Random: Any way to calculate Transcendental numbers using abacus?

In summary, the conversation discusses the possibility of using a Japanese abacus to approximate transcendental quantities, such as cos(17). The speaker also mentions a work-in-progress guide on using the abacus for advanced calculations and the similarity between an abacus and an electronic computer. The conversation concludes with the speaker expressing uncertainty about calculating certain numbers and joking about the possibility of using the abacus to defeat robotic overlords.
  • #1
Pinu7
275
5
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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  • #2
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:​
 
  • #3
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
 
  • #4
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.
 
  • #5
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. :'(
 

What is a transcendental number?

A transcendental number is a real number that is not a root of any non-zero polynomial equation with integer coefficients. Examples of transcendental numbers include pi and e.

Can transcendental numbers be calculated using an abacus?

No, it is not possible to calculate transcendental numbers using an abacus. Abacuses are limited to performing basic arithmetic operations and cannot handle the complexity of transcendental numbers.

Is there any way to approximate transcendental numbers using an abacus?

Yes, it is possible to approximate transcendental numbers using an abacus by using a series of rational numbers that get closer and closer to the desired transcendental number. However, this is not an exact calculation and will only provide an approximation.

What is the significance of calculating transcendental numbers?

Transcendental numbers are important in mathematics as they are used in various mathematical proofs and can help to solve complex equations. They also have applications in fields such as physics, engineering, and computer science.

Are there any other methods or tools that can be used to accurately calculate transcendental numbers?

Yes, there are various mathematical methods and computer programs that can accurately calculate transcendental numbers. These include infinite series, algorithms, and computer software such as Mathematica or MATLAB.

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