Why are the hypergeometric functions called “hypergeometric”?












4












$begingroup$


I was wondering where the term "hypergeometric" for the hypergeometric function $_2F_1(a, b; c; z)$ comes from. Wikipedia says that the term was coined by J. Wallis, but I couldn't find any (mathematical) reason why these functions are anything like hyper-geometric.



Does anyone know where this comes from?






terminology special-functions







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    mathworld.wolfram.com/HypergeometricFunction.html
    $endgroup$
    – Karn Watcharasupat
    Apr 12 '18 at 8:42






  • 1




    $begingroup$
    see also math.stackexchange.com/q/295258/442
    $endgroup$
    – GEdgar
    Apr 12 '18 at 12:50










  • $begingroup$
    In Graham, Knuth, and Patashnik's Concrete Mathematics they have a comment when introducing the hypergeometric series on the etymology of the name in relation to the geometric series. I do not have the book in front of me right now. Maybe someone else can check.
    $endgroup$
    – KCd
    Apr 12 '18 at 13:21








  • 2




    $begingroup$
    On Page 206 (Second Edition) they write: "... is called hypergeometric series because it includes the geometric series as a very special case."
    $endgroup$
    – p4sch
    Apr 12 '18 at 16:14
















4












$begingroup$


I was wondering where the term "hypergeometric" for the hypergeometric function $_2F_1(a, b; c; z)$ comes from. Wikipedia says that the term was coined by J. Wallis, but I couldn't find any (mathematical) reason why these functions are anything like hyper-geometric.



Does anyone know where this comes from?






terminology special-functions







share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    mathworld.wolfram.com/HypergeometricFunction.html
    $endgroup$
    – Karn Watcharasupat
    Apr 12 '18 at 8:42






  • 1




    $begingroup$
    see also math.stackexchange.com/q/295258/442
    $endgroup$
    – GEdgar
    Apr 12 '18 at 12:50










  • $begingroup$
    In Graham, Knuth, and Patashnik's Concrete Mathematics they have a comment when introducing the hypergeometric series on the etymology of the name in relation to the geometric series. I do not have the book in front of me right now. Maybe someone else can check.
    $endgroup$
    – KCd
    Apr 12 '18 at 13:21








  • 2




    $begingroup$
    On Page 206 (Second Edition) they write: "... is called hypergeometric series because it includes the geometric series as a very special case."
    $endgroup$
    – p4sch
    Apr 12 '18 at 16:14














4












4








4


1



$begingroup$


I was wondering where the term "hypergeometric" for the hypergeometric function $_2F_1(a, b; c; z)$ comes from. Wikipedia says that the term was coined by J. Wallis, but I couldn't find any (mathematical) reason why these functions are anything like hyper-geometric.



Does anyone know where this comes from?






terminology special-functions







share|cite|improve this question











$endgroup$




I was wondering where the term "hypergeometric" for the hypergeometric function $_2F_1(a, b; c; z)$ comes from. Wikipedia says that the term was coined by J. Wallis, but I couldn't find any (mathematical) reason why these functions are anything like hyper-geometric.



Does anyone know where this comes from?






terminology special-functions




terminology special-functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Apr 12 '18 at 12:49









Jack D'Aurizio

291k33284666




291k33284666










asked Apr 12 '18 at 8:24









StevenSteven

2,0081733




2,0081733








  • 1




    $begingroup$
    mathworld.wolfram.com/HypergeometricFunction.html
    $endgroup$
    – Karn Watcharasupat
    Apr 12 '18 at 8:42






  • 1




    $begingroup$
    see also math.stackexchange.com/q/295258/442
    $endgroup$
    – GEdgar
    Apr 12 '18 at 12:50










  • $begingroup$
    In Graham, Knuth, and Patashnik's Concrete Mathematics they have a comment when introducing the hypergeometric series on the etymology of the name in relation to the geometric series. I do not have the book in front of me right now. Maybe someone else can check.
    $endgroup$
    – KCd
    Apr 12 '18 at 13:21








  • 2




    $begingroup$
    On Page 206 (Second Edition) they write: "... is called hypergeometric series because it includes the geometric series as a very special case."
    $endgroup$
    – p4sch
    Apr 12 '18 at 16:14














  • 1




    $begingroup$
    mathworld.wolfram.com/HypergeometricFunction.html
    $endgroup$
    – Karn Watcharasupat
    Apr 12 '18 at 8:42






  • 1




    $begingroup$
    see also math.stackexchange.com/q/295258/442
    $endgroup$
    – GEdgar
    Apr 12 '18 at 12:50










