Construction of a Perron tree by dividing a triangle into <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2^{n}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle 2^{n}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8226f30650ee4fe4e640c6d2798127e80e9c160d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.381ex; height:2.343ex;" alt="{\displaystyle 2^{n}}"></span> subtriangles and recombining them with partial overlaps. Cases <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=1}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>n</mi><mo>=</mo><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle n=1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9ec7e1edc2e6d98f5aec2a39ae5f1c99d1e1425" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=1}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=3}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>n</mi><mo>=</mo><mn>3</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle n=3}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c5a5a42ced00df920fad4ab2d4acdb960a4105b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=3}"></span> are illustrated.
<ul><li><a href="//commons.wikimedia.org/wiki/File:Perrontree2.jpg" title="File:Perrontree2.jpg">Perrontree2.jpg</a>: <a href="//commons.wikimedia.org/w/index.php?title=User:Jazzam&amp;action=edit&amp;redlink=1" class="new" title="User:Jazzam (page does not exist)">Jazzam</a></li>
<li>derivative work: <a href="//commons.wikimedia.org/w/index.php?title=User:Mikhail_Ryazanov&amp;action=edit&amp;redlink=1" class="new" title="User:Mikhail Ryazanov (page does not exist)">Mikhail Ryazanov</a></li></ul>
2013-01-30 04:26
This file was derived from: <a href="//commons.wikimedia.org/wiki/File:Perrontree2.jpg" title="File:Perrontree2.jpg">Perrontree2.jpg</a>: <a href="//commons.wikimedia.org/wiki/File:Perrontree2.jpg" class="image"><img alt="Perrontree2.jpg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Perrontree2.jpg/50px-Perrontree2.jpg" decoding="async" width="50" height="55" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Perrontree2.jpg/75px-Perrontree2.jpg 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Perrontree2.jpg/100px-Perrontree2.jpg 2x" data-file-width="1155" data-file-height="1270"></a><br>