Problem 58244. Easy Sequences 113: Almost Golden Integer Rectangles 2

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Golden_rectangle\"><w:r><w:rPr><w:b/></w:rPr><w:t>golden rectangle</w:t></w:r></w:hyperlink><w:r><w:t> is a rectangle whose side lengths are in the golden ratio, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\phi/1</w:t></w:r></w:customXml><w:r><w:t>, where: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\phi=\\frac^{\\sqrt{5}+1}_2=1.61803398...</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                                                                       </w:t></w:r><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"128\"/><w:attr w:name=\"width\" w:val=\"204\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The ancient Greeks consider the golden rectangle as the most aesthetically pleasing rectangular shape. Unfortunately for the ancients this ratio cannot be achieved if the sides are rational numbers let alone integers.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>We define </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{P}(A)</w:t></w:r></w:customXml><w:r><w:t> as a function that calculates the perimeter of the rectangle with integer sides with area equal to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A</w:t></w:r></w:customXml><w:r><w:t>, and in which the side ratio is as close as possible to the golden ratio, that is the absolute value, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>|\\frac^b_a-\\phi|</w:t></w:r></w:customXml><w:r><w:t>, is minimized.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A=20000</w:t></w:r></w:customXml><w:r><w:t>, the correct dimensions should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[125,\\ 160]</w:t></w:r></w:customXml><w:r><w:t>, since the ratio </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\frac^{160}_{125}=1.28</w:t></w:r></w:customXml><w:r><w:t> is the closest we can get to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\phi</w:t></w:r></w:customXml><w:r><w:t> for rectangle with area of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>20000</w:t></w:r></w:customXml><w:r><w:t> (see below code). Therefore, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>\\text{P}(20000)=2\\times(125+160)=570</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[>>  A = 20000; phi = (sqrt(5)+1)/2; a = Inf;\n>>  for i = 1:A\n      if mod(A,i) == 0\n         j = A / i;\n         r = max(j/i,i/j);\n         if abs(r-phi) < a\n            ds = [i j];\n            a = abs(r-phi);\n         end\n      end\n    end\n>> ds\nds =\n    125 160]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>In this problem, </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>we are asked to evaluate the following summation:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>                        </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\sum_{a=1}^A \\ \\text{P}(a)</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>that is, the sum of perimeter of all almost golden integer rectangles with areas from </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> to </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>A=25</w:t></w:r></w:customXml><w:r><w:t>, summation output should be </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>s = 464</w:t></w:r></w:customXml><w:r><w:t>:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>        </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>s=\\sum_{a=1}^{25} \\ \\text{P}(a) = \\text{P}(1) + \\text{P}(2)+ \\text{P}(3)+ \\text{P}(4)+ \\text{P}(5)+ \\text{P}(6)+ \\text{P}(7)+ \\text{P}(8)+ \\text{P}(9)+ \\text{P}(10)+ \\text{P}(11)+ \\text{P}(12)+ \\text{P}(13)\\\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ + \\text{P}(14)+ \\text{P}(15)+ \\text{P}(16)+ \\text{P}(17)+ \\text{P}(18)+ \\text{P}(19)+ \\text{P}(20)+ \\text{P}(21)+ \\text{P}(22)+ \\text{P}(23)+ \\text{P}(24)+ \\text{P}(25) 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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 939.067px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 469.533px; transform-origin: 407px 469.533px; vertical-align: baseline; "><div style="block-size: 31px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 15.5px; text-align: left; transform-origin: 384px 15.