  • $begingroup$
    In Graham, Knuth, and Patashnik's Concrete Mathematics they have a comment when introducing the hypergeometric series on the etymology of the name in relation to the geometric series. I do not have the book in front of me right now. Maybe someone else can check.
    $endgroup$
    – KCd
    Apr 12 '18 at 13:21








  • 2




    $begingroup$
    On Page 206 (Second Edition) they write: "... is called hypergeometric series because it includes the geometric series as a very special case."
    $endgroup$
    – p4sch
    Apr 12 '18 at 16:14








1




1




$begingroup$
mathworld.wolfram.com/HypergeometricFunction.html
$endgroup$
– Karn Watcharasupat
Apr 12 '18 at 8:42




$begingroup$
mathworld.wolfram.com/HypergeometricFunction.html
$endgroup$
– Karn Watcharasupat
Apr 12 '18 at 8:42




1




1




$begingroup$
see also math.stackexchange.com/q/295258/442
$endgroup$
– GEdgar
Apr 12 '18 at 12:50




$begingroup$
see also math.stackexchange.com/q/295258/442
$endgroup$
– GEdgar
Apr 12 '18 at 12:50












$begingroup$
In Graham, Knuth, and Patashnik's Concrete Mathematics they have a comment when introducing the hypergeometric series on the etymology of the name in relation to the geometric series. I do not have the book in front of me right now. Maybe someone else can check.
$endgroup$
– KCd
Apr 12 '18 at 13:21






$begingroup$
In Graham, Knuth, and Patashnik's Concrete Mathematics they have a comment when introducing the hypergeometric series on the etymology of the name in relation to the geometric series. I do not have the book in front of me right now. Maybe someone else can check.
$endgroup$
– KCd
Apr 12 '18 at 13:21






2




2




$begingroup$
On Page 206 (Second Edition) they write: "... is called hypergeometric series because it includes the geometric series as a very special case."
$endgroup$
– p4sch
Apr 12 '18 at 16:14




$begingroup$
On Page 206 (Second Edition) they write: "... is called hypergeometric series because it includes the geometric series as a very special case."
$endgroup$
– p4sch
Apr 12 '18 at 16:14










2 Answers
2






active

oldest

votes


















1












$begingroup$

The probability mass function of the hypergeometric distribution (related to the binomial distribution and the geometric distribution) is given by a ratio of products of binomial coefficients, just like the coefficients of the MacLaurin series of a hypergeometric function. This is my bet on the reason for picking the adjective hypergeometric for describing the $phantom{}_p F_q$ functions.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    It would be nice to know if the downvote is due to the fact that I am wrong, or something else.
    $endgroup$
    – Jack D'Aurizio
    Apr 12 '18 at 12:48










  • $begingroup$
    So the etymology is "geometric sequence" $to$ "geometric distribution" $to$ "hypergeometric distribution" $to$ "hypergeometric function"? I found it slightly disorienting that the answer started in the middle of that chain rather than at one of the ends -- but not so disorienting that I'd downvote.
    $endgroup$
    – Henning Makholm
    Apr 12 '18 at 12:59












  • $begingroup$
    @HenningMakholm: I am not sure that is the historical chain of events, but is sounds likely, doesn't it?
    $endgroup$
    – Jack D'Aurizio
    Apr 12 '18 at 13:16



















1












$begingroup$

This is the reason I believe: a geometric sequence is defined as a sequence where the ratio of two consecutive numbers is a constant
$$
frac{a_{n+1}}{a_n} = x,.
$$
You can generalize this notion by assuming the ratio to be any rational function of $n$ instead
$$
frac{a_{n+1}}{a_n} = frac{P(n)}{Q(n)},.
$$
Any such rational function can be factorized and rewritten as
$$
frac{P(n)}{Q(n)} = frac{(n+a_1)cdots(n+a_p)}{(n+b_1)cdots(n+b_q)(n+1)}x,.
$$
If $Q(n)$ doesn't have an $n+1$ factor we can always say, for example, $a_p=1$, so we don't lose generality. With this parametrization it's easy to check that
$$
sum_{n=0}^infty a_n = {}_pF_q(a_1,ldots, a_p;b_1,ldots, b_q;x),.
$$
Hypergeometric then suggests that this is a generalization of the geometric sequence. More precisely
$$
frac{1}{1-x} = {}_1F_0(1;;x),.
$$



