<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2020000100033</article-id>
<article-id pub-id-type="doi">10.18273/revint.v38n1-2020003</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Can we detect Gaussian curvature by counting paths and measuring their length?]]></article-title>
<article-title xml:lang="es"><![CDATA[¿Podemos detectar la curvatura gaussiana contando caminos y midiendo sus longitudes?]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cano G.]]></surname>
<given-names><![CDATA[Leonardo A]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Carrillo]]></surname>
<given-names><![CDATA[Sergio A]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional de Colombia Facultad de Ciencias ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Sergio Arboleda Escuela de Ciencias Exactas e Ingeniería ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2020</year>
</pub-date>
<volume>38</volume>
<numero>1</numero>
<fpage>33</fpage>
<lpage>42</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2020000100033&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2020000100033&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2020000100033&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. The aim of this paper is to associate a measure for certain sets of paths in the Euclidean plane &#8477;2 with fixed starting and ending points. Then, working on parameterized surfaces with a specific Riemannian metric, we define and calculate the integral of the length over the set of paths obtained as the image of the initial paths in &#8477;2 under the given parameterization. Moreover, we prove that this integral is given by the average of the lengths of the external paths times the measure of the set of paths if, and only if, the surface has Gaussian curvature equal to zero. MSC2010: 53B99, 05A10, 33C10.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. El objetivo de este artículo es asociar una medida a ciertos conjuntos de caminos en el plano euclídeo &#8477;2 con puntos inicial y final fijos. Luego, trabajando en superficies parametrizadas con una métrica riemaniana específica, definimos y calculamos la integral de la longitud sobre el conjunto de caminos obtenidos como imagen bajo la parametrización dada de los caminos considerados inicialmente en &#8477;2. Además, demostramos que esta integral está dada por el promedio de las longitudes de los caminos externos multiplicada por la medida del conjunto de caminos si, y solo si, la superficie tiene curvatura gaussiana constante igual a cero.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Gaussian curvature]]></kwd>
<kwd lng="en"><![CDATA[continuous binomial coefficients.]]></kwd>
<kwd lng="es"><![CDATA[Curvatura gaussiana]]></kwd>
<kwd lng="es"><![CDATA[coeficientes binomiales continuos.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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