©2020 Compass Learning Technologies ← Live Mathematics on the Web ← Geometry Expressions Showcase ← Fractured Fractions → Exploring Continued Fractions with GXWeb

## Exploring Continued Fractions with GXWeb

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Download a Geometry Expressions Model for Fractured Fractions

Take Continued Fractions to the Next Level

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

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 anextremelyaccurate approximation!

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

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

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!

More to Explore

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©2020 Compass Learning Technologies← Live Mathematics on the Web ← Geometry Expressions Assessment Showcase ← Exploring Continued Fractions with GXWeb