cutting plane

USAGE SUMMARY

The phrase "cutting plane" is correct and usable in written English.
It is typically used in mathematical or engineering contexts, particularly in relation to geometry or optimization problems. Example: "To solve the problem, we need to define the cutting plane that separates the feasible region from the infeasible one."

✓ Grammatically correct

Science

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

54 human-written examples

Algorithms include the interior-point, barrier function, and cutting plane methods.

Stanford University

Includes batch and incremental subgradient, cutting plane, proximal, and bundle methods.

Massachusetts Institute of Technology

Synapses were first categorized by their orientation with respect to the cutting plane.

Nature

The solution procedure is based on the well known cutting plane idea and column generation technique.

Computational Statistics & Data Analysis

A cutting plane algorithm is adopted to solve this robust centralized planning model.

International Journal of Hydrogen Energy

The second is a piecewise linearization that is solved by a cutting plane method.

Operations Research Letters

Human-verified similar examples from authoritative sources

Similar Expressions

6 human-written examples

Subgradient, cutting-plane, and ellipsoid methods.

Stanford University

The generated LP solution is improved using cutting-plane inequalities.

Applied Soft Computing

For large datasets, it is several orders of magnitude faster than the old cutting-plane algorithm.

Cornell University

Moreover, they can also be used in a cutting-plane approach to solve the SCP.

European Journal of Operational Research

We develop cutting-plane algorithms and several heuristic approaches for solving the two models.

Computers & Operations Research

Expert writing Tips

Best practice

When describing surgical procedures or 3D modeling, use "cutting plane" to precisely indicate the surface along which a cut or section is made for clarity.

Common error

Avoid using "cutting plane" in contexts where a simple division or separation is meant, as it implies a specific, often geometric or surgical, operation. Simpler terms like "dividing line" or "separation point" might be more appropriate.

Linguistic Context

The phrase "cutting plane" functions primarily as a noun phrase, often used to describe a specific surface or plane along which something is cut or divided. This is evident in examples from Ludwig showing its usage in surgical contexts and 3D modeling.

Expression frequency: Very common

Frequent in

Science

75%

Academia

20%

News & Media

5%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The term "cutting plane" is a noun phrase predominantly used in scientific and academic contexts to describe a specific surface used for division or sectioning. Ludwig AI confirms its grammatical correctness and high frequency, particularly within scientific literature. While alternatives like "section plane" or "slice plane" exist, "cutting plane" provides a technical and precise description essential in fields like surgery, 3D modeling, and mathematical optimization. Its formal register and common usage in authoritative sources like Nature and ScienceDirect highlight its importance in technical communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

section plane

Replaces 'cutting' with 'section', emphasizing the act of creating a section or view.

slicing plane

Substitutes 'cutting' with 'slicing', highlighting the process of dividing something into slices.

division plane

Uses 'division' instead of 'cutting', focusing on the act of separating or dividing.

separation plane

Replaces 'cutting' with 'separation', emphasizing the act of distinguishing or setting apart.

planar cut

Inverts the structure and uses 'planar' to describe the cut, suitable for geometrical contexts.

geometric plane

Focuses on the geometric aspect of the plane itself, rather than the action of cutting.

intersecting plane

Highlights the intersection aspect, referring to a plane that intersects an object.

tangential plane

Specifies a plane that touches a surface at a single point.

cross-sectional plane

Emphasizes the creation of a cross-section.

trim plane

This specifies a plane used for trimming or removing excess material.

FAQs

How is "cutting plane" used in mathematical optimization?

In mathematical optimization, a "cutting plane" refers to an algorithm that iteratively refines a feasible set or objective function by adding linear inequalities.

What's the difference between "slice plane" and "cutting plane"?

While both phrases relate to creating sections, "cutting plane" often implies a more deliberate or calculated division, especially in fields like surgery or optimization, while "slice plane" may refer to a more general or less precise division.

When is "intersecting plane" a good substitute for "cutting plane"?

"Intersecting plane" is a suitable alternative when you want to emphasize the act of the plane crossing through a three-dimensional object rather than the action of cutting or separating.

Can "cutting plane" refer to something other than a physical cut?

Yes, in the context of optimization algorithms, a "cutting plane" is a constraint added to an optimization problem to cut off parts of the feasible region that do not contain the optimal solution.