May 27, 2012

Play with scientific calculator

I posted an entry where I showed a very simple method to solve x = cos(x) by using a scientific calculator. Now, let's continue playing with a scientific calculator.
  1. Bring your scientific calculator (you can use your iphone or a web calculator).
  2. Change the mode to "rad" (radian).
  3. Push "1" (one) key.
  4. Push "sin" key.
  5. Push "1/x" key.
  6. Go back to step 4, unless you want out.
You will see two numbers:
  • 0.8975395... (after step 4.)
  • 1.1141571... (after step 5.)
The second number is a solution of the equation x = 1/sin(x)(this equation has infinite number of solutions), and the first number is its inverse.

Then, change "sin" to "cos" in step 4. Does it converge?


I simulated the procedure by using SCILAB, and obtained a sequence shown below.

This looks like a chaotic sequence.

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