©2022 Compass Learning TechnologiesGXWeb Continued Fractions Collection → Unpacking Continued Logarithms

Unpacking Continued Logarithms

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Symbolic computations on this page use Nerdamer Symbolic JavaScript to complement the in-built CAS of GXWeb


An Introduction to Continued Fractions by Dr Ron Knott

Chaos in Numberland: The secret life of continued fractions by John D. Barrow

Bill Gosper (1972): Continued Fraction Arithmetic

Borwein, J.,Calkin, N., Lindstrom, S. and Mattingly, A. Continued Logarithms And Associated Continued Fractions

Borwein, J.,Calkin, N., Lindstrom, S. and Mattingly, A. Continued Logarithms And Associated Continued Fractions (Overview PDF)

Borwein, Jonathan M, Hare, Kevin G, and Lynch, Jason Continued Logarithms And Related Continued Fractions

Online Mathematics Research: The Ramanujan Machine


Scott Lindstrom YouTube: Continued Logarithms And Associated Continued Fractions (22:08)

YouTube: Unpacking Continued Logarithms (34:52)


\[g(x) = \left\{ \begin{array}{ll} \frac{x}{b} & x\geq b \\ \frac{b-1}{x-1} & 1\lt x\lt b \\ terminate & x=1 \\ \end{array} \right. \]

\[19 = [4,2,1,1]_{cl(2)}\] \[⇒ 2^4+\cfrac{2^4}{2^2+\cfrac{2^2}{2^1+\cfrac{2^1}{2^1}}}\]

\[\frac{21}{5} = [1,1,1]_{cl(3)}\] \[⇒ 3^1+\cfrac{2\cdot 3^1}{3^1+\cfrac{2\cdot 3^1}{3^1}}\]
 

 

Introduction

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

Defining Continued Logarithms

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit


 

 

Continued Logarithms in More Flavours

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

 

Computing Continued Logarithms

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

 

GXWeb Continued Logarithm Explorer


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App generated by GXWeb

Gosper's (expanded) continued logarithm array (base \(2)\) for \[\frac{22}{9}\]

= [1,0,1,1,0,1,1,1,0]

and Type I (compact) array:

⇒ \([1,2,3]\)

⇒ \([2,4,8]\)

Continued fraction array:

\([2,2,3,1]\)


Use the Input and Base buttons (or drag point P if on a supported device) to explore other numbers and their continued logarithm and continued fraction forms.

Use the Type buttons and the continued logarithm <=> continued fraction button to explore further.


To dig more deeply, begin with the Introduction, and make sure you try the Mathematical ToolKit!

And remember: blue text is an invitation to play!


Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

Mathematical ToolKit

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

About the MathBoxes...

 
 

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

Share with QR Code

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

Explore Further

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

Construct your own Model with GXWeb

Index

GXWeb Continued Logarithm Explorer

Defining Continued Logarithms

Continued Logarithms in More Flavours!

Computing Continued Logarithms

Mathematical ToolKit

Share Your Results

Explore Further

 

 

Behind the Scenes

Index

GXWeb Continued Logarithm Explorer

Mathematical ToolKit

 

 

©2022 Compass Learning TechnologiesGXWeb Continued Fractions Collection → Unpacking Continued Logarithms