figurate number: meaning, definition, pronunciation and examples
C2 / Highly SpecializedAcademic / Technical / Mathematical
Quick answer
What does “figurate number” mean?
A number that can be represented as a regular geometric arrangement of equally spaced points, forming shapes such as triangles, squares, pentagons, etc.
Audio
Pronunciation
Definition
Meaning and Definition
A number that can be represented as a regular geometric arrangement of equally spaced points, forming shapes such as triangles, squares, pentagons, etc.
In broader mathematical contexts, the term can refer to any number pattern that forms a discrete geometric shape. In recreational mathematics and number theory, it extends to include more complex polygonal numbers and three-dimensional arrangements (like pyramidal numbers).
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. The term is identical in both dialects within mathematical literature.
Connotations
Neutral technical term in both regions. Slightly more likely to appear in UK contexts under the historical term 'polygonal number'.
Frequency
Extremely low frequency in general discourse. Usage is confined to specific textbooks, academic papers, and advanced mathematical discussions with identical frequency in US and UK academic settings.
Grammar
How to Use “figurate number” in a Sentence
[Number] is a figurate number.[Shape] numbers are a subset of figurate numbers.The concept of figurate numbers dates back to...Vocabulary
Collocations
Examples
Examples of “figurate number” in a Sentence
verb
British English
- Mathematicians can figurate a series of integers to reveal polygonal patterns.
American English
- The algorithm figurates the data points into a triangular array.
adverb
British English
- The points are arranged figurately, forming a hexagon.
American English
- The dots were placed figurately to demonstrate the square number.
adjective
British English
- The figurate sequence was explored in the Victorian era.
- It possesses interesting figurate properties.
American English
- We studied the figurate representation of the dataset.
- His work focuses on figurate number theory.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Used in mathematics textbooks, history of mathematics, and number theory papers. Example: 'The Pythagoreans had a mystical reverence for figurate numbers.'
Everyday
Never used in everyday conversation.
Technical
Core term in recreational mathematics, certain branches of number theory, and mathematical enrichment materials.
Vocabulary
Synonyms of “figurate number”
Strong
Neutral
Weak
Vocabulary
Antonyms of “figurate number”
Watch out
Common Mistakes When Using “figurate number”
- Using 'figurative number' (which relates to language, not mathematics).
- Confusing it with 'perfect number' or 'Fibonacci number'.
- Treating it as a countable singular without 's' (e.g., 'a figurate' – incorrect; must be 'a figurate number').
FAQ
Frequently Asked Questions
Yes, 1 is conventionally considered a figurate number for all polygons (a single point can represent the degenerate case of any shape).
'Polygonal number' is essentially a synonym for the most common 2D figurate numbers. 'Figurate number' is a broader term that can also include 3D arrangements like pyramidal numbers.
The study of figurate numbers is attributed to the ancient Pythagoreans (6th century BCE), who invested them with mystical and philosophical significance.
While primarily of historical and recreational interest, they appear in modern number theory (e.g., in identities involving sums of powers) and have applications in cryptography and computer science for certain spatial partitioning algorithms.
A number that can be represented as a regular geometric arrangement of equally spaced points, forming shapes such as triangles, squares, pentagons, etc.
Figurate number is usually academic / technical / mathematical in register.
Figurate number: in British English it is pronounced /ˈfɪɡ.ər.ət ˈnʌm.bər/, and in American English it is pronounced /ˈfɪɡ.jə.rət ˈnʌm.bɚ/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “To think in figurate terms (rare, meaning to think geometrically or pattern-based).”
Learning
Memory Aids
Mnemonic
Imagine FIGures that you RATE as numbers. A triangle of dots (3, 6, 10...) is a number you can rate as a figure.
Conceptual Metaphor
NUMBERS ARE SHAPES / MATHEMATICAL PROPERTIES ARE PHYSICAL FORMS. The abstract quantity is conceptualised as a concrete, visual arrangement.
Practice
Quiz
Which of the following is NOT a type of figurate number?