spherical law

USAGE SUMMARY

The phrase "spherical law" is correct and usable in written English.
It can be used in contexts related to geometry, particularly in discussions about spherical geometry or theorems involving spheres. Example: "According to the spherical law of cosines, the relationship between the sides and angles of a spherical triangle can be expressed mathematically."

✓ Grammatically correct

Science

Encyclopedias

Wiki

Human-verified examples from authoritative sources

Exact Expressions

6 human-written examples

For example, there is a spherical law of sines and a spherical law of cosines.

Encyclopedia Britannica

The vertex angle at C is defined to be the spherical angle between the sides of △ joining C to A and C to B. Proposition 2.2 (The Spherical Law of Cosines [12], I.2.13]).

Fixed Point Theory and Applications

The spherical law of cosines [29] lets us write γ in terms of θ and φ, cos(gamma_)=cos(theta cos(theta_)+sin(theta)sin( theta_ cos (varphi-varphi_), (42) which, from spherical harmonic addition theorem [48], allows us to expand (P_{mu}) in terms of (Y_{mu}^{nu}), P_{mu}bigl(cos(gamma_ bigr)=frac{4 pi}{2 mu+1}sum _{nu=-mu}^{mu} Y_{mu}^{nu}( theta,varphi) Y_{mu}^{-nu}(theta_,varphi_).

The Journal of Mathematical Neuroscience

This equation can be derived as a special case of the spherical law of cosines that applies to all spherical triangles: : \cos \left(\frac{c}{R}\right)=\cos \left(\frac{a}{R}\right)\cos \left(\frac{b}{R}\right) +\sin\left(\frac{a}{R}\right) \sin\left(\frac{b}{R}\right) \cos \gamma \.

Wikipedia

The distance (d) of each longline set to the closest seamount was estimated using the simple spherical law of cosines.

Plosone

Under this model the probability that a trip from origin A terminates at B is: <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0004403.e003.PNG" class= inline-graphic"/> where DA,B is the distance between A and B calculated based on their latitude and longitude using the spherical law of cosines.

Plosone

Human-verified similar examples from authoritative sources

Similar Expressions

53 human-written examples

Other references on generalized spherical laws are Arnold et al. (2008), Kamiya et al. (2008), Rattihalli and Basugade (2009), Rattihalli and Patil (2010), and Balkema and Nolde (2010).

Journal of Statistical Distributions and Applications

A large part of the technical complexity of working with generalized spherical laws is in representing the contours and evaluating the norming constant (k_{mathcal {C}}) in (2) and simulating from the contour (mathcal {C}).

Journal of Statistical Distributions and Applications

The third step above also provides a way to simulate from paths and surfaces unrelated to generalized spherical laws, giving new classes of probability distributions on paths and surfaces.

Journal of Statistical Distributions and Applications

Polyphenols extraction was modelled by application of second Fick's law to spherical particles of 0.5 mm diameter, so obtaining the effective diffusion coefficient as parameter.

Bioresource Technology

For spherical indentation into power law engineering materials, we showed that this problem can be solved by using the concept of the representative strain.

Materials Science and Engineering: A

Expert writing Tips

Best practice

When discussing calculations on a sphere, specify the precise "spherical law" you are referring to, such as the law of cosines or sines, to avoid ambiguity. If the context is clear, simply using "the law" might be sufficient.

Common error

Avoid applying planar trigonometric laws directly to spherical geometry. "Spherical laws" account for the curvature of the sphere, which planar laws do not. Always use the appropriate formulas for spherical triangles.

Linguistic Context

The phrase "spherical law" functions primarily as a noun phrase that identifies a specific rule or principle within the context of spherical geometry or trigonometry. Ludwig examples showcase its use in mathematical and scientific contexts, as Ludwig AI confirms its grammatical correctness.

Expression frequency: Uncommon

Frequent in

Science

70%

Encyclopedias

20%

Wiki

10%

Less common in

News & Media

0%

Formal & Business

0%

Social Media

0%

Ludwig's WRAP-UP

The term "spherical law" is a grammatically sound phrase primarily used within the domains of mathematics and science to denote principles or formulas applicable to spherical geometry. As Ludwig AI confirms, the phrase is correct and usable in English, albeit more specialized. While examples are somewhat limited, "spherical law" appears most frequently in scientific publications and encyclopedic entries, indicating a formal and technical register. When employing the phrase, it's vital to specify the exact law being referenced, such as the spherical law of cosines or sines, to ensure clarity and avoid confusion with planar geometry. Remember to adapt your language to ensure precision. The information above should serve as a reference for correctly utilizing and understanding this term.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

spherical trigonometry law

More specific, explicitly mentioning the branch of mathematics.

law of cosines for spheres

Focuses on a specific law applicable to spheres.

spherical geometry principle

Replaces "law" with a more general term, "principle".

spherical rule

Substitutes "law" with "rule", which has a slightly less formal connotation.

formula for spherical calculations

Broader, referring to any formula used in spherical calculations.

spherical distance formula

Specifically relates to distance calculations on a sphere.

equation for spherical surfaces

Refers to any equation describing spherical surfaces.

geometric law for spheres

Emphasizes the geometric aspect of the law.

spherical coordinate principle

Relates to principles involving spherical coordinates.

spherical theorem

Swaps "law" with "theorem", implying a more formal mathematical statement.

FAQs

How does the spherical law of cosines differ from the planar law of cosines?

The spherical law of cosines accounts for the curvature of a sphere, using trigonometric functions of the sides as angles subtended at the sphere's center. The planar law applies to flat triangles.

When should I use the spherical law of sines?

Use the spherical law of sines when relating the sides and angles of spherical triangles, often in navigation or astronomy. It's analogous to the planar law of sines but adapted for spherical geometry.

What is an example of a spherical law used in navigation?

The haversine formula, derived from the spherical law of cosines, is used to calculate distances between two points on a sphere given their longitudes and latitudes.

Where can I find reliable information about spherical laws and formulas?

Consult textbooks on spherical trigonometry, geodesy, or astronomy, as well as reputable online resources like Encyclopedia Britannica or academic publications.