Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created...

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Newton Itera+on Based π Calcula+on Jason Cannon-Silber, Neal C. Gallagher III, Maura F. Gallagher, Brandon W. Mayle, Joshua C. Fair, Nicolas M. Fair, Samuel J. Konkol Socrates Preparatory School www.socprep.org

Transcript of Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created...

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

NewtonItera+onBasedπCalcula+on

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

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

SocratesPreparatorySchoolwww.socprep.org

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Newton’sMethod

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

Findx>0wheresin(x)=0

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

OurImprovement

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RapidConvergence

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

€

xn+1 = xn + sin(xn )

Page 6: Newton Iteraon Based π Calculaon - AAPT.org · Presentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...

TryThisonYourCalculator

Forπ/2≤x≤3π/2

π=x+arcsin(sin(x))

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y=arcsin(sin(x))


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Newton Iteraon Based π CalculaonPresentation1.pptx Author: Neal Gallagher Created Date: 1/3/2016 4:07:30 PM ...

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