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GXWeb Fractured Fractions Collection

Saltire Software, home of Geometry Expressions and GXWeb

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

Explore Bill Gosper (1972): Continued Fraction Arithmetic

Calkin and Wilf (1999): Recounting the Rationals

Bruce Bates (2014): The Stern-Brocot Continued Fraction

Bates, B., Bunder, M. and Tognetti, K. (2010): Linking the Calkin–Wilf and Stern–Brocot trees


 

With thanks to the late Dr Keith Tognetti for pointing me in the direction of continued fractions many years ago and igniting in me a life-long passion, and to Dr Bruce Bates (both of the University of Wollongong) for revealing to us all the beautiful Stern-Brocot Continued Fraction. With colleague Dr Martin Bunder they have brought to light many wonderful and often surprising connections between binary trees and continued fractions.

 
 

Welcome to the Fractured Fractions Collection!

Try the Continued Fraction JigSaw! Just rearrange the squares to fill the given rectangle, and then press INPUT (or the JIGSAW button again) to enter your answer.

Then go on and explore some of the wonderful connections between continued fractions and some surprising and important corners of mathematics. Did you know, for example, that fractions grow on trees?

Then dig deeper into Continued Fractions.

 

 

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Introduction

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Some Examples

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Explore the Magic Table

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Build Your Own Continued Fraction

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About the MathBoxes...

 
 







 

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More to Explore: the Continued Fractions Collection

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Interested to learn more? Delve more deeply into Continued Fractions with GXWeb Fractured Fractions and then on to the following...

 
 

Golden Numbers and More

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Negative (or Reversal) Continued Fractions

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Fractured Functions: Generalised Continued Fractions

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Some Matrix Fraction Magic

Index

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Continued Fraction Arithmetic

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Continued Logarithms

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Continued Fractions and Farey Trees

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Climb Around the Farey (Stern-Brocot) Tree

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Follow a Binary Path to Continued Fractions

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Explore the Stern-Brocot Tree

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Explore the Calkin-Wilf Tree

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Bessel Functions

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Gamma Functions

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Chaos Theory and Cobweb Functions

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Musical Continued Fractions

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And more...

 
 

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Construct your own Model with GXWeb

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Test Yourself

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Share Your Results

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GXWeb Jigsaws

QR Codes are a great way to share data and information with others, even when no Internet connection is available. Most modern devices either come equipped with QR readers in-built, or freely available.

The default link here is the GXWeb Jigsaws and Quizzes, but you can use it as an alternative to sending your assessment data via email, web or share with others in your class. You can even use it to send your own messages!

 

 

Why not Listen to your Continued Fraction?

Timing: Key Signature:

 

 

Behind the Scenes

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