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.5px 8px; transform-origin: 6.5px 8px; unicode-bidi: normal; "><span style="">A </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Golden_rectangle"><span style=""><span style="font-weight: 700; ">golden rectangle</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; "><span style=""> is a rectangle whose side lengths are in the golden ratio, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 28px; height: 18.5px;" width="28" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; "><span style="">, where: </span></span><span style="vertical-align:-10px"><img src="data:image/png;base64,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" style="width: 159px; height: 31px;" width="159" height="31"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">.</span></span></div><div style="block-size: 133.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 66.75px; text-align: left; transform-origin: 384px 66.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 142px 8px; transform-origin: 142px 8px; unicode-bidi: normal; "><span style="">                                                                       </span></span><img class="imageNode" style="vertical-align: baseline;width: 204px;height: 128px" 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" data-image-state="image-loaded" width="204" height="128"></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; "><span style="">The ancient Greeks consider the golden rectangle as the most aesthetically pleasing rectangular shape. Unfortunately for the ancients this ratio cannot be achieved if the sides are rational numbers let alone integers.</span></span></div><div style="block-size: 50px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25px; text-align: left; transform-origin: 384px 25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 34px 8px; transform-origin: 34px 8px; unicode-bidi: normal; "><span style="">We define </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 33.5px; height: 18.5px;" width="33.5" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 302px 8px; transform-origin: 302px 8px; unicode-bidi: normal; "><span style=""> as a function that calculates the perimeter of the rectangle with integer sides with area equal to </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">A</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 24.325px 8px; transform-origin: 24.325px 8px; unicode-bidi: normal; "><span style="">, and in which the side ratio is as close as possible to the golden ratio, that is the absolute value, </span></span><span style="vertical-align:-10px"><img src="data:image/png;base64,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" style="width: 47.5px; height: 29px;" width="47.5" height="29"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 43.5px 8px; transform-origin: 43.5px 8px; unicode-bidi: normal; "><span style="">, is minimized.</span></span></div><div style="block-size: 50px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25px; text-align: left; transform-origin: 384px 25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; "><span style="">For example, if </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 70px; height: 18px;" width="70" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110.5px 8px; transform-origin: 110.5px 8px; unicode-bidi: normal; "><span style="">, the correct dimensions should be </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIsAAAAlCAYAAAByDxphAAAF6klEQVR4Xu2cycseRRDGkz/A/SYKQeNBFBSM8eACBlzQi6Cg4lFxBQ8iruQgLmgiCh7cUMhNRb1piArmYAiKIgqKBxfEgyf3f0CfH0xB0fRSM/M637x5p6H48s1093RXPf1UdXV/2b5tKYsGghrYHqy3VFs0sG0BywKCsAZqYHmg0MtRPT8S/sJSca4a6G3fGlj+1Sy/kPyezPaAfn9zrhpYxhXWwKFMzd169rRkX66XFlguXVgkrPxjoSIA+ngrwHKePvp1Dw2eobqndvW/yzBaqatT9OLswsvj9fxiyaM9xrHqqszr7x7zSb+PHq+S7OhevKefByuD9HrsGy5MDpabNJEnJLgw/t0q16jCC5Izk4of6Pe7JT81OsD3PlOps1XsiNHul9wlOV/SZ+GwAG6V3N7p5UH9fKehC6/3Lztw8ezhrm0aTuRUNhlYUqO/FQDLk6rzSMXQf+rdroqSUOr3kpMKfQC4q1toXfF7xvR4BxLrug9YYJJ3O5BEF8yL3fee0k/Ponfo95cl9HOLpAWYScCC0X/pNMPgKC2wXKI6n0hekjzbAQJFXyGBmYxpYKgLCwaFVVh9FwUUsWJMZLtjwZwr+UbymASgU6JggQne6Npg+OcC8zJA/FjQAwDAjaVAyk1gErD4D7OLorTA8rnqILiatKSMUVL2H2oI2LYyJsmiRg+9e4yAxRYP/UWZwOupBAYPwNY4ZgkWo9oaI3gXdacU+EpiFVMC7z6V9IkJSgZe5fM+YPFGb7leP0ZjFZ5dK8kFvsROsA6lxS6zBAt0fXoGAF4RfqXlwPKDKvugGCWT/wFUcwBOH7BYzBExqNcRzGyuDl2UNgMwMHEdoNlZWRGzBEtkBXuwpDsaT625vnBNeyWtgC4yjqF1omCBVX5zHzGjw77HSX6tgMBcPgvl5AYIiFsoNVCtLVgMEKXAzfIJ50gBl0tuTJQV9ftDwdBqFwWLdyXM9VXJQx0T2Dd4vl/iXTFg+qqr0AcsJXdFV2sLFqNmcgzZ9HNiLcCDT/agibZtGX7I+yhYcJ1+zLAiibd/JKdJ/M7QxxyeefuAJefSbX5rCRYL+PC1fbfF3kWhxLMkW+GOomDxcUfOkOgCI1psYszgwdLaefqxHHNgsckNzb76ndTQPoawiW8TBYuPO0oJSDYE73edW6Ix3WrXko+tneXaMov54ps1g6Gn2367WFtJYwFRaz8ELLUg1YMKtuQ8jKQmZSPdEJT7mQRaHZtoM3qfO1hsW9vH4JZcG7IbqiXm1iZmMd/84QqAwmqzNPcYhhrDPFFmsXG24iurx5jM4JZrigKtlfBbC7CsGigo1JilllcYA4ZW2yhYfDzRWvXkSjyofDKv1tYYqHbOZgts0vss0bMhr2wM22IUgrzaPQ7fn8UsLeW0DD7mfRQsPl9SY0FjET8nH+SW2vr+Wy559szC6sC4tWie7fBlEjt0tOxm6XKPrbjcTggWu0FygoSdxf91NBAFi2fBErh9ljcFhbmn0nUMY65SctMviFmDxd/D4DZZruzQQy4QmeHTjOf1icEtz1JKyHnq9v5/DIvk2vYBS4shrK8cIFhogIyzn9QV+QPKSAphUrB4BYHkKyWlw63UaDVjlajX2pD1/FmyR8JB2b2SksvKZUxz1yTGgAcD4lbtoDOSSQbk6ASjwx4fSUgm2uJgh3hP9ywdG0x7uHvI0QdsyRhoQ+6mluL3fU0CFiZ6neTEjIYJmFK6J/7AoNFyQBV9zgVFcO3wAtcB3+ECVis3g2K5ashYd3f1VwWW3LhsiCwajJhetfA6MBeJwU2XzCvy5zdp27/UDgAButbVVBvDJGCJGn1u9VBOCsS5jXHK8SxgKWg7cgFrSkPN4VsLWDJWACivSW7rXMMcDDWHMYwCC/vyb5NZ1C7jzGHCrTHg2++TvN7Dl7f6XMf37MDS8rwevC0Z9BeJOSVEIvt1VN6mjdmSp+m8i/Zd/heFTYPIiPkuYBmhvE1ruoBl0yw+Yr4LWEYob9OaLmDZNIuPmO9/LQ32NRsI+MMAAAAASUVORK5CYII=" style="width: 69.5px; height: 18.5px;" width="69.5" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50.5px 8px; transform-origin: 50.5px 8px; unicode-bidi: normal; "><span style="">, since the ratio </span></span><span style="vertical-align:-10px"><img src="data:image/png;base64,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" style="width: 63px; height: 29px;" width="63" height="29"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; "><span style=""> is the closest we can get to </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">ϕ</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 82.5px 8px; transform-origin: 82.5px 8px; unicode-bidi: normal; "><span style=""> for rectangle with area of </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 40.5px; height: 18px;" width="40.5" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95.5px 8px; transform-origin: 95.5px 8px; unicode-bidi: normal; "><span style=""> (see below code). Therefore, </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 217.5px; height: 18.5px;" width="217.5" height="18.5"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">.</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 286.067px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 143.033px; transform-origin: 404px 143.033px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 176px 8.5px; tab-size: 4; transform-origin: 176px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">&gt;&gt;  A = 20000; phi = (sqrt(5)+1)/2; a = Inf;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; ">&gt;&gt;  </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 16px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 16px 8.5px; ">for </span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 28px 8.5px; transform-origin: 28px 8.5px; ">i = 1:A</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 88px 8.5px; tab-size: 4; transform-origin: 88px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; ">      </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">if </span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 52px 8.5px; transform-origin: 52px 8.5px; ">mod(A,i) == 0</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 76px 8.5px; tab-size: 4; transform-origin: 76px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">         j = A / i;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 104px 8.5px; tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">         r = max(j/i,i/j);</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 104px 8.5px; tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; ">         </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">if </span><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 56px 8.5px; transform-origin: 56px 8.5px; ">abs(r-phi) &lt; a</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">            ds = [i j];</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">            a = abs(r-phi);</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 48px 8.5px; tab-size: 4; transform-origin: 48px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 36px 8.5px; transform-origin: 36px 8.5px; ">         </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">end</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 36px 8.5px; tab-size: 4; transform-origin: 36px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 24px 8.5px; transform-origin: 24px 8.5px; ">      </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">end</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 16px 8.5px; transform-origin: 16px 8.5px; ">    </span><span style="border-block-end-color: rgb(14, 0, 255); border-block-start-color: rgb(14, 0, 255); border-bottom-color: rgb(14, 