How Can We Generate Trig Tables with the 'Many Worlds' Approach?

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Discussion Overview

The discussion revolves around methods for generating trigonometric tables, exploring various mathematical approaches and a speculative "many worlds" perspective. It includes theoretical considerations and practical implications of different calculation methods.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about the necessary knowledge for generating a trigonometric table.
  • Another suggests using a Taylor expansion to achieve arbitrary precision, emphasizing the need for addition and multiplication skills, along with computational resources.
  • A different participant proposes using angle addition formulas and known triangles as an alternative method for calculation.
  • One participant introduces a non-deterministic "many worlds" approach, humorously suggesting that writing down random digits could yield correct results in only those universes where the results are accurate, although they note the challenge of implementing this idea.
  • This participant also mentions the difficulty of calculating certain constants, like Chaitlin's \Omega, without straightforward methods.

Areas of Agreement / Disagreement

Participants present multiple competing views on how to generate trigonometric tables, with no consensus reached on a preferred method.

Contextual Notes

The discussion includes speculative elements, particularly regarding the "many worlds" approach, and lacks resolution on the practicality or validity of the proposed methods.

Who May Find This Useful

Individuals interested in mathematical methods for trigonometric calