as the radius of

USAGE SUMMARY

The phrase "as the radius of" is correct and usable in written English.
It can be used when discussing geometric concepts, measurements, or relationships involving circles or spheres. Example: "The area of a circle increases as the radius of the circle increases."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

As the radius of influence is tightened, results become more representative of the observed data.

Columbia University

Conventionally, the length a is defined as the radius of the smallest sphere which completely encapsulates the antenna7,8.

Nature

In addition, it predicts the increase of hardness as the radius of indent cylinder decreasing.

International Journal of Solids and Structures

Previous studies have shown that a number of factors effect this process such as the radius of curvature of the teapot lip, the speed of the flow and the "wettability" of the teapot material.

MIT Technology Review

In agreement with probabilistic considerations of failure, the "local failure strength" at the root of a notch clearly increases as the radius of curvature becomes smaller.

Journal of the Mechanics and Physics of Solids

Characterization of the architectures proceeds by calculating the topological variables seniority and priority as well as the radius of gyration Macromol Theor Simul 10 (2001) 870.

Polymer

The PBG properties of the three PCs are similar to the properties of silicon-based system as the radius of the scatterer cylinder increases.

Microelectronic Engineering

The pitch radius is replaced by the distance between the gear center and the tooth center as the radius of gears.

Mechanism and Machine Theory

Rn is defined as the radius of the sphere with the same product M, where M is the molar mass and the intrinsic viscosity.

Polymer

The results of this study showed that the discrepancy of the sulfate concentration profile increases as the radius of a cast-in-situ pile decrease.

Construction and Building Materials

Their solution showed that the concentration of stress could become far greater, as the radius of curvature at an end of the hole becomes small compared with the overall length of the hole.

Encyclopedia Britannica

Expert writing Tips

Best practice

When using the phrase "as the radius of", ensure that the relationship you are describing is clear and mathematically or scientifically sound. Quantify the relationship whenever possible for greater precision.

Common error

Avoid using "as the radius of" to describe relationships that involve more than just the radius. Consider other influencing factors and specify them in your explanation.

Linguistic Context

The phrase "as the radius of" functions as a prepositional phrase, introducing a dependent clause that describes a relationship or condition based on the radius of a geometric shape. Ludwig confirms its correct and usable nature.

Expression frequency: Very common

Frequent in

Science

88%

Encyclopedias

6%

News & Media

6%

Less common in

Formal & Business

0%

Wiki

0%

Social Media

0%

Ludwig's WRAP-UP

The phrase "as the radius of" is a prepositional phrase used to describe relationships or conditions influenced by the size of a circle or sphere. Ludwig AI confirms that the phrase is grammatically correct and widely used, especially in scientific and formal contexts. Common usages often involve describing mathematical relationships, physical phenomena, or the behavior of systems in relation to changes in radius. When using "as the radius of", ensure clarity and precision in describing the relationship, quantifying it whenever possible to avoid oversimplification. Alternatives include "in relation to the radius of" and "with respect to the radius of", each offering a subtle shift in emphasis. Frequency analysis indicates it is very common in scientific contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

in relation to the radius of

Emphasizes the connection or dependency between a factor and the radius.

with respect to the radius of

Highlights a specific perspective or parameter being considered in connection to the radius.

depending on the radius of

Indicates that an outcome or characteristic varies based on the radius.

proportional to the radius of

Specifies a direct or inverse relationship between the element and the radius.

a function of the radius of

Indicates that the element's value or state is determined by the radius.

as a consequence of the radius of

Highlights the radius as the cause or reason for a specific effect.

in terms of the radius of

Focuses on evaluating or understanding something using the radius as a key measurement.

based on the radius of

Signals that a decision, calculation, or categorization relies on the radius.

given the radius of

Implies that the radius is a known quantity or condition affecting subsequent aspects.

considering the radius of

Highlights the radius as an important factor taken into account for analysis or planning.

FAQs

How do I use "as the radius of" in a sentence?

Use "as the radius of" to describe how something changes in relation to a circle or sphere's radius. For instance, "The area increases "as the radius of" a circle increases".

What are some alternatives to "as the radius of"?

Consider using phrases like "in relation to the radius of", "with respect to the radius of", or "depending on the radius of" depending on the specific context.

Which is more accurate: "as the radius increases" or "as the radius of"?

Both phrases are grammatically correct, but "as the radius increases" is more concise. Use ""as the radius of"" when you need to specifically emphasize that you're referring to the radius in relation to another object or concept.

What's the difference between "as the radius of" and "based on the radius of"?

"As the radius of" indicates a direct relationship or correlation, while "based on the radius of" suggests that the radius is a factor used for calculation or decision-making.