0, 255); border-inline-end-color: rgb(14, 0, 255); border-inline-start-color: rgb(14, 0, 255); border-left-color: rgb(14, 0, 255); border-right-color: rgb(14, 0, 255); border-top-color: rgb(14, 0, 255); caret-color: rgb(14, 0, 255); color: rgb(14, 0, 255); column-rule-color: rgb(14, 0, 255); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(14, 0, 255); perspective-origin: 12px 8.5px; text-decoration-color: rgb(14, 0, 255); text-emphasis-color: rgb(14, 0, 255); transform-origin: 12px 8.5px; ">end</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 20px 8.5px; tab-size: 4; transform-origin: 20px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">&gt;&gt; ds</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 16px 8.5px; tab-size: 4; transform-origin: 16px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">ds =</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; tab-size: 4; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">    125 160</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; "><span style="">In this problem, </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 177.5px 8px; transform-origin: 177.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">we are asked to evaluate the following summation:</span></span></div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">                        </span></span><span style="vertical-align:-17px"><img src="data:image/png;base64,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" style="width: 59px; height: 45px;" width="59" height="45"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294.5px 8px; transform-origin: 294.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">that is, the sum of perimeter of all almost golden integer rectangles with areas from </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);">1</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; "><span style="font-weight: 700; "> to </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">A</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; "><span style="">For example, for </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 47.5px; height: 18px;" width="47.5" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 95px 8px; transform-origin: 95px 8px; unicode-bidi: normal; "><span style="">, summation output should be </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" style="width: 50px; height: 18px;" width="50" height="18"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">:</span></span></div><div style="block-size: 68.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 34.25px; text-align: left; transform-origin: 384px 34.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "><span style="">        </span></span><span style="vertical-align:-28px"><img 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" 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A golden rectangle is a rectangle whose side lengths are in the golden ratio, , where: .
                                                                       
The ancient Greeks consider the golden rectangle as the most aesthetically pleasing rectangular shape. Unfortunately for the ancients this ratio cannot be achieved if the sides are rational numbers let alone integers.
We define  as a function that calculates the perimeter of the rectangle with integer sides with area equal to , and in which the side ratio is as close as possible to the golden ratio, that is the absolute value, , is minimized.
For example, if , the correct dimensions should be , since the ratio  is the closest we can get to  for rectangle with area of  (see below code). Therefore, .
>>  A = 20000; phi = (sqrt(5)+1)/2; a = Inf;
>>  for i = 1:A
      if mod(A,i) == 0
         j = A / i;
         r = max(j/i,i/j);
         if abs(r-phi) < a
            ds = [i j];
            a = abs(r-phi);
         end
      end
    end
>> ds
ds =
    125 160
In this problem, we are asked to evaluate the following summation:
                        
that is, the sum of perimeter of all almost golden integer rectangles with areas from  to .
For example, for , summation output should be :

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Last Solution submitted on Sep 17, 2023

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Problem 58244. Easy Sequences 113: Almost Golden Integer Rectangles 2

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Problem 58244. Easy Sequences 113: Almost Golden Integer Rectangles 2

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