Source: http://mathworld.wolfram.com/HypergeometricFunction.html






share|cite|improve this answer









$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2733600%2fwhy-are-the-hypergeometric-functions-called-hypergeometric%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    The probability mass function of the hypergeometric distribution (related to the binomial distribution and the geometric distribution) is given by a ratio of products of binomial coefficients, just like the coefficients of the MacLaurin series of a hypergeometric function. This is my bet on the reason for picking the adjective hypergeometric for describing the $phantom{}_p F_q$ functions.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      It would be nice to know if the downvote is due to the fact that I am wrong, or something else.
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 12:48










    • $begingroup$
      So the etymology is "geometric sequence" $to$ "geometric distribution" $to$ "hypergeometric distribution" $to$ "hypergeometric function"? I found it slightly disorienting that the answer started in the middle of that chain rather than at one of the ends -- but not so disorienting that I'd downvote.
      $endgroup$
      – Henning Makholm
      Apr 12 '18 at 12:59












    • $begingroup$
      @HenningMakholm: I am not sure that is the historical chain of events, but is sounds likely, doesn't it?
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 13:16
















    1












    $begingroup$

    The probability mass function of the hypergeometric distribution (related to the binomial distribution and the geometric distribution) is given by a ratio of products of binomial coefficients, just like the coefficients of the MacLaurin series of a hypergeometric function. This is my bet on the reason for picking the adjective hypergeometric for describing the $phantom{}_p F_q$ functions.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      It would be nice to know if the downvote is due to the fact that I am wrong, or something else.
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 12:48










    • $begingroup$
      So the etymology is "geometric sequence" $to$ "geometric distribution" $to$ "hypergeometric distribution" $to$ "hypergeometric function"? I found it slightly disorienting that the answer started in the middle of that chain rather than at one of the ends -- but not so disorienting that I'd downvote.
      $endgroup$
      – Henning Makholm
      Apr 12 '18 at 12:59












    • $begingroup$
      @HenningMakholm: I am not sure that is the historical chain of events, but is sounds likely, doesn't it?
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 13:16














    1












    1








    1





    $begingroup$

    The probability mass function of the hypergeometric distribution (related to the binomial distribution and the geometric distribution) is given by a ratio of products of binomial coefficients, just like the coefficients of the MacLaurin series of a hypergeometric function. This is my bet on the reason for picking the adjective hypergeometric for describing the $phantom{}_p F_q$ functions.






    share|cite|improve this answer









    $endgroup$



    The probability mass function of the hypergeometric distribution (related to the binomial distribution and the geometric distribution) is given by a ratio of products of binomial coefficients, just like the coefficients of the MacLaurin series of a hypergeometric function. This is my bet on the reason for picking the adjective hypergeometric for describing the $phantom{}_p F_q$ functions.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Apr 12 '18 at 10:25









    Jack D'AurizioJack D'Aurizio

    291k33284666




    291k33284666












    • $begingroup$
      It would be nice to know if the downvote is due to the fact that I am wrong, or something else.
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 12:48










    • $begingroup$
      So the etymology is "geometric sequence" $to$ "geometric distribution" $to$ "hypergeometric distribution" $to$ "hypergeometric function"? I found it slightly disorienting that the answer started in the middle of that chain rather than at one of the ends -- but not so disorienting that I'd downvote.
      $endgroup$
      – Henning Makholm
      Apr 12 '18 at 12:59












    • $begingroup$
      @HenningMakholm: I am not sure that is the historical chain of events, but is sounds likely, doesn't it?
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 13:16


















    • $begingroup$
      It would be nice to know if the downvote is due to the fact that I am wrong, or something else.
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 12:48










    • $begingroup$
      So the etymology is "geometric sequence" $to$ "geometric distribution" $to$ "hypergeometric distribution" $to$ "hypergeometric function"? I found it slightly disorienting that the answer started in the middle of that chain rather than at one of the ends -- but not so disorienting that I'd downvote.
      $endgroup$
      – Henning Makholm
      Apr 12 '18 at 12:59












    • $begingroup$
      @HenningMakholm: I am not sure that is the historical chain of events, but is sounds likely, doesn't it?
      $endgroup$
      – Jack D'Aurizio
      Apr 12 '18 at 13:16
















    $begingroup$
    It would be nice to know if the downvote is due to the fact that I am wrong, or something else.
    $endgroup$
    – Jack D'Aurizio
    Apr 12 '18 at 12:48




    $begingroup$
    It would be nice to know if the downvote is due to the fact that I am wrong, or something else.
    $endgroup$
    – Jack D'Aurizio
    Apr 12 '18 at 12:48












