Problem 51580. Construct a continued fraction for a square root

Created by ChrisR

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>Numbers can be expressed as continued fractions of the form</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"x = a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/...)))\"/></w:customXmlPr><w:r><w:t>x =a_0+\\frac{1}{a_1+\\frac{1}{a_2+\\frac{1}{a_3+\\frac{1}{\\ddots}</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:t>Some continued fractions—such as those for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"e\"/></w:customXmlPr><w:r><w:t>e</w:t></w:r></w:customXml><w:r><w:rPr><w:i/></w:rPr><w:t> </w:t></w:r><w:r><w:t>and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"pi\"/></w:customXmlPr><w:r><w:t>\\pi</w:t></w:r></w:customXml><w:r><w:t>--continue forever without a discernable pattern in the coefficients, while the coefficients of continued fractions for square roots eventually repeat. For example, </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"sqrt(2) = 1+(1/(2+1/(2+1/(2+1/...))))\"/></w:customXmlPr><w:r><w:t>\\sqrt{2} =1+\\frac{1}{2+\\frac{1}{2+\\frac{1}{2+\\frac{1}{\\ddots}</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:t>or</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"sqrt(14) = 3+1/(1+1/(2+1/(1+1/(6+1/...))))\"/></w:customXmlPr><w:r><w:t>\\sqrt{14} =3+\\frac{1}{1+\\frac{1}{2+\\frac{1}{1+\\frac{1}{6+\\frac{1}{\\ddots}</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:t>Write a function that takes a non-square integer and returns the values 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>a_i</w:t></w:r></w:customXml><w:r><w:t> until the values repeat. </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>This problem celebrates my finally cracking </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215\"><w:r><w:rPr><w:u/></w:rPr><w:t>Cody Problem 1215</w:t></w:r></w:hyperlink><w:r><w:t> by James. If you struggle with Test 8, as I did, remember that MATLAB cannot represent decimals with infinite precision.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<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: 483.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 241.958px; transform-origin: 407px 241.958px; vertical-align: baseline; "><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: 190.983px 7.91667px; transform-origin: 190.983px 7.91667px; unicode-bidi: normal; "><span style="">Numbers can be expressed as continued fractions of the form</span></span></div><div style="block-size: 85.3333px; 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 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-69px"><img src="data:image/png;base64,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" alt="x = a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/...)))" style="width: 160.5px; height: 85.5px;" width="160.5" height="85.5"></span></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: 141.192px 7.91667px; transform-origin: 141.192px 7.91667px; unicode-bidi: normal; "><span style="">Some continued fractions—such as those for </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);">e</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: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "><span style="font-style: italic; "> </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: 