Problem 42721. Fun with a compass

Created by James

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>Each night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. Your teacher gives you a number, and asks you if it is possible to construct a regular polygon with that many sides inside the unit circle using nothing but the compass and straight edge.</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>After waking up in a cold sweat again, you decide to write a MATLAB script to see if you can solve your nightmare. The dream is burned into your memory, so you remember all of the numbers that your teacher gave to you. Write a script that will allow you to solve this problem, and sleep peacefully once again.</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>Note - You don't actually have to construct the n-sided polygon. You just need to determine if it's possible to do so. You can assume that all of the numbers are integers greater than 2.</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: 207px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 103.5px; transform-origin: 407px 103.5px; vertical-align: baseline; "><div style="block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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="">Each night for the past week, you have been having the same nightmare: You find yourself back in your junior high school geometry class, armed with nothing but a compass and a straight edge. Your teacher gives you a number, and asks you if it is possible to construct a regular polygon with that many sides inside the unit circle using nothing but the compass and straight edge.</span></span></div><div style="block-size: 63px; 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 31.5px; text-align: left; transform-origin: 384px 31.5px; 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: 374px 8px; transform-origin: 374px 8px; unicode-bidi: normal; "><span style="">After waking up in a cold sweat again, you decide to write a MATLAB script to see if you can solve your nightmare. The dream is burned into your memory, so you remember all of the numbers that your teacher gave to you. Write a script that will allow you to solve this problem, and sleep peacefully once again.</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: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; "><span style="">Note - You don't actually have to construct the n-sided polygon. You just need to determine if it's possible to do so. You can assume that all of the numbers are integers greater than 2.</span></span></div></div></div>

Solve

Solution Stats

61 Solutions
30 Solvers

Last Solution submitted on Jan 04, 2022

Last 200 Solutions

Problem Comments

Solution Comments

Solution 826285

1 Comment

1 Comment

Peng Liu on 14 Feb 2016

In order to make this work, the combination of multiple *distinct* Fermat primes needs to be considered.

Problem Recent Solvers30

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 42721. Fun with a compass

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers30

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Problem 42721. Fun with a compass

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers30

Suggested Problems

More from this Author80

Problem Tags

Community Treasure Hunt

Players