    $begingroup$
    So the etymology is "geometric sequence" $to$ "geometric distribution" $to$ "hypergeometric distribution" $to$ "hypergeometric function"? I found it slightly disorienting that the answer started in the middle of that chain rather than at one of the ends -- but not so disorienting that I'd downvote.
    $endgroup$
    – Henning Makholm
    Apr 12 '18 at 12:59






    $begingroup$
    So the etymology is "geometric sequence" $to$ "geometric distribution" $to$ "hypergeometric distribution" $to$ "hypergeometric function"? I found it slightly disorienting that the answer started in the middle of that chain rather than at one of the ends -- but not so disorienting that I'd downvote.
    $endgroup$
    – Henning Makholm
    Apr 12 '18 at 12:59














    $begingroup$
    @HenningMakholm: I am not sure that is the historical chain of events, but is sounds likely, doesn't it?
    $endgroup$
    – Jack D'Aurizio
    Apr 12 '18 at 13:16




    $begingroup$
    @HenningMakholm: I am not sure that is the historical chain of events, but is sounds likely, doesn't it?
    $endgroup$
    – Jack D'Aurizio
    Apr 12 '18 at 13:16











    1












    $begingroup$

    This is the reason I believe: a geometric sequence is defined as a sequence where the ratio of two consecutive numbers is a constant
    $$
    frac{a_{n+1}}{a_n} = x,.
    $$
    You can generalize this notion by assuming the ratio to be any rational function of $n$ instead
    $$
    frac{a_{n+1}}{a_n} = frac{P(n)}{Q(n)},.
    $$
    Any such rational function can be factorized and rewritten as
    $$
    frac{P(n)}{Q(n)} = frac{(n+a_1)cdots(n+a_p)}{(n+b_1)cdots(n+b_q)(n+1)}x,.
    $$
    If $Q(n)$ doesn't have an $n+1$ factor we can always say, for example, $a_p=1$, so we don't lose generality. With this parametrization it's easy to check that
    $$
    sum_{n=0}^infty a_n = {}_pF_q(a_1,ldots, a_p;b_1,ldots, b_q;x),.
    $$
    Hypergeometric then suggests that this is a generalization of the geometric sequence. More precisely
    $$
    frac{1}{1-x} = {}_1F_0(1;;x),.
    $$



    Source: http://mathworld.wolfram.com/HypergeometricFunction.html






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      This is the reason I believe: a geometric sequence is defined as a sequence where the ratio of two consecutive numbers is a constant
      $$
      frac{a_{n+1}}{a_n} = x,.
      $$
      You can generalize this notion by assuming the ratio to be any rational function of $n$ instead
      $$
      frac{a_{n+1}}{a_n} = frac{P(n)}{Q(n)},.
      $$
      Any such rational function can be factorized and rewritten as
      $$
      frac{P(n)}{Q(n)} = frac{(n+a_1)cdots(n+a_p)}{(n+b_1)cdots(n+b_q)(n+1)}x,.
      $$
      If $Q(n)$ doesn't have an $n+1$ factor we can always say, for example, $a_p=1$, so we don't lose generality. With this parametrization it's easy to check that
      $$
      sum_{n=0}^infty a_n = {}_pF_q(a_1,ldots, a_p;b_1,ldots, b_q;x),.
      $$
      Hypergeometric then suggests that this is a generalization of the geometric sequence. More precisely
      $$
      frac{1}{1-x} = {}_1F_0(1;;x),.
      $$



      Source: http://mathworld.wolfram.com/HypergeometricFunction.html






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        This is the reason I believe: a geometric sequence is defined as a sequence where the ratio of two consecutive numbers is a constant
        $$
        frac{a_{n+1}}{a_n} = x,.
        $$
        You can generalize this notion by assuming the ratio to be any rational function of $n$ instead
        $$
        frac{a_{n+1}}{a_n} = frac{P(n)}{Q(n)},.
        $$
        Any such rational function can be factorized and rewritten as
        $$
        frac{P(n)}{Q(n)} = frac{(n+a_1)cdots(n+a_p)}{(n+b_1)cdots(n+b_q)(n+1)}x,.
        $$
        If $Q(n)$ doesn't have an $n+1$ factor we can always say, for example, $a_p=1$, so we don't lose generality. With this parametrization it's easy to check that
        $$
        sum_{n=0}^infty a_n = {}_pF_q(a_1,ldots, a_p;b_1,ldots, b_q;x),.
        $$
        Hypergeometric then suggests that this is a generalization of the geometric sequence. More precisely
        $$
        frac{1}{1-x} = {}_1F_0(1;;x),.
        $$



