by symmetry to

USAGE SUMMARY

The phrase "by symmetry to" is not standard in written English and may cause confusion.
It could be used in mathematical or scientific contexts where symmetry is being discussed, but it would need to be part of a clearer expression. Example: "The properties of the triangle can be derived by symmetry to those of the square."

⚠ May contain grammatical issues

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

This is impossible, because you need a square to cover angles 1 and 2, and a square of the same size, by symmetry, to fill in angles 3 and 4. Hence, either they both cover angle 5, or neither does.

The New York Times

By symmetry, to prove that (mathcal E _1 = mathcal E _2), it suffices to prove the existence of a (k -embedding (mathcal E _1 hook -embeddingmathcal E _1).

Bulletin of Mathematical Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

The method of Shaw and Holmes [1] is enhanced by exploiting symmetry to obtain closed form expressions of the Poincaré section and mapping.

Journal of Sound and Vibration

It is, however, related by crystal symmetry to Cys52 of another molecule with an approach of sulfur atoms at 6.9 Å.

Biochemistry

The three MnIII ions are inequivalent by symmetry due to the presence of one coordinated solvent molecule and one oxime or phenoxo oxygen atom in the axial position of each MnIII ion.

Chemistry - A European Journal

Ratio below 1.0 was inverted, multiplied by -1 for symmetry to give the flip ratio [FR].

BMC Genomics

Alternative starting models were also created by applying sixfold symmetry to single classes and then using the resultant 3D map, generally composed of three discs corresponding to the three layers of the molecule, to generate an anchor set for Euler angle assignment.

eLife

In the calculations, the potential for quantum confinement was derived by the actual shape of a randomly chosen TCQR, measured by AFM and by imposing a cylindrical symmetry to the confining potential.

Nanoscale Research Letters

The Ho Phra That Monthien is located to the west side of the Phaisan Thaksin Hall and is also connected by a corridor in symmetry to the Suralai Phiman on the other side.

Wikipedia

This size difference was seen in the earlier work, but the symmetry measurement was less clear, and it was explained by assigning a lower symmetry to the prepore (31 vs 38 for the pore) (Tilley et al., 2005).

eLife

The ZnT3 protein dimer was built by applying the non-crystallographic symmetry to the model that relates to the two monomers of Yiip in the 2QFI crystal structure.

Plosone

Expert writing Tips

Best practice

Consider the context. In technical writing, ensure the relationship implied by symmetry is explicitly stated, using phrases that specify the symmetrical property (e.g. "symmetric with respect to the y-axis").

Common error

Avoid assuming that "symmetry" automatically implies a direct causal relationship. Instead, clearly articulate the specific symmetrical property and its effect (e.g. 'Due to the symmetry of the design, the forces are evenly distributed' rather than just 'by symmetry').

Linguistic Context

The phrase "by symmetry to" attempts to function as a prepositional phrase indicating a relationship or correspondence based on symmetry. However, according to Ludwig AI, this construction is not standard English and may cause confusion. Standard usage requires alternative phrasing.

Expression frequency: Rare

Frequent in

Science

67%

News & Media

33%

Formal & Business

0%

Less common in

Wiki

0%

Encyclopedias

0%

Reference

0%

Ludwig's WRAP-UP

In summary, while the phrase "by symmetry to" aims to express a relationship based on symmetrical properties, it's considered non-standard and potentially confusing according to Ludwig AI. More appropriate alternatives include "due to symmetry", "owing to symmetry", or "because of symmetry". The phrase is rare, primarily appearing in scientific contexts. When writing, clarity is crucial. Explicitly state the symmetrical property and its effect rather than relying on the ambiguous "by symmetry to". Opt for phrases that specify the nature of the relationship implied by symmetry for clearer communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

due to symmetry with

Replaces the preposition "by" with "due to", emphasizing the cause of the relationship, and uses "with" instead of "to".

owing to symmetry

Similar to "due to symmetry", this option highlights the causal link between symmetry and a specific outcome or property.

because of symmetry

A direct and simple way of saying that symmetry is the reason for something.

in virtue of symmetry

A more formal alternative that emphasizes symmetry as the basis or justification for something.

through symmetry

Suggests that something is achieved or understood through the application or consideration of symmetry.

via symmetry

Similar to "through symmetry", indicating a pathway or method involving symmetry.

by means of symmetry

Highlights the use of symmetry as a tool or method to achieve a certain result.

in light of symmetry

Indicates that symmetry provides a particular perspective or understanding.

considering the symmetry

Suggests an evaluation or judgment based on the symmetrical aspects of something.

taking symmetry into account

Emphasizes the inclusion of symmetry as a relevant factor in a calculation or analysis.

FAQs

What are some alternatives to "by symmetry to"?

While "by symmetry to" is not standard English, you can use phrases like "due to symmetry with", "owing to symmetry", or "because of symmetry" depending on the context.

Is "by symmetry to" grammatically correct?

No, "by symmetry to" is not considered grammatically correct. It's better to use phrases like "due to symmetry" or "by virtue of symmetry".

How can I use symmetry in a sentence correctly?

To use symmetry correctly, specify the type of symmetry and the relationship it creates. For example, "The results are equivalent "due to symmetry" in the experimental setup".

What does it mean when something is related "by symmetry"?

When something is related by symmetry, it means there's a correspondence or equivalence based on symmetrical properties. However, it's better to clarify the nature of the relationship, such as, "The two halves are identical "owing to symmetry"".