Continued fractions are awesome. 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!

Use the f(x) MathBox or the x-value box above to enter a value to express as a continued fraction.

For example, try \(\pi\) or \(\phi\) or even \(\frac{225}{157}\).

Would you like to explore them further?

Reference: Nerdamer Symbolic JavaScript

Use the CAS Evaluate option from the dropdown menu above to solve an expression or equation in the \(f(x)\) MathBox. Click on the following to try:

• Solve(x^2=x+1,x)

• Solve(x^2=x+1,x),x

Notice the difference between these two results? Adding an extra \(,x\) at the end forces an \(exact\) rather than a \(numeric\) result!

And some more to try (just click on each line):

• pFactor(320) (Prime factors)

• sqcomp(x^2-4*x+3,x),x (Complete the Square)

• nthroot(10,3) (Enter into the MathBox as
  \ nthroot [space] 3 [space] 10 [space])

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Use the Solve option from the dropdown menu above to solve an expression or equation in the \(f(x)\) MathBox, or enter solve(an equation) in \(f(x), g(x)\) or \(h(x)\).

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Use the Derivative option from the dropdown menu above to differentiate a function in the \(f(x)\) MathBox, or enter \(d/dx\)(a function) in \(f(x), g(x)\) or \(h(x)\).

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Use the Integral option from the dropdown menu above to integrate a function in the \(f(x)\) MathBox, or enter \(int\)(a function) in \(f(x)\).

For definite integrals, perform the integration as described using the dropdown, and enter end values when requested. Use the \(x\) box or slider to vary this.

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Display the tangent (or Normal) of \(f(x)\) for the current value of \(x\) using the Tangent/Normal button, or enter tangent (or tngnt) or normal directly into the graph mathBoxes - set the desired x-value first.

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