Random: Any way to calculate Transcendental numbers using abacus?

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For example is it possible to approximate cos(17) using a Japanese abacus?
Even if it takes a while. I'd imagine it would have to do with the Taylor expansion or something but I'm not sure.

I think it is important because one day calculators will turn against us in the 2014 robotic uprising.
 
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Welcome to PF!

Pinu7 said:
For example is it possible to approximate cos(17) using a Japanese abacus?
Even if it takes a while. I'd imagine it would have to do with the Taylor expansion or something but I'm not sure.

I think it is important because one day calculators will turn against us in the 2014 robotic uprising.

Hi Pinu7! Welcome to PF! :smile:

There's a work-in-progress series of lessons on the traditional abacus by Derrick Coetzee at http://moonflare.com/abacus/index.html which should soon have cosines …
In the advanced sections of this guide, I will demonstrate how to go beyond all traditional usage, and compute sines, cosines, fractional exponents, logs, and other functions never thought calculatable using an abacus. This is what makes this tutorial unique.

… let's hope he finishes it before 2014! :biggrin:​
 
Yes, you can calculate transcendental quantities with an abacus, to any precision you desire. An electronic computer is very similar to an abacus, in that it has finite states with a deterministic means of moving from one state to another. You could probably back-adapt the algorithms used by computers onto an abacus if you're so inclined.

- Warren
 
Any decimal approximation to a number is a rational number and it is possible to calculate any rational number on an abacus. Thus, you can approximate any number on an abacus.
 
Well, I am still unsure how exactly to calculate some of these basic numbers. I guess I could use the Maclaurin series for some of them. However, I can't find an algorithm for finding powers of numbers that are needed.

Perhaps, my dream of defeating our robotic overlords is doomed. :'(