at the boundary of vs on the boundary of

Both 'at the boundary of' and 'on the boundary of' are correct and commonly used phrases in English. They can be used interchangeably depending on the context, with 'at the boundary of' emphasizing a specific point or location and 'on the boundary of' emphasizing the surface or edge of a boundary.

Last updated: April 13, 2024 • 818 views

This phrase is correct and commonly used in English.

"at the boundary of"

This phrase is used to indicate a specific point or location where something is located in relation to a boundary.

Examples:

The house is located at the boundary of the forest.
The park is at the boundary of the city limits.
She stood at the boundary of the property.

Show examples from the web [+]

Specifically, we argue that the quantum phase transitions at the boundary of topological superconductors in both two and three dimensions display ...
Nov 1, 2017 ... Nutrient amendment experiments at the boundary of the South Atlantic gyre reveal extensive regions in which nitrogen and iron are ...
Sep 12, 2019 ... Anomalous localization at the boundary of an interacting topological insulator. Authors:Itamar Kimchi, Yang-Zhi Chou, Rahul M. Nandkishore, Leo ...
Aperiodicity at the boundary of chaos. Published online by Cambridge University Press: 04 May 2017. STEVEN HURDER and. ANA RECHTMAN. Show author details ...
Nutrient co-limitation at the boundary of an oceanic gyre. Nature. 2017 Nov 9;551(7679):242-246. doi: 10.1038/nature24063. Epub 2017 Nov 1.
Jul 19, 2010 ... ... Detection and Full-Range ZVS Operating at the Boundary of DCM/CCM ... which operates at the boundary of discontinuous-conduction mode ...

Alternatives:

on the edge of
near the border of
adjacent to the boundary of
along the boundary of

This phrase is correct and commonly used in English.

"on the boundary of"

This phrase is used to indicate the surface or edge of a boundary where something is located.

Examples:

The house is built on the boundary of the property.
The playground is on the boundary of the school grounds.
The river flows on the boundary of the national park.

Show examples from the web [+]

A power station is located on the boundary of a square region that measures 10 miles on each side. Three substations are located inside the square region.
Feb 11, 2019 ... ... determines exactly which metrics on the sphere are induced on the boundary of a compact convex subset of hyperbolic three-space.
may lie on the boundary of the maintained hypothesis and (ii) there may be a nuisance parameter that appears under the alternative hypothesis, but not under ...
Coexistence of phage and bacteria on the boundary of self-organized refuges. Proc Natl Acad Sci U S A. 2012 Jul 31;109(31):12828-33. doi: ...
Transition in pipe flow: the saddle structure on the boundary of turbulence. Published online by Cambridge University Press: 01 October 2008.

Alternatives:

at the edge of
along the border of
adjacent to the boundary of
near the boundary of

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at the boundary of vs on the boundary of