Processing math: 64%
 

©2022 Compass Learning TechnologiesGXWeb Climbing Around Fraction Trees → Extending Stern-Brocot and Continued Fractions


Extending Stern-Brocot and Continued Fractions

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


I have been fascinated by continued fractions since being first introduced to them by the late Dr Keith Tognetti of the University of Wollongong, almost 4 decades ago. More recently, the work of Dr Bruce Bates (also of Wollongong University) on the Stern-Brocot Continued Fraction has caught my eye and captured my interest.

Here I describe some discoveries I have come across recently which have not only extended my thinking and understanding of Stern-Brocot, but of continued fractions in general, potentially opening new doorways for further exploration.

New to continued fractions?

New to fraction trees? (Press the 'Show more' button)


Tap the images to climb around and explore the fraction trees

View a short YouTube video on the Stern-Brocot Tree and its Continued Fraction

 

 

Introducing Stern-Brocot

Index

Jump to MathBox

 

 

Explore the Magic Table

Index

Jump to MathBox

 

 

Building the Fraction Trees

Index

Jump to MathBox

 
 

Explore the Calkin-Wilf Tree

Index

Jump to MathBox

 

 

Some Matrix Fraction Magic

Index

Jump to MathBox

 

 

A Proposed Alternative Form

Index

Jump to MathBox

 

Mathematics ToolKit

About the MathBoxes...

Index

To compute an entry, tap the f, g or h buttons.


 




App generated by GXWeb

 
 

Index

Introducing Stern-Brocot

Explore the Magic Table

Building the Fraction Trees

Explore the Calkin-Wilf Tree

Some Matrix Fraction Magic

A Proposed Alternative Form

Negative (or Reversal) Continued Fractions

Negative Terms in a Continued Fraction

Proof by Mathematical Induction

Jump to MathBox

References

Timing: Key Signature:

   

 

References

Index

Jump to MathBox

 

 

Behind the Scenes

Index

Jump to MathBox

 

 

©2022 Compass Learning TechnologiesGXWeb Climbing Around Fraction Trees → Extending Stern-Brocot and Continued Fractions