©2020 Compass Learning TechnologiesLive Mathematics on the WebGeometry Expressions ShowcaseFractured Fractions → Exploring Continued Fractions with GXWeb

 

Exploring Continued Fractions with GXWeb

Saltire Software, home of Geometry Expressions and GXWeb

Download a Geometry Expressions Model for Fractured Fractions

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

Take Your Continued Fractions to the Next Level

 


   

 

Every real number, rational and irrational, can be represented by a continued fraction - the rational ones are finite, of course, but both finite and infinite offer some wonderful patterns and opportunities to explore!

Continued fractions have many practical applications but one of the most important lies in their ability to offer VERY good approximations to irrational numbers - the more convergents, the better the approximation. Indeed, each convergent gives the Best Approximation of the First Kind (look that up!) AND if a large value turns up in the list, then cutting the continued fraction just before that large value gives an extremely accurate approximation!

Step-by-Step Guide to building your own continued fractions

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f(x)
g(x)
h(x)

App generated by GXWeb

Drag the point P or enter coordinates in the text boxes to explore (and even ♬ listen to!) your own continued fractions.


a =
b =


Go beyond the rational - try your own continued fractions!



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More to Explore

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Need a Little CAS?

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Construct your own Model with GXWeb

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Behind the Scenes

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©2020 Compass Learning TechnologiesLive Mathematics on the WebGeometry Expressions Assessment Showcase ← Exploring Continued Fractions with GXWeb