Matt McIrvin on Nostr: Chris Staecker has been continuing his wonderful "12 Days of Curtsmas" series on the ...
Chris Staecker has been continuing his wonderful "12 Days of Curtsmas" series on the vintage Curta calculator, and one of the later segments covered a mildly cryptic method supplied by the manufacturer for computing square roots on the Curta. Of course, it is not specific to the Curta but would really work with any functionally similar calculator, or with hand calculation:
https://www.youtube.com/watch?v=Wj3_VUQkBJI
There was a lot of puzzlement in his comments. This method uses a lookup table; if you're going to look up something in a table, why not just have a table of square roots and dispense with the Curta entirely?
Staecker pointed out that the method gives 5-digit accuracy and the table is much shorter than you'd need to get that kind of accuracy with a simple list of square roots. What it's really doing is giving you a piecewise linear approximation method, with the numbers processed slightly to get you past the initial steps.
Each entry has two numbers labeled 𝑅² and 1/(2𝑅). If you have 𝑁² and you want to find the square root 𝑁, you find the value of 𝑅² closest to 𝑁², and then add the first number and multiply the second to compute (𝑁²+𝑅²)/(2𝑅) . And that's it, your five-digit approximation.
https://www.youtube.com/watch?v=Wj3_VUQkBJI
There was a lot of puzzlement in his comments. This method uses a lookup table; if you're going to look up something in a table, why not just have a table of square roots and dispense with the Curta entirely?
Staecker pointed out that the method gives 5-digit accuracy and the table is much shorter than you'd need to get that kind of accuracy with a simple list of square roots. What it's really doing is giving you a piecewise linear approximation method, with the numbers processed slightly to get you past the initial steps.
Each entry has two numbers labeled 𝑅² and 1/(2𝑅). If you have 𝑁² and you want to find the square root 𝑁, you find the value of 𝑅² closest to 𝑁², and then add the first number and multiply the second to compute (𝑁²+𝑅²)/(2𝑅) . And that's it, your five-digit approximation.