<p>Two copies of a triangle <i>T</i> of the positive homothetic ratio <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2024_615_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(a_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>a</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2024_615_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(a_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>a</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> are non-blocking, provided that <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2024_615_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\(a_1+a_2\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Any collection of pairwise non-blocking homothetic copies of <i>T</i>, whose total area does not exceed 5/9 the area of <i>T</i>, can be packed into <i>T</i>.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Packing a triangle by collections of its non-blocking homothetic copies

  • Janusz Januszewski,
  • Łukasz Zielonka

摘要

Two copies of a triangle T of the positive homothetic ratio \(a_1\) a 1 and \(a_2\) a 2 are non-blocking, provided that \(a_1+a_2\le 1\) a 1 + a 2 1 . Any collection of pairwise non-blocking homothetic copies of T, whose total area does not exceed 5/9 the area of T, can be packed into T.