13.6167px 7.91667px; transform-origin: 13.6167px 7.91667px; unicode-bidi: normal; "><span style="">and </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);">π</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: 206.033px 7.91667px; transform-origin: 206.033px 7.91667px; unicode-bidi: normal; "><span style="">--continue forever without a discernable pattern in the coefficients, while the coefficients of continued fractions for square roots eventually repeat. For example, </span></span></div><div style="block-size: 85.3333px; 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 42.6667px; text-align: left; transform-origin: 384px 42.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-69px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATIAAACrCAYAAADl2BD6AAAIgklEQVR4nO3dMW7bQBYG4Fduu1C3pdoUvoDKrdwv4BuoTKc6W/gKOoOO4Du43VJn8BW8xXhAWrFIiRyRGur7gAcEscwotvl7OHyciQAAAICqPEXEZu43ATDGMSL+GxG/BhbArF4i4iMiPkcUwKyOEbGLiD8jCmqziojt3G+CMjaRRmOrud8ITGQV6Rf3x1exAG+RvqnwCLbxfRpFkC2A0RiPZBvpZ34VaTpFkC3EW0S8zv0mYAZvIcgWYRPpG7nueM060mXn21cdIv1WW8IILs+TvMz9RpiFIFuIt4jYd3x8F+dbLY6RGmhr1J7o/Qx3rR6VIFuAvtHYNprA2n3VIf4Os67R3D16iYj3+D7ZK8gekyBbgH2cH42tI31zf5o7W0cKghwCNc2vraMZRT7H7YMs/wKoLewfhSCr3Dq6R2N5TuycPJr7jBRqNWr/H24VZPn4tV6CL50gq1zXaCwihVPfw+O137oWZAiyivWNxiIuO/HyD8GxxJuagSBDkN2R17hu6Z19dF82Xir/EHSN7O6ZIEOQ3YH2pPulwZRHYyXWHMsn6bXHeoqmJ21Mje39EmQIspk9R2qFeInrTpZSo7F8x+8w4HPbATKmxoaPIEOQzaw9CsqT7n2XeKsoNxrLPwBD2gpWX+9hbI19skCQIcjuSHtU1hUsfS0Vl8qjsecCx5pTiSB7je7L33z8vstk5iHI7kzuUj/XnLr6es3Y0VhulF3Ckj8lgqwdVkPLSTQfQXZn8jOR55bj2cX4xtXV1zFq6uTvUiLI8mYt56p9/HOvcdk5n3yzTJDdiTzi+oy/R0v5Y2Pu8pUMMXctmVte0aU9Mt7FMlZ0qd4+fm5Q3f3wd9coPRJz15I5baJ5Bvanqn3ut3q5R+wzmtFKidHYIfrviO7i8vk3dy2BTqejsm2MG43to39uLa9/XhtBBneqfXJuIoXY0NFYDsVLqsYbAO22lVvdhRVkMFD7lvLQ0dg1ITa0MXYum0jB215YMS8eWeKStU2QwUDtBQOHjsaumauq7STt+/+UJMhghGPY4g2oXG7UZBn+FRG/lKqs4Jv2fJ5StdTvgJbfEfFHqcoKAAAAAAAWYRXpqZGxy04BTC4HWG6dudXCBAA38RJp1Zh2/58gA6qxjubZ2vZzz4IMqNIUa94B3JQgA6onyKBD3gUo7yh1iHSiWLbpvggyOON0G7N2HcMijvdEkMEPttEEVt6+7BB/h1lNS48vmSCDE+tIfUk/bfSyjmbX7M8zrxkqB6ZwvJ4ggxN5Tuyc9knzXvDfzcd0yXo9QQYn3qN/+fJjpJOm5D6jgmw4QQYnLgmSvBXgmE2ZTwmy4QQZDJCDbF/wmIJsOEEGA+STpuQOWoJsOEEGV8oPKB8KH1eQDSfI4Er5srJ0m4QgG06QwRXyaOx5wOe+RvOo00+VT8Su13S1hTyyl2i+fruZ3wvctdwoO/REaYfV0CrZ7rEEm0i/INoLK+anMTbhmVj4ZhWpv2xMJ/9TpJPrXLUvjc69xmXnd11fz5I3YqB6JULsEubIgJuYKsQiBBlwI4fob3rN8zFjCTKguH30PxS+jXIT8IIMKGofl99JLHXZKciAYq4JsZKNsYIMKKbvlv6t2iFKBdkf9XAFi/LPGN90q+qr3wEL80s9XAEAAAAAABdYR+oxLL0yMMDN5QDLrQ6CDKjKNppRmCADqtR+/EyQAdUTZED1BBlQPUEGVE+QAdUTZDCjdaR9BfIGv4dIbQX2fLyOIIOZ7OL8GlbHsBrtNQQZzGAbTWDtvqrd2Jk/Vmqp7qUTZDCxdaTdnX7aGGUdaXeofGKW2jwlX8LuCh3v3ggymFieEztnE82J2bfl3aXyMUttj3dvBBlM7D36Nw0+RtngEWRAUZdM4r9FM09WgiADJpeDbF/oeIIMmFw+MfsuQS8lyIBJPUf5k3LJQXaLmyPASPmysmQP2RKD7CX+7r1r9+ZpKIaZ5NHY84DPfeuo3Jv20fO6Un1rwIPKjbJDm1bPPe50TZljAgZbRRo1jRkRbToqPxL12fM6j0QBg5QIsT5LnCMD7sQUIRYhyIAbOkR/0+suxveTCTLgJvbR3/e0jTLhI8iA4tq7Y/dVicvOUkH2j4j4n7qq/j3oKw137poQK9UYK8gEGRTV1f5wWqW6011aAgAAAAAlvITHuIBKvUSzj4LlgYCqbKIJsFyCDKjG81et4vsCjoIMqNIuBBlQOUEGVE+QAdUTZED1BBlQPUEGVE+QAdUTZLBwm0ir2OZNfveRHulZEkEGC3Xa8X5ab1+vWQJBBguVQ+wt0om+i7SZymmYLYEggwV6jnRSP//wsU2kJbU/O14zxDqawJyaIIMFyqOwc9onfqnNh+fcd0CQwcKsIp3QXdbRnPiHQv+uIAOKWcVlq6TmE79vJ/VLzRlkryHI4CHlE79UK8YcQbaK9P7bc36HsNw1PIQcOn2XoEOOOVWQtW8u/FTbid4HMJN8KVbyZLfJMDCZVaSwORY+riADJvMaKWyGzCO9dVRutv3oeV2pdg/gQeVG2c3Azz/3uNM1VardA3hAT5FGS2M6+TcdtY0mrLpe544iMEiJEOtjjgy4mSlCLKJskP2asIA7t4p0d7Kv6fUQ45f0KRVk/4kyc3GX1u+R7xe4oVWkO4lddwlXkR5RKjEBX3JE9mfCAu5UDrFLRyUlLjvNkQHFXBtipRpjBRlQzCq62x9u1Q4hyAAAAAAAAIDl20Ra/XXo6h0As2ovz/0RwgyoUHvLt9LLdANMYh3NbkkfMf4hd4BZ5KcWAAC4N3mPy1KbDQNMKm9v5yYAUK12W4ZdmoBqtddfczMAqNYmtGQAAABQ3FOkyf/D158BqnOM5ibA+8zvBWCQdn9Zqd2iACb1EinMPqLM3p0AAAAAAAAAAAAAcL/+DzvD2ZeOiVp9AAAAAElFTkSuQmCC" alt="sqrt(2) = 