<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03767784</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-17T23:22:15+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">On Graphs, Geometry, Motion and Turbulences in Leonardo's Virgin and Child with Saint Anne</title>
            <author role="aut">
              <persName>
                <forename type="first">Didier</forename>
                <surname>El Baz</surname>
              </persName>
              <email type="md5">69018d8e5c7e7e5f8ec67ebd0f862044</email>
              <email type="domain">laas.fr</email>
              <idno type="idhal" notation="string">didier-el-baz</idno>
              <idno type="idhal" notation="numeric">3899</idno>
              <idno type="halauthorid" notation="string">14943-3899</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0427-0692</idno>
              <idno type="IDREF">https://www.idref.fr/05072620X</idno>
              <affiliation ref="#struct-388967"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Didier</forename>
                <surname>EL BAZ</surname>
              </persName>
              <email type="md5">69018d8e5c7e7e5f8ec67ebd0f862044</email>
              <email type="domain">laas.fr</email>
            </editor>
            <funder ref="#projanr-49786"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2022-09-02 11:30:39</date>
              <date type="whenWritten">2022-09-02</date>
              <date type="whenModified">2025-10-22 18:04:09</date>
              <date type="whenReleased">2022-09-12 08:37:08</date>
              <date type="whenProduced">2022-09-02</date>
              <date type="whenEndEmbargoed">2022-09-02</date>
              <ref type="file" target="https://laas.hal.science/hal-03767784v1/document">
                <date notBefore="2022-09-02"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://laas.hal.science/hal-03767784v1/file/elbazHAL.pdf" id="file-3767784-3294527">
                <date notBefore="2022-09-02"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="314810">
                <persName>
                  <forename>Didier</forename>
                  <surname>EL BAZ</surname>
                </persName>
                <email type="md5">69018d8e5c7e7e5f8ec67ebd0f862044</email>
                <email type="domain">laas.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03767784</idno>
            <idno type="halUri">https://laas.hal.science/hal-03767784</idno>
            <idno type="halBibtex">elbaz:hal-03767784</idno>
            <idno type="halRefHtml">2022</idno>
            <idno type="halRef">2022</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3767784-3294527"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="SHS">Sciences de l'Homme et de la Société</idno>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSA-TOULOUSE">Institut National des Sciences Appliquées de Toulouse</idno>
            <idno type="stamp" n="LAAS">Laboratoire d'analyse et d'architecture des systèmes</idno>
            <idno type="stamp" n="LAAS-SARA" corresp="LAAS-RISC">Équipe Services et Architectures pour Réseaux Avancés</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</idno>
            <idno type="stamp" n="LAAS-RESEAUX-ET-COMMUNICATIONS" corresp="LAAS">LAAS-Réseaux et Communications</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="LAAS-RISC" corresp="LAAS">Réseaux, Informatique, Systèmes de Confiance</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="CIMI-TOULOUSE">Centre International de Mathématiques et d'Informatique de Toulouse</idno>
            <idno type="stamp" n="TOULOUSE-INP">Toulouse - INP</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-INP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="TEST7-HALCNRS">test 7 du portail hal cnrs</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">Cet article concerne aussi le domaine de l'histoire de l'art</note>
            <note type="audience" n="2">International</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">On Graphs, Geometry, Motion and Turbulences in Leonardo's Virgin and Child with Saint Anne</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Didier</forename>
                    <surname>El Baz</surname>
                  </persName>
                  <email type="md5">69018d8e5c7e7e5f8ec67ebd0f862044</email>
                  <email type="domain">laas.fr</email>
                  <idno type="idhal" notation="string">didier-el-baz</idno>
                  <idno type="idhal" notation="numeric">3899</idno>
                  <idno type="halauthorid" notation="string">14943-3899</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0427-0692</idno>
                  <idno type="IDREF">https://www.idref.fr/05072620X</idno>
                  <affiliation ref="#struct-388967"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">Rapport LAAS n° 22304</idno>
