WordGarden.ioextremal
C2Pronunciation
UK
US
Meanings
Adjective
relating to a maximum, minimum, or other extreme case in mathematics
Noun
a curve, function, or configuration that gives an extreme value
Beyond the definition
"Extremal" is not a word you hear every day, but it has a clear job. It describes something that is at an extreme point, or something connected to the largest or smallest possible value. Think of the very top, the very bottom, or the outer edge of what is allowed. The word appears most often in mathematics, physics, and similar fields. A mathematician might talk about "extremal points" on a curve, meaning the points where a function reaches its highest or lowest value. You may also see it in phrases like "extremal problem," where the goal is to find the best, smallest, or largest result under certain limits.
Imagine a graph rising and falling like a range of hills. The highest peak and the lowest dip are the places this word points to. It is less about strong emotion and more about being at the edge of a range.
The word "extremal" refers to something that is related to, or represents, an extreme case or limit. While similar to "extreme," "extremal" carries a more technical and precise connotation, often used in fields like mathematics, physics, and optimization theory. It doesn't simply mean very large or small; it specifically denotes the point where something reaches its absolute maximum or minimum value within a given set of conditions.
In mathematics, an extremal problem seeks to find the largest or smallest possible value of a function subject to certain constraints. For example, finding the shortest path between two points is an extremal problem. The solution—that shortest path—represents an "extremal" solution.
Outside mathematics, the word still keeps that same sense of being tied to an outer limit or boundary case, but this broader use is much less common. In careful writing, it may describe a case, condition, or example that stands at one end of a range rather than something that is merely intense or dramatic. That is why it sounds more natural in technical phrases such as "extremal values," "extremal points," or "extremal problem" than in everyday phrases about courage, effort, or emotion.
However, it's important to note that "extremal" isn't as common in everyday conversation as its synonym, "extreme." You're more likely to encounter it in technical writing or academic discussions where precision is key. It implies a rigorous and often calculated approach to reaching the furthest possible point within defined parameters.
So, if something is at its absolute limit, representing the highest or lowest possibility within a system, you're dealing with something that can be described as "extremal."
Examples
- 1
Optimization problem
The chapter opens with an extremal problem: which shape encloses the largest area for a fixed perimeter?
- 2
Proof strategy
In the proof, we start with an extremal example and show that it cannot actually exist.
- Domainan extremal example
one chosen because it is the largest, smallest, or otherwise most extreme case
- 3
Graph theory
Her research is in extremal graph theory, a branch of math that studies the largest possible networks that avoid certain patterns.
See also
Forms and spellings
1 form open this card.
Main spelling
- extremal