©2022 Compass Learning Technologies ← GXWeb 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
GXWeb Continued Logarithm Explorer
Defining Continued Logarithms
GXWeb Continued Logarithm Explorer
Continued Logarithms in More Flavours
GXWeb Continued Logarithm Explorer
Computing Continued Logarithms
GXWeb Continued Logarithm Explorer
GXWeb Continued Logarithm Explorer
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!
GXWeb Continued Logarithm Explorer
Mathematical ToolKit
GXWeb Continued Logarithm Explorer
About the MathBoxes...
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GXWeb Continued Logarithm Explorer
Explore Further
GXWeb Continued Logarithm Explorer
Construct your own Model with GXWeb
GXWeb Continued Logarithm Explorer
Continued Logarithms in More Flavours!
Computing Continued Logarithms
Behind the Scenes
GXWeb Continued Logarithm Explorer
©2022 Compass Learning Technologies ← GXWeb Continued Fractions Collection → Unpacking Continued Logarithms