        Source: http://mathworld.wolfram.com/HypergeometricFunction.html






        share|cite|improve this answer









        $endgroup$



        This is the reason I believe: a geometric sequence is defined as a sequence where the ratio of two consecutive numbers is a constant
        $$
        frac{a_{n+1}}{a_n} = x,.
        $$
        You can generalize this notion by assuming the ratio to be any rational function of $n$ instead
        $$
        frac{a_{n+1}}{a_n} = frac{P(n)}{Q(n)},.
        $$
        Any such rational function can be factorized and rewritten as
        $$
        frac{P(n)}{Q(n)} = frac{(n+a_1)cdots(n+a_p)}{(n+b_1)cdots(n+b_q)(n+1)}x,.
        $$
        If $Q(n)$ doesn't have an $n+1$ factor we can always say, for example, $a_p=1$, so we don't lose generality. With this parametrization it's easy to check that
        $$
        sum_{n=0}^infty a_n = {}_pF_q(a_1,ldots, a_p;b_1,ldots, b_q;x),.
        $$
        Hypergeometric then suggests that this is a generalization of the geometric sequence. More precisely
        $$
        frac{1}{1-x} = {}_1F_0(1;;x),.
        $$



        Source: http://mathworld.wolfram.com/HypergeometricFunction.html







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 15 '18 at 22:31









        Mane.andreaMane.andrea

        1265




        1265






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2733600%2fwhy-are-the-hypergeometric-functions-called-hypergeometric%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Plaza Victoria

            Image
            Plaza Victoria Plaza Victoria en 2017 Otros nombres Plaza de La Victoria Localización El Almendral, Valparaíso, Chile Vías adyacentes Chacabuco, Molina, Plaza Victoria y Edwards Creación 1841 Metro Bellavista Ubicación 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 Coordenadas: 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 [editar datos en Wikidata] La Plaza Victoria , también llamada Plaza de la Victoria , [ 1 ] ​ es una plaza ubicada en el sector El Almendral del plan de la ciudad de Valparaíso, Chile, de importancia patrimonial, que incluye valiosas estatuas y especies vegetales. [ 2 ] ​ La plaza se creó como tal en la primera mitad del siglo XIX, tomando previamente los nombres de Plaza Nueva y Plaza de Orrego . Si bien desde sus inicios tuvo relevancia histórica, no fue sino a partir de fines de los años 1860 cuando comenzó a cobrar mayor importancia y se convirtió en uno de los principales centros sociales de l
            Read more

            Puebla de Zaragoza

            Image
            Para otros usos de este término, véase Puebla (desambiguación). Heroica Puebla de Zaragoza Localidad De arriba a abajo de izquierda a derecha: Estrella de Puebla, Volcán Popocatépetl, Catedral de Puebla, Monumento a Ignacio Zaragoza, Estadio Cuauhtémoc, Angelópolis y Vista panorámica de la ciudad. Escudo Otros nombres: El relicario de América/ La ciudad de los Ángeles/ La Angelópolis Lema: Muy noble y muy leal ciudad de Puebla de los Ángeles Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en México Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en Puebla Mapa interactivo Coordenadas 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Coordenadas: 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Idioma oficial Español Entidad Localidad  • País   México  • Estado Puebla  • Municipio Puebla Presidente municipal Claudia Rivera Vivanc
            Read more

            Musa

            Image
            Para el género de plantas, véase Musa (planta). Apolo y la Nueve Musas En la mitología griega, las musas (en griego antiguo μοῦσαι « mousai» ) son, según los escritores más antiguos, las divinidades inspiradoras de las Artes: cada una de ellas está relacionada con ramas artísticas y del conocimiento. Son hijas de Zeus y de Mnemósine, compañeras del séquito de Apolo, dios olímpico de la música y patrón de las bellas artes, quien tuvo romances con cada una de ellas, dejando descendientes. Bajaban a la tierra a susurrar ideas e inspirar a aquellos mortales que las invocaran. En la época más arcaica eran las ninfas inspiradoras de las fuentes, en las cuales eran adoradas. Finalmente, alrededor de los siglos VIII-VII a. C. [ 1 ] ​ prevaleció en todo el territorio de la Hélade la adoración de las nueve Musas, que son Calíope, Clío, Erato, Euterpe, Melpómene, Polimnia, Talía, Terpsícore y Urania. El culto a las musas era originalmente de Tracia y Beocia, y fueron de vital impo
            Read more