                <imprint/>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Virgin and Child with Saint Anne</term>
                <term xml:lang="en">Turbulences</term>
                <term xml:lang="en">Celestial mechanics</term>
                <term xml:lang="en">Conic sections</term>
                <term xml:lang="en">Geometry</term>
                <term xml:lang="en">Graphs</term>
                <term xml:lang="en">Renaissance painting</term>
                <term xml:lang="en">Leonardo da Vinci</term>
                <term xml:lang="en">Saint Anne Trinitarian</term>
              </keywords>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halDomain" n="sdu">Sciences of the Universe [physics]</classCode>
              <classCode scheme="halDomain" n="shs.art">Humanities and Social Sciences/Art and art history</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this study, we focus on the composition of the Virgin and Child with Saint Anne by Leonardo da Vinci. The composition is considered first from the point of view of graphs and the genealogy of the Christ is analyzed accordingly. Then, the composition of the masterpiece is studied from the perspective of scientific knowledges in geometry. The many ellipses or part of ellipses in the composition are detailed. This study permits us to revisit the movement of the figures. Knowledges on celestial mechanics at the time of Leonardo are presented and themes like destiny and resurrection are examined consequently. Finally, the representation of instabilities and turbulences is considered in the painting and the renewal of forms is examined.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-388967" status="OLD">
          <orgName>Équipe Services et Architectures pour Réseaux Avancés</orgName>
          <orgName type="acronym">LAAS-SARA</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.laas.fr/public/fr/sara</ref>
          </desc>
          <listRelation>
            <relation active="#struct-459" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="indirect"/>
            <relation active="#struct-217752" type="indirect"/>
            <relation name="UPR8001" active="#struct-441569" type="indirect"/>
            <relation active="#struct-448187" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-459" status="OLD">
          <idno type="IdRef">199278792</idno>
          <idno type="ISNI">0000 0001 2188 216X </idno>
          <idno type="RNSR">199517454Y</idno>
          <idno type="ROR">https://ror.org/03vcm6439</idno>
          <orgName>Laboratoire d'analyse et d'architecture des systèmes</orgName>
          <orgName type="acronym">LAAS</orgName>
          <date type="start">1968-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>7 Av du colonel Roche 31077 TOULOUSE CEDEX 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.laas.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UPR8001" active="#struct-441569" type="direct"/>
            <relation active="#struct-448187" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116255" status="VALID">
          <idno type="IdRef">026388766</idno>
          <idno type="ISNI">0000 0001 2286 8343</idno>
          <idno type="ROR">https://ror.org/01h8pf755</idno>
          <idno type="Wikidata">Q858979</idno>
          <orgName>Institut National des Sciences Appliquées - Toulouse</orgName>
          <orgName type="acronym">INSA Toulouse</orgName>
          <date type="start">1963-10-21</date>
          <desc>
            <address>
              <addrLine>135, avenue de Rangueil - 31077 Toulouse cedex 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-toulouse.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-217752" status="OLD">
          <idno type="IdRef">026404672</idno>
          <idno type="ISNI">0000000121617331</idno>
          <idno type="ROR">https://ror.org/02v6kpv12</idno>
          <idno type="Wikidata">Q1273188</idno>
          <orgName>Université Toulouse III - Paul Sabatier</orgName>
          <orgName type="acronym">UT3</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne - 31062 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-448187" status="VALID">
          <idno type="IdRef">026388820</idno>
          <idno type="ISNI">0000000121766169</idno>
          <idno type="ROR">https://ror.org/033p9g875</idno>
          <orgName>Institut National Polytechnique (Toulouse)</orgName>
          <orgName type="acronym">Toulouse INP</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.inp-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-49786" status="VALID">
          <idno type="anr">ANR-11-LABX-0040</idno>
          <orgName>CIMI</orgName>
          <desc>Centre International de Mathématiques et d'Informatique (de Toulouse)</desc>
          <date type="start">2011</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>