isoperimetrical
Definition
Adjective (toán học): - Isoperimetrical refers to a property in geometry where two or more shapes have the same perimeter. Specifically, it describes figures that are equal in perimeter, often used in the context of the isoperimetric problem, which seeks the shape with the maximum area for a given perimeter.
Usage Examples
- (The circle has the greatest area among all shapes with the same perimeter.)
- (Mathematicians examine shapes that share the same boundary length.)
Advanced Usage
- Isoperimetrical inequality: a mathematical principle stating that, for a given perimeter, the circle has the maximum area; conversely, for a given area, the circle has the minimum perimeter.
- The isoperimetrical inequality is fundamental in calculus of variations and optimization problems. (This inequality governs the relationship between perimeter and area.)
Variants and Related Words
- Isoperimetric (adj): a shorter, more common variant of "isoperimetrical," meaning the same thing.
- The isoperimetric problem is a classic question in geometry. (The problem concerns shapes with equal perimeters.)
- Isoperimetry (n): the study or property of having equal perimeters.
- Isoperimetry has applications in physics, such as in the shape of soap bubbles. (The study of equal-perimeter shapes.)
Synonyms
- Equiperimetric: having an equal perimeter (a synonym, though less common).
- Perimeter-equal: a descriptive phrase meaning the same as isoperimetrical.
Related Idioms
- Isoperimetrical problem: a classic mathematical problem that asks which shape maximizes area for a given perimeter.
- Solving the isoperimetrical problem involves proving that the circle is optimal. (This problem is a key topic in geometry.)
Note
This word is highly technical and primarily used in advanced mathematics, geometry, and physics. It is not common in everyday language.