Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...

Page 1 <img data-url='document/newton-iteraon-based-calculaon-aaptorg-author-neal-gallagher-created-date.html?page=1' data-page='1' class='cut-thumb lazyload' alt='Page 1: Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader042.cupdf.com/reader042/viewer/2022040610/5ed00517b802fd5a5e59d651/html5/thumbnails/1.jpg' width='140' height='200' /> NewtonItera+onBasedπCalcula+on

JasonCannon-Silber,NealC.GallagherIII,MauraF.Gallagher,BrandonW.

Mayle,JoshuaC.Fair,NicolasM.Fair,SamuelJ.Konkol

SocratesPreparatorySchoolwww.socprep.org

Page 2 <img data-url='document/newton-iteraon-based-calculaon-aaptorg-author-neal-gallagher-created-date.html?page=2' data-page='2' class='cut-thumb lazyload' alt='Page 2: Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader042.cupdf.com/reader042/viewer/2022040610/5ed00517b802fd5a5e59d651/html5/thumbnails/2.jpg' width='140' height='200' /> Newton’sMethod

Page 3 <img data-url='document/newton-iteraon-based-calculaon-aaptorg-author-neal-gallagher-created-date.html?page=3' data-page='3' class='cut-thumb lazyload' alt='Page 3: Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader042.cupdf.com/reader042/viewer/2022040610/5ed00517b802fd5a5e59d651/html5/thumbnails/3.jpg' width='140' height='200' /> Findx>0wheresin(x)=0

Page 4 <img data-url='document/newton-iteraon-based-calculaon-aaptorg-author-neal-gallagher-created-date.html?page=4' data-page='4' class='cut-thumb lazyload' alt='Page 4: Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader042.cupdf.com/reader042/viewer/2022040610/5ed00517b802fd5a5e59d651/html5/thumbnails/4.jpg' width='140' height='200' /> OurImprovement

Page 5 <img data-url='document/newton-iteraon-based-calculaon-aaptorg-author-neal-gallagher-created-date.html?page=5' data-page='5' class='cut-thumb lazyload' alt='Page 5: Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader042.cupdf.com/reader042/viewer/2022040610/5ed00517b802fd5a5e59d651/html5/thumbnails/5.jpg' width='140' height='200' /> RapidConvergence

• x0=2.0• x1=2.90929743• x2=3.13950913• x3=3.141592653.1415926535897932384626433832795028842

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xn+1 = xn + sin(xn )

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Forπ/2≤x≤3π/2

π=x+arcsin(sin(x))

Page 7 <img data-url='document/newton-iteraon-based-calculaon-aaptorg-author-neal-gallagher-created-date.html?page=7' data-page='7' class='cut-thumb lazyload' alt='Page 7: Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...' loading='lazy' src='data:image/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVR42mNk+P+/HgAFhAJ/wlseKgAAAABJRU5ErkJggg==' data-src='https://reader042.cupdf.com/reader042/viewer/2022040610/5ed00517b802fd5a5e59d651/html5/thumbnails/7.jpg' width='140' height='200' /> y=arcsin(sin(x))

Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...

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