# Name for Most Interior Point of a Plane Figure **URL:** \ **Category:** Factual Questions\ **Created:** [August 31, 2026, 10:22pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728 "2026-08-31T22:22:57Z")\ **Posts on this page:** 16\ **Page:** 3
**Author:** ![Jasmine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jasmine/32/2964_2.png) [@Jasmine](https://boards.straightdope.com/u/Jasmine)\ **Post date:** [September 4, 2026, 12:59pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/42 "2026-09-04T12:59:54Z")
> [@Chronos](#): > > What do you mean “on any side” of a point? True, it was a sloppy way of describing something. How about, " **Displacement** : A vector quantity representing the straight-line distance and direction from an initial reference point to a new position."? In any case, I discovered I was wrong because, according to math minds much greater than mine, one can actually calculate a central point inside an irregularly shaped figure even though it contains an infinite amount of points, and that central point is called a “Centroid”. So, as usual, I learned something from a discussion at the SDMB. ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [September 4, 2026, 4:21pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/43 "2026-09-04T16:21:32Z")
The OP themself explained why the centroid does not satisfy their requirements. For some non-convex shapes, the centroid is not even in the interior of the figure, let alone far from the edges. ---
**Author:** ![Jasmine](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jasmine/32/2964_2.png) [@Jasmine](https://boards.straightdope.com/u/Jasmine)\ **Post date:** [September 4, 2026, 7:32pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/44 "2026-09-04T19:32:46Z")
Impressive. You guys know more than my AI source. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [September 5, 2026, 1:07am UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/45 "2026-09-05T01:07:00Z")
> [@Chronos](#): > > If it’s the center, then it’s that same distance from three different coasts. Why? Suppose we’re dealing with a rectangle. Its center is obvious, and it’s the same distance from two sides and the same larger distance from the other two sides. Clearly the UK (and even Great Britain) is not a rectangle, but your statement doesn’t seem to be specific. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 5, 2026, 1:15am UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/46 "2026-09-05T01:15:28Z")
There is a set of measure zero of shapes where it’d be equidistant from only two points on the edge, and even there, there would be multiple points that would qualify, at least one of which would still include a third point on the edge. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [September 5, 2026, 4:12am UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/47 "2026-09-05T04:12:04Z")
OK, but your use of the word coast indicated to me that there was some notion of different sides like a polygon. If its an arbitrary perimeter, and “coast” means and single point, I can see it. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 5, 2026, 2:41pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/48 "2026-09-05T14:41:06Z")
You can slice “different coasts” as finely or as coarsely as you like. You can say that North America has an Atlantic Coast and a Pacific Coast, or both of those plus Arctic, or the Gulf Coast, or even go as fine as things like the “Maine Coast”, or go the other way and say that it’s all one coast. ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [September 6, 2026, 12:18pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/49 "2026-09-06T12:18:32Z")
> [@bob\_2](#): > > The centre of mainland UK (the point furthest from the sea) is Church Flatts Farm, located less than a mile southeast of Coton in the Elms, Derbyshire, approximately 70 miles (113 km) from the nearest coast. I’m not contradicting you, because I have no special knowledge of the matter. But when curiosity drove me to try to find out what the equivalent point is for Ireland, I came across sources that said that the furthest place from the sea in England is a town called Fillingley in Warwickshire. I wonder if there are different definitions in play. ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [September 6, 2026, 1:42pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/50 "2026-09-06T13:42:44Z")
Filongley is the furthest settlement from the sea (at 75 miles), rather than just a point in a field. Interesting that it’s in a different county. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [September 6, 2026, 2:41pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/51 "2026-09-06T14:41:47Z")
> [@markn\_1](#): > > For some non-convex shapes, the centroid is not even in the interior of the figure, let alone far from the edges. Any definition of centroid or Chebyshev center can be used with a restriction to points within the figure. Or, the finding of the closest point(s) to it. ---
**Author:** ![enipla](https://avatars.discourse-cdn.com/v4/letter/e/54ee81/32.png) [@enipla](https://boards.straightdope.com/u/enipla)\ **Post date:** [September 6, 2026, 4:02pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/52 "2026-09-06T16:02:50Z")
**Understanding Centroids** - **Center of mass:** It acts as the mathematical “center of gravity” for the shape based on its area. [[1](https://postgis.net/docs/ST_Centroid.html), [2] - - ([Centroid Definition | GIS Dictionary](https://support.esri.com/en-us/gis-dictionary/centroid))] - **Outside the boundary:** For irregular, concave, or horseshoe-shaped polygons (like a “C” shape), the true mathematical centroid can fall completely outside the actual polygon’s physical boundary. [[1](https://www.spatialanalysisonline.com/HTML/centroids_and_centers.htm), [2](https://postgis.net/docs/ST_Centroid.html)] - **Guaranteed interior points:** Many GIS software packages offer an “inside” or “point on surface” option (such as `ST_PointOnSurface` in PostGIS) if you need a representative point that is guaranteed to sit inside the polygon. [[1](https://enterprise.arcgis.com/en/portal/10.8/use/find-centroids.htm), [2](https://www.spatialanalysisonline.com/HTML/centroids_and_centers.htm), [3](https://postgis.net/docs/ST_Centroid.html)] That’s GIS. Often very important to have the centroid inside the polgon for labeling the polygon with whatever associated data. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 6, 2026, 5:41pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/53 "2026-09-06T17:41:35Z")
> [@bob\_2](#): > > The centre of mainland UK (the point furthest from the sea) is Church Flatts Farm, located less than a mile southeast of Coton in the Elms, Derbyshire, approximately 70 miles (113 km) from the nearest coast. > [@bob\_2](#): > > Filongley is the furthest settlement from the sea (at 75 miles), rather than just a point in a field. Interesting that it’s in a different county. That’s still a conflict, though, because if there exists a place (Filongley) that’s 75 miles from a coast, then a place (Church Flatts Farm) that’s 70 miles from the nearest coast can’t be the furthest from the coast. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [September 6, 2026, 6:16pm UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/54 "2026-09-06T18:16:49Z")
The spot you get will depend on the geographic data set you start with. I am also seeing one in Austrey in Warwickshire, yet other data putting it off Maids Moreton… ---
**Author:** ![vbob](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/vbob/32/4439_2.png) [@vbob](https://boards.straightdope.com/u/vbob)\ **Post date:** [September 7, 2026, 12:12am UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/55 "2026-09-07T00:12:12Z")
I wonder if there’s a way to let this figure itself out with soap bubble film or a rubber sheet and rolling weight…ok, that might help FIND the most interior point, but we’d still have to pick a name to satisfy the OP. ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [September 7, 2026, 3:04am UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/56 "2026-09-07T03:04:05Z")
The problem isn’t that it’s hard to define the most interior point; the problem is that it’s too easy. As mentioned upthread, there are over 70,000 definitions that might qualify (and they all have names). You have to pick the one that seems best to you, and different people might choose different ones, because there isn’t one that is clearly the best. ---
**Author:** ![Saffer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saffer/32/6440_2.png) [@Saffer](https://boards.straightdope.com/u/Saffer)\ **Post date:** [September 7, 2026, 7:48am UTC](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728/57 "2026-09-07T07:48:46Z")
> [@vbob](#): > > rubber sheet and rolling weight This is an interesting idea, though it could be multimodal for a weird shape. [Previous page](https://boards.straightdope.com/t/name-for-most-interior-point-of-a-plane-figure/1032728.md?page=2)