Antipodal point GudangMovies21 Rebahinxxi LK21

      In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center.
      Given any point on a sphere, its antipodal point is the unique point at greatest distance, whether measured intrinsically (great-circle distance on the surface of the sphere) or extrinsically (chordal distance through the sphere's interior). Every great circle on a sphere passing through a point also passes through its antipodal point, and there are infinitely many great circles passing through a pair of antipodal points (unlike the situation for any non-antipodal pair of points, which have a unique great circle passing through both). Many results in spherical geometry depend on choosing non-antipodal points, and degenerate if antipodal points are allowed; for example, a spherical triangle degenerates to an underspecified lune if two of the vertices are antipodal.
      The point antipodal to a given point is called its antipodes, from the Greek ἀντίποδες (antípodes) meaning "opposite feet"; see Antipodes § Etymology. Sometimes the s is dropped, and this is rendered antipode, a back-formation.


      Higher mathematics


      The concept of antipodal points is generalized to spheres of any dimension: two points on the sphere are antipodal if they are opposite through the centre. Each line through the centre intersects the sphere in two points, one for each ray emanating from the centre, and these two points are antipodal.
      The Borsuk–Ulam theorem is a result from algebraic topology dealing with such pairs of points. It says that any continuous function from




      S

      n




      {\displaystyle S^{n}}

      to





      R


      n




      {\displaystyle \mathbb {R} ^{n}}

      maps some pair of antipodal points in




      S

      n




      {\displaystyle S^{n}}

      to the same point in





      R


      n


      .


      {\displaystyle \mathbb {R} ^{n}.}

      Here,




      S

      n




      {\displaystyle S^{n}}

      denotes the



      n


      {\displaystyle n}

      -dimensional sphere and





      R


      n




      {\displaystyle \mathbb {R} ^{n}}

      is



      n


      {\displaystyle n}

      -dimensional real coordinate space.
      The antipodal map



      A
      :

      S

      n


      →

      S

      n




      {\displaystyle A:S^{n}\to S^{n}}

      sends every point on the sphere to its antipodal point. If points on the



      n


      {\displaystyle n}

      -sphere are represented as displacement vectors from the sphere's center in Euclidean



      (
      n
      +
      1
      )


      {\displaystyle (n+1)}

      -space, then two antipodal points are represented by additive inverses




      v



      {\displaystyle \mathbf {v} }

      and



      −

      v

      ,


      {\displaystyle -\mathbf {v} ,}

      and the antipodal map can be defined as



      A
      (

      x

      )
      =
      −

      x

      .


      {\displaystyle A(\mathbf {x} )=-\mathbf {x} .}

      The antipodal map preserves orientation (is homotopic to the identity map) when



      n


      {\displaystyle n}

      is odd, and reverses it when



      n


      {\displaystyle n}

      is even. Its degree is



      (
      −
      1

      )

      n
      +
      1


      .


      {\displaystyle (-1)^{n+1}.}


      If antipodal points are identified (considered equivalent), the sphere becomes a model of real projective space.


      See also


      Cut locus


      References




      External links


      "Antipodes", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
      "antipodal". PlanetMath.

    Kata Kunci Pencarian:

    antipodal points on earthantipodal pointsantipodal point finderantipodal pointantipodal point calculatorantipodal point of my locationantipodal point of indiaantipodal points meaningantipodal point of londonantipodal point melbourne
    antipodal-point · GitHub

    antipodal-point · GitHub

    Antipodal Point

    Antipodal Point

    Antipodal Point

    Antipodal Point

    Antipodal Point

    Antipodal Point

    Antipodal Point

    Antipodal Point

    Antipodal Flight - ARCHALIEN.TV

    Antipodal Flight - ARCHALIEN.TV

    Wordcloud Antipodal Point Art Graphic by laurenejlevinson · Creative ...

    Wordcloud Antipodal Point Art Graphic by laurenejlevinson · Creative ...

    Make Your Point: ANTIPODAL

    Make Your Point: ANTIPODAL

    (Left) A 2-antipodally symmetric map where the antipodal mapping is ...

    (Left) A 2-antipodally symmetric map where the antipodal mapping is ...

    (Left) A 2-antipodally symmetric map where the antipodal mapping is ...

    (Left) A 2-antipodally symmetric map where the antipodal mapping is ...

    (Left) Antipodal pair of vertices of med(G) in case (a). (Right ...

    (Left) Antipodal pair of vertices of med(G) in case (a). (Right ...

    Solved EXERCISES 1. Constructing an antipodal point. Suppose | Chegg.com

    Solved EXERCISES 1. Constructing an antipodal point. Suppose | Chegg.com

    Search Results

    antipodal point

    Daftar Isi

    Antipode Finder - Find the opposite side of the world - Geodatos

    Find out the opposite side of the world from: What is an antipode? An antipode, or antipodal point, is the point on the planet that is located diametrically opposite to a specific geographic location, and therefore, is the farthest point in the world from that location.

    Antipodal point - Wikipedia

    Given any point on a sphere, its antipodal point is the unique point at greatest distance, whether measured intrinsically (great-circle distance on the surface of the sphere) or extrinsically (chordal distance through the sphere's interior).

    Antipodes Map - Tunnel to the other side of the world

    Antipodes map helps you find the other side of the world, the antipodes of any place on Earth. This map shows diametrically opposite location named antipode or antipodal point.

    Antipodes - Wikipedia

    In geography, the antipode (/ ˈæntɪˌpoʊd, ænˈtɪpədi /) of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points antipodal (/ ænˈtɪpədəl /) to each other are situated such that a straight line connecting the two would pass through Earth's center.

    Antipode Calculator

    May 30, 2024 · Here you will learn a little bit of history, what the antipode of a point is, and how to find the antipode using a tiny bit of math. What is an antipode? The antipode is the diametrically opposite point of a given location on a sphere .

    Antipode Finder - February 18, 2025

    Oct 21, 2024 · An antipode is the point on the Earth’s surface that is diametrically opposite to a given location. In other words, if you could drill a hole straight through the center of the Earth from any point, where you would come out on the other side is the antipode of your starting location.

    Antipode Calculator | Geocaching Distance Between Two Points

    An antipode is a point on the Earth’s surface that is diametrically opposite to another given point. In other words, if you could dig a straight tunnel through the center of the Earth from one location, you would emerge at its antipodal point on the opposite side of the globe.

    Antipode Finder (Opposed Point on Earth) - Online Antipodal …

    Tool to find the point on the other side of the Earth (Antipodal Coordinates). Two points are said to the antipodes if they are diametrically opposite on a sphere.

    Antipodal Points -- from Wolfram MathWorld

    Feb 14, 2025 · Two points are antipodal (i.e., each is the antipode of the other) if they are diametrically opposite. Examples include endpoints of a line segment, or poles of a sphere.

    Here's How You Find a Point on the Opposite Side of the Earth

    Oct 24, 2019 · An antipode is a point on the opposite side of the Earth from another point; the place you'd end up if you were able to dig directly through the Earth. Unfortunately, if you try to dig to China from most places in the U.S., you would end up in the Indian Ocean as the Indian Ocean contains most of the antipodes for the United States.