Commensurable definitions
| Word backwards | elbarusnemmoc |
|---|---|
| Part of speech | adjective |
| Syllabic division | com-men-su-ra-ble |
| Plural | The plural of the word commensurable is commensurables. |
| Total letters | 13 |
| Vogais (4) | o,e,u,a |
| Consonants (7) | c,m,n,s,r,b,l |
Commensurable is a term used in mathematics to describe two quantities that can be measured using the same unit of measurement, making them comparable to each other. When two quantities are commensurable, it means that they can be expressed as a ratio of whole numbers.
Definition of Commensurable
In mathematics, commensurable refers to two quantities that can be measured using the same unit, allowing for direct comparison. This concept is essential in fields such as geometry and algebra where precise measurements are required. When two quantities are commensurable, it means that they can be represented as a ratio of integers.
Examples of Commensurable Quantities
For example, the lengths of two line segments are commensurable if they can both be measured using the same unit of length. Similarly, the areas of two rectangles are commensurable if they can both be expressed in square units. In contrast, quantities that cannot be measured using the same unit are considered incommensurable.
Applications of Commensurability
Commensurability is a fundamental concept in mathematics that underpins many geometric and algebraic principles. In geometry, commensurable quantities are crucial for comparing lengths, areas, and volumes. In algebra, commensurability allows for the simplification of equations and the comparison of different quantities.
Overall, understanding commensurability is essential for making accurate measurements and comparisons in various mathematical contexts. By recognizing when two quantities are commensurable, mathematicians can simplify calculations and make connections between different mathematical concepts.
Commensurable Examples
- The two buildings were commensurable in size and shape.
- The company's sales figures were not commensurable with those of its competitors.
- It is important to ensure that the benefits of a project are commensurable with the costs.
- The quality of the product was commensurable to its price.
- Employee salaries should be commensurable to their skills and experience.
- The risks associated with the investment were not commensurable to the potential rewards.
- The amount of work required for the project was not commensurable with the resources available.
- The time commitment for the task was not commensurable with the expected outcome.
- His achievements were commensurable with his dedication and hard work.
- The complexity of the problem was commensurable to the expertise of the team.