Problem 57750. Radius of an inner N-dimensional sphere

Created by HH

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/Hypercube\"><w:r><w:t>hypercube</w:t></w:r></w:hyperlink><w:r><w:t> is an N-dimensional analogue of a square (N=2). Similarly, an </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/N-sphere\"><w:r><w:t>N-sphere</w:t></w:r></w:hyperlink><w:r><w:t> is an N-dimensional analogue of a circle. Note that a circle is considered a 1-sphere set in 2D space. In this problem, we will consider a circle as having a dimensionality of 2, a sphere as 3, and so on.</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 begin by considering a square (2D hypercube) of length 2R centered around the origin of a 2D Cartesian plane. Four circles (2D 1-spheres) of radius R are placed, such that each one is centered around one of the square's corners. Each circle is tangent to its two neighers. In the illustration below, the square is represented by the gray area and the four circles are displayed in blue.</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=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"548\"/><w:attr w:name=\"width\" w:val=\"607\"/><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>An additional inner circle or radius r, displayed in red, is centered around the origin, such that it is tangent to all other circles. Your task is to compute this radius.</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 3D, there would be a cube of length 2R, with eight spheres centered on the cube's corneres and an inner sphere centered around the origin. This continues similarly in higher dimensions.</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>Given the number of dimensions, N, and the radius of the corner N-spheres, R, return the radius of the inner N-sphere, r. Round your answer to 3 decimal places.</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>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[N = 2;\nR = 1;\nr = 0.414]]></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 example represents the 2D case, as illustrated above, in which the radius of the corner circles is equal to 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","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: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 1003.95px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.989px 501.974px; transform-origin: 406.996px 501.974px; vertical-align: baseline; "><div style="block-size: 63.0256px; 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: 383.991px 31.5057px; text-align: left; transform-origin: 383.999px 31.5128px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">A </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Hypercube"><span style=""><span style="">hypercube</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: 0px 0px; transform-origin: 0px 0px; "><span style=""> is an N-dimensional analogue of a square (N=2). Similarly, an </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/N-sphere"><span style=""><span style="">N-sphere</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: 0px 0px; transform-origin: 0px 0px; "><span style=""> is an N-dimensional analogue of a circle. Note that a circle is considered a 1-sphere set in 2D space. In this problem, we will consider a circle as having a dimensionality of 2, a sphere as 3, and so on.</span></span></div><div style="block-size: 84.0341px; 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: 383.991px 42.017px; text-align: left; transform-origin: 383.999px 42.017px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">We begin by considering a square (2D hypercube) of length 2R centered around the origin of a 2D Cartesian plane. Four circles (2D 1-spheres) of radius R are placed, such that each one is centered around one of the square's corners. Each circle is tangent to its two neighers. In the illustration below, the square is represented by the gray area and the four circles are displayed in blue.</span></span></div><div style="block-size: 553.551px; 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: 383.991px 276.776px; text-align: left; transform-origin: 383.999px 276.776px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" 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" data-image-state="image-loaded"></div><div style="block-size: 42.017px; 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: 383.991px 21.0085px; text-align: left; transform-origin: 383.999px 21.0085px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">An additional inner circle or radius r, displayed in red, is centered around the origin, such that it is tangent to all other circles. Your task is to compute this radius.</span></span></div><div style="block-size: 42.017px; 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: 383.991px 21.0085px; text-align: left; transform-origin: 383.999px 21.0085px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">In 3D, there would be a cube of length 2R, with eight spheres centered on the cube's corneres and an inner sphere centered around the origin. This continues similarly in higher dimensions.</span></span></div><div style="block-size: 42.017px; 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: 383.991px 21.0085px; text-align: left; transform-origin: 383.999px 21.0085px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">Given the number of dimensions, N, and the radius of the corner N-spheres, R, return the radius of the inner N-sphere, r. Round your answer to 3 decimal places.</span></span></div><div style="block-size: 21.0085px; 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: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">Example:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 61.321px; 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: 403.991px 30.6534px; transform-origin: 403.999px 30.6605px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; 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: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; 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: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">N = 2;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; 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: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; 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: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">R = 1;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4403px; 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: 0.909091px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.909091px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.909091px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.909091px; 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: 403.991px 10.2131px; transform-origin: 403.999px 10.2202px; 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: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">r = 0.414</span></span></div></div><div style="block-size: 21.0085px; 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: 383.991px 10.4972px; text-align: left; transform-origin: 383.999px 10.5043px; 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: 0px 0px; transform-origin: 0px 0px; "><span style="">This example represents the 2D case, as illustrated above, in which the radius of the corner circles is equal to 1.</span></span></div></div></div>

A hypercube is an N-dimensional analogue of a square (N=2). Similarly, an N-sphere is an N-dimensional analogue of a circle. Note that a circle is considered a 1-sphere set in 2D space. In this problem, we will consider a circle as having a dimensionality of 2, a sphere as 3, and so on.
We begin by considering a square (2D hypercube) of length 2R centered around the origin of a 2D Cartesian plane. Four circles (2D 1-spheres) of radius R are placed, such that each one is centered around one of the square's corners. Each circle is tangent to its two neighers. In the illustration below, the square is represented by the gray area and the four circles are displayed in blue.

An additional inner circle or radius r, displayed in red, is centered around the origin, such that it is tangent to all other circles. Your task is to compute this radius.
In 3D, there would be a cube of length 2R, with eight spheres centered on the cube's corneres and an inner sphere centered around the origin. This continues similarly in higher dimensions.
Given the number of dimensions, N, and the radius of the corner N-spheres, R, return the radius of the inner N-sphere, r. Round your answer to 3 decimal places.
Example:
N = 2;
R = 1;
r = 0.414
This example represents the 2D case, as illustrated above, in which the radius of the corner circles is equal to 1.

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Problem 57750. Radius of an inner N-dimensional sphere

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