The following is the simplest way to solve the equation "

**x=cos(x)**" by using a scientific calculator:

- Bring your scientific calculator (you can use your iphone or a web calculator).
- Change the mode to "rad" (radian).
- Push "1" (one) key.
- Continue to push "cos" key until you feel bored.

The result should be an approximated value of the solution,

**x=0.73908513...**

Why?

The procedure is exactly the following iteration:

By a fixed-point theorem, you can prove that the sequence {x[n]} converges to the solution.

I used this demo when I taucht iteration methods in a "numerical computation" class. This is a nice example for motivating students to learn more abstract theory.

**x[n+1] = cos(x[n]), n=0,1,2,..., x[0]=1.**

I used this demo when I taucht iteration methods in a "numerical computation" class. This is a nice example for motivating students to learn more abstract theory.

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