1+(1/(2+1/(2+1/(2+1/...))))" style="width: 153px; height: 85.5px;" width="153" height="85.5"></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: 6.225px 7.91667px; transform-origin: 6.225px 7.91667px; unicode-bidi: normal; "><span style="">or</span></span></div><div style="block-size: 103px; 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 51.5px; text-align: left; transform-origin: 384px 51.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-87px"><img src="data:image/png;base64,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" alt="sqrt(14) = 3+1/(1+1/(2+1/(1+1/(6+1/...))))" style="width: 185px; height: 103px;" width="185" height="103"></span></div><div style="block-size: 21.25px; 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 10.625px; text-align: left; transform-origin: 384px 10.625px; 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: 228.192px 7.91667px; transform-origin: 228.192px 7.91667px; unicode-bidi: normal; "><span style="">Write a function that takes a non-square integer and returns the values of </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABsAAAAoCAYAAAAPOoFWAAABC0lEQVRYhe2VTRGDMBBGnwcc1AAGogAFOMABDrCABiTEQy2gAQv0wO6Q0oSkkB46kzeTA1nYb3/YBAqFQqHwN9RAB/SAkT0jz3VOEQvMImaAEXgCq6xHDqFWnM1AdbCtju2nQq7YcFeocZwZj/0RsSdTAYs4mgLvaNYL/qyT6dmjDv1lVuw24qOLiWlWIUfGCaa/I5biyBLPPAm3hI3H3rFnnrVfR7GWbQwm3ss8sldBT5RJ9k+pHTErkVfiQOdNMxtlHf9YDThp/jRyd03sJVsO+6HvfW3w0kiEHZ/nXuzwXdiqkOW8PEPbEBqbrCQPcw50Bmu+6NlV9JZoyXAbxNALdeDmwBcKhWu8ANZGYx8ObIHOAAAAAElFTkSuQmCC" style="width: 13.5px; height: 20px;" width="13.5" height="20"></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: 74.2917px 7.91667px; transform-origin: 74.2917px 7.91667px; unicode-bidi: normal; "><span style=""> until the values repeat. </span></span></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: 135.758px 7.91667px; transform-origin: 135.758px 7.91667px; unicode-bidi: normal; "><span style="">This problem celebrates my finally cracking </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/groups/25/problems/1215"><span style=""><span style="text-decoration: underline; text-decoration-line: underline; ">Cody Problem 1215</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: 178.892px 7.91667px; transform-origin: 178.892px 7.91667px; unicode-bidi: normal; "><span style=""> by James. If you struggle with Test 8, as I did, remember that MATLAB cannot represent decimals with infinite precision.</span></span></div></div></div>

Solve

Solution Stats

83 Solutions
8 Solvers

Last Solution submitted on Sep 16, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 51580. Construct a continued fraction for a square root

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author166

Problem Tags

Community Treasure Hunt

Problem 51580. Construct a continued fraction for a square root

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author166

Problem Tags

Community Treasure Hunt

Players