a given sphere

USAGE SUMMARY

The phrase "a given sphere" is correct and usable in written English.
It can be used in contexts where you are referring to a specific sphere that has been previously defined or is understood in the discussion. Example: "In the context of geometry, we can analyze the properties of a given sphere to understand its volume and surface area."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

10 human-written examples

In addition, for a given sphere diameter, FCC packing featured larger equilibrium capacitance than SC packing.

Electrochimica Acta

The lift coefficient of a freely falling sphere is 1.8 times that of a fixed sphere at a given sphere density of 4000 kg m−3 and sphere to fluid density ratio of 4. This is attributed to the Robin's force which arises due to the rotation of the sphere.

Chemical Engineering Science

Book XI sets out results on solid figures analogous to those for planes in Books I and VI; Book XII proves theorems on the ratios of circles, the ratios of spheres, and the volumes of pyramids and cones; Book XIII shows how to inscribe the five regular solids known as the Platonic solids in a given sphere (compare the constructions of plane figures in Book IV).

Encyclopedia Britannica

The precipitating solar wind spectrum, averaged over a given sphere, would peak at the mean energy of the upstream solar wind.

Earth, Planets and Space

For the technically or mathematically minded, a geodesic dome is a spherical structure composed of triangular elements forming part of a network of circles, or 'geodesics', on the surface of a given sphere.

BBC

If W is the set of all worlds, let $ be a function from worlds to sets of subsets of W, so that $(w) = {S1, S2, …, Sn}, with S1 ⊆ S2 ⊆ … ⊆ Sn = W. Worlds within a given sphere Si, 1 ≤ i ≤ n, are more similar to w than worlds outside it.

SEP

Human-verified similar examples from authoritative sources

Similar Expressions

50 human-written examples

The resulting interpolation curve is the intersection of the given sphere and the composite conical surface patch.

Advances in Engineering Software

The recovery coefficient for each sphere was finally computed as the ratio of the fitted profile at the sphere centre, F 0), and the known actual activity concentration in the given sphere.

EJNMMI Research

For example, the given and solution spheres can be resized so that one given sphere is shrunk to point while maintaining tangency.

Wikipedia

Inversion in this point reduces Apollonius' problem to finding a plane that is tangent to three given spheres.

Wikipedia

Second, to draw a sphere which shall cut each of four given spheres at the same angle.

University of Chicago

Expert writing Tips

Best practice

When using "a given sphere", ensure the context clearly identifies or defines the sphere being referenced. Clarity is essential in technical and academic writing.

Common error

Avoid using "a given sphere" without providing sufficient background information. If the sphere's properties or characteristics are not clear from the context, it can lead to ambiguity.

Linguistic Context

The phrase "a given sphere" functions as a determiner phrase followed by a noun, where "given" acts as an adjective specifying that the sphere is a known or pre-defined entity. This aligns with Ludwig AI's assessment of the phrase as correct and usable.

Expression frequency: Uncommon

Frequent in

Science

70%

Encyclopedias

20%

Academia

10%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "a given sphere" is a phrase used to denote a specific sphere that is under consideration or previously defined. As Ludwig AI confirms, the phrase is grammatically correct and most commonly found in scientific and academic contexts. When using this phrase, it's important to ensure the context clearly identifies the sphere to avoid ambiguity. Alternative phrases like "a specific sphere" or "a particular sphere" can be used for similar meanings. The phrase functions to introduce a known entity for further analysis.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a particular sphere

Replaces "given" with "particular", emphasizing the specific nature of the sphere being referred to.

a specific sphere

Substitutes "given" with "specific", highlighting the definite and well-defined nature of the sphere.

a designated sphere

Uses "designated" instead of "given", suggesting that the sphere has been appointed or chosen for a certain purpose.

a certain sphere

Replaces "given" with "certain", indicating that the sphere is known or definite, though perhaps not explicitly identified.

the sphere in question

Expresses the idea of "a given sphere" by explicitly stating that it is the one being discussed or examined.

the specified sphere

Uses "specified" instead of "given", indicating that the sphere has been clearly defined or indicated beforehand.

a pre-defined sphere

Uses "pre-defined" instead of "given", suggesting that the sphere has parameters that have been previously set.

a set sphere

Replaces "given" with "set", conveying that the sphere has been established or fixed in some context.

an established sphere

Substitutes "given" with "established", highlighting the recognized or already existing nature of the sphere.

a posited sphere

Uses "posited" instead of "given", suggesting that the sphere is assumed or proposed as a basis for reasoning.

FAQs

How can I use "a given sphere" in a sentence?

"A given sphere" is used to refer to a specific sphere that is under consideration or has been previously mentioned. For example: "We can analyze the volume of "a given sphere" to understand its properties."

What are some alternatives to "a given sphere"?

Alternatives include "a specific sphere", "a particular sphere", or "the sphere in question", depending on the context.

Is it better to say "a given sphere" or "a specific sphere"?

Both "a given sphere" and "a specific sphere" are grammatically correct. The choice depends on the context. "Given" implies it's already known or under consideration, while "specific" emphasizes its distinct nature.

What does "a given sphere" mean in mathematics?

In mathematics, "a given sphere" refers to a sphere whose properties (such as radius or center) are known or assumed for the purpose of solving a problem or proving a theorem.