"goat grazing problem" meaning in All languages combined

See goat grazing problem on Wiktionary

Noun [English]

Forms: goat grazing problems [plural]
Head templates: {{en-noun}} goat grazing problem (plural goat grazing problems)
  1. The problem: given a field of radius 1, and a goat tied to a point on the edge of said field; how long a rope should the goat be tied to, so that the goat has access to exactly half of the field? Equivalently: given a unit circle C and a point P on the rim of C, what is the value of r such that exactly half of the area within C, is within distance r of point P?
    Sense id: en-goat_grazing_problem-en-noun-tgy~GCuz Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries, Circle, Geometry, Higher-dimensional geometry, Trigonometry Disambiguation of English entries with incorrect language header: 50 50 Disambiguation of Pages with 1 entry: 53 47 Disambiguation of Pages with entries: 49 51 Disambiguation of Circle: 56 44 Disambiguation of Geometry: 53 47 Disambiguation of Higher-dimensional geometry: 46 54 Disambiguation of Trigonometry: 65 35
  2. The same problem generalized to any number of dimensions: given a unit n-sphere (n-dimensional hypersphere) S, and a point P on the edge of S, what is r such that exactly one-half of the space (content) within S, is within distance r of P?
    Sense id: en-goat_grazing_problem-en-noun-G4t1msXj Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries, Algebra, Geometry, Higher-dimensional geometry, Sphere Disambiguation of English entries with incorrect language header: 50 50 Disambiguation of Pages with 1 entry: 53 47 Disambiguation of Pages with entries: 49 51 Disambiguation of Algebra: 0 100 Disambiguation of Geometry: 53 47 Disambiguation of Higher-dimensional geometry: 46 54 Disambiguation of Sphere: 36 64
The following are not (yet) sense-disambiguated
Synonyms: goat problem

Inflected forms

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      "glosses": [
        "The problem: given a field of radius 1, and a goat tied to a point on the edge of said field; how long a rope should the goat be tied to, so that the goat has access to exactly half of the field? Equivalently: given a unit circle C and a point P on the rim of C, what is the value of r such that exactly half of the area within C, is within distance r of point P?"
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        "The same problem generalized to any number of dimensions: given a unit n-sphere (n-dimensional hypersphere) S, and a point P on the edge of S, what is r such that exactly one-half of the space (content) within S, is within distance r of P?"
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      "_dis1": "55 45",
      "word": "goat problem"
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        "The problem: given a field of radius 1, and a goat tied to a point on the edge of said field; how long a rope should the goat be tied to, so that the goat has access to exactly half of the field? Equivalently: given a unit circle C and a point P on the rim of C, what is the value of r such that exactly half of the area within C, is within distance r of point P?"
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-05-27 from the enwiktionary dump dated 2025-05-20 using wiktextract (a4e883e and f1c2b61). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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