©2023 Compass Learning Technologies → GXWeb Showcase → GXWeb Continued Fraction Collection → Continued Fractions and Magic Tables

Continued Fractions and Magic Tables

Saltire Software, home of Geometry Expressions and GXWeb

Symbolic computations on this page use the Nerdamer Symbolic JavaScript to complement the in-built computer algebra system of GXWeb.

---

Exploring the Magic Table for Continued Fractions Mathematical Toolkit An Introduction to Continued Fraction Arithmetic Dig Deeper: Related References Behind the Scenes

 

---

---

 

Hide

Exploring the Magic Table for Continued Fractions

 

---

---

 

Magic Table Index

 

\[f\]

\[f(x)\]

More MathBoxes

---

 

\[g\]

\[g(x)\]

\[h\]

\[h(x)\]

RESET
ALL Numeric
ToolKit CAS
ToolKit Play
♬

Graph Table Steps Axes TextBoxes Sliders

---

---

Back to Top

This document requires an HTML5-compliant browser.

\(a = \)					▶
		-1	5	0
\(b = \)					▶
		-1	5	0
\(c = \)					▶
		-1	5	0
\\(d\\)				▶
	-1	0	5
\\(e\\)				▶
	-1	0	5

App generated by GXWeb

Show More Tools

 

---

---

 

Show Spreadsheet

Continued Fraction Spreadsheet Explorer

This browser-based spreadsheet uses the handsontable JavaScript library.

 

43/30 Phi Pi Pi+ e e+

Show/Hide Convergents Plot

Hide Spreadsheet

Back to Top

Jump to MathBox

 

---

 

Show Wolfram Alpha

WolframAlpha: CAS+

 

Sometimes, to deal with those stubborn, hard to reach problems, you need something stronger! The powerful Wolfram Alpha online CAS engine will answer almost anything you care to ask - within reason! From the continued fraction of pi to Solve x^2=x+1 to the population of Australia!

Hide Wolfram Alpha

Back to Top

Jump to MathBox

   

---

 

GeoGebra

GeoGebra offers another fast and accurate CAS alternative. You may also like to explore the GeoGebra web app.

Back to Top

Jump to MathBox

Timing: Key Signature:

Play ♬

Switch Views: notes <=> frequencies

 

---

---

 

Hide QR

Share with QR Code

Back to Top

Jump to MathBox

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!

GXWeb Jigsaws and Quizzes Send Your Own QR Code Reset QR Code

Send Web Address ⇑

Hide QR

 

---

Show Results

Share Your Results

Back to Top

Jump to MathBox

 

Enter your name:	? Abel, Nils Agnesi, Maria Bernoulli, Daniel Cantor, Georg Descartes, Rene Euler, Leonhard Fermat, Pierre Galois, Evariste Germain, Sophie Hypatia Johnson, Katherine Liebniz, Gottfried Lovelace, Ada Monge, Gaspard Newton, Isaac Noether, Emmy Pythagoras Ramanujan, Srinivasa Riemann, Bernhard Sylvester, James Tao, Terence Weierstrass, Karl' Zeno
My class:
Email to:

Session report length: 0 characters.

⇒ Web

⇒Email

Clear

Back to Top

Jump to MathBox

Hide Results

Hide More Tools

---

 

 

Back to Top

Jump to MathBox

Timing: Key Signature:

Play ♬

Switch Views: notes <=> frequencies

 

---

---

 

Show

Continued Fraction Arithmetic

Contrary to everybody, this self contained paper will show that continued fractions are not only perfectly amenable to arithmetic, they are amenable to perfect arithmetic. (Bill Gosper, 1972)

For Gosper, the appealing concept of perfect arithmetic may well have involved using continued fractions to perform calculations to any desired degree of accuracy. Continued fractions are ideal tools for successive approximation.

The examples explored here may offer a glimpse into one of the enduring questions regarding continued fractions: they are wonderful at representing numbers, both rational and irrational, but can they also serve as practical tools for computation?

While some of these examples involve simple, finite rational values, it is unlikely that anyone would realistically wheel in continued fraction arithmetic for such questions as \(\frac{10}{7} + \frac{22}{5}\).

But for those convoluted rationals and especially those infinite irrationals? Well... it was made for such as these!

Gosper
Method Matrix
Method

A Quick Overview

GXWeb Continued Fraction Arithmetic ⇒

Hide

Back to Top

Magic Table Index

Mathematical ToolBox

 

---

---

 

Show

Dig Deeper: Related References

• GXWeb Continued Fraction Collection

• GXWeb Fractured Fractions

• GXWeb Fractured Functions

• GXWeb Dragons, Folds and Fractions

• GXWeb Continued Fraction Arithmetic

• Extending Stern Brocot and Continued Fractions

• Unpacking Continued Logarithms

---

Bill Gosper (1972) Appendix 2: Continued Fraction Arithmetic.

Rosetta Code: Continued Fraction Arithmetic.

Continued Fraction Arithmetic

An Introduction to Continued Fractions by Dr Ron Knott

Continued Fractions by Ben Lynne

Arithmetic with...Continued Fractions?? (YouTube)

---

GXWeb Dragons, Folds and Fractions (YouTube)

A Quick Paperfold (YouTube)

The Summed PaperFolding Sequence (YouTube)

---

Hide

Back to Top

Magic Table Index

Mathematical ToolBox

 

---

---

 

Show

Behind the Scenes

Back to Top

Magic Table Index

Mathematical ToolBox

 

View JavaScript GXWeb Code (gxmathbox.js)

View JavaScript Latex2Jath Code (latex2mth.js)

View JavaScript Shared Code (sharedcodend.js)

Back to Top

Magic Table Index

Mathematical ToolBox

---

---

 

©2023 Compass Learning Technologies ← GXWeb Showcase ← GXWeb Continued Fraction Collection ← Continued Fractions and Magic Tables