 'radius': /-ˈreɪ.di.əs/.
- Confusing with 'circumference'.
- Using it as a general term for any outer radius instead of the specific geometric one.
- Spelling as 'circumradious'.
FAQ
Frequently Asked Questions
No, it applies to any polygon (square, pentagon, etc.) and polyhedron (e.g., tetrahedron), referring to the radius of the circumscribed circle or sphere.
The circumradius is the radius of the circle that goes *around* the figure, touching its vertices. The inradius is the radius of the circle that fits *inside* the figure, touching its sides.
One common formula is R = (a * b * c) / (4 * Area), where a, b, c are side lengths. For a right triangle, it's simply half the length of the hypotenuse.
No, it is a highly specialised term. You will almost never encounter it in everyday English, literature, or general news.
The radius of a circle that passes through all the vertices of a given polygon or polyhedron (its circumscribed circle or sphere).
Circumradius is usually formal / technical / academic in register.
Circumradius: in British English it is pronounced /ˌsɜː.kəmˈreɪ.di.əs/, and in American English it is pronounced /ˌsɝː.kəmˈreɪ.di.əs/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Imagine a CIRCUS tent (CIRCUM-) around a RADIUS (RADIUS) that touches all the performers (vertices) standing in a ring. The CIRCUM-RADIUS is the distance from the tent's central pole to any performer.
Conceptual Metaphor
ENCLOSURE / CONTAINMENT: The polygon is contained within the perfect circle that just touches its corners. The circumradius measures the reach of that perfect, enclosing shape.
Practice
Quiz
What is the circumradius of a geometric figure?