Problem 313. Pythagorean perfect squares: find the square of the hypotenuse and the length of the other side

Created by Bruce Raine

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given the square root of a square number,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>seed</w:t></w:r><w:r><w:t>, and a range,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>n</w:t></w:r><w:r><w:t>, find the square number,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>Z</w:t></w:r><w:r><w:t> as well as the other side,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>y</w:t></w:r><w:r><w:t>, the square root of a square number i.e. return the hypotenuse squared as well as the length of the other side. Note that</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>n</w:t></w:r><w:r><w:t> is the number of squares to search through starting with one.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>HINT: Z = seed^2 + y^2 where Z = z^2, find Z first and then y.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Note that Z, seed^2 and y^2 are all perfect squares.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&gt;&gt; [z s] = findPerfectZ(3,6)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>z = 25</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>s = 4</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&gt;&gt;</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

138 Solutions
44 Solvers

Last Solution submitted on Jun 25, 2021

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Peter Wittenberg on 2 Jan 2014

There's a problem with the solution suite. For seed=12 and n=16, the proposed answer of 5, 12, 13 as a Pythagorean triple is indeed a good one. However, 9, 12, 15 is equally valid but not included as an answer. To avoid this, I would suggest changing the problem so that it requires finding the answer with the minimum Z^2 to avoid ambiguity.

Problem Recent Solvers44

Problem Tags

pythagoras

Community Treasure Hunt

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

Start Hunting!

Problem 313. Pythagorean perfect squares: find the square of the hypotenuse and the length of the other side

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers44

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Problem 313. Pythagorean perfect squares: find the square of the hypotenuse and the length of the other side

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers44

Suggested Problems

More from this Author16

Problem Tags

Community Treasure Hunt

Players