The Babylonian method of finding square roots
G'day G'day Folks,
The Babylonians had a method of calculating square roots which is now often known as Heron's method after Heron of Alexandria. I like it because it is fun to implement on a Casio 82TL calculator. These are one of the least expensive calculators on the market yet do most algebraic calculations.
Let us find the square root of a real integer, R.
For example let’s find
Step 1. Find the largest integer such that,
On the Casio 82TL simply enter, 3 =
The importance of this step is that 3 is stored as the first answer.
Step 2. Improve the estimate.
ANS = the previous answer, which in the first instance is 3.
On the Casio 82 TL the previous answer is given automatically by the ANS key .
What makes the process fun to do is that the Casio 82TL has a fraction key.
This allows fractions to be entered as written.
Amazing as it may seem to get the next approximation simply press the = key.
The Casio 82 TL substitutes in the previous approximation into the same expression.
The magic continues as the = key is pressed again.
The answer is displayed as a decimal when fractions exceed three digits.
The fourth approximation, agrees with the Casio 82TL calculator’s
evaluation of
to 8 decimal places.
Have fun and let me know how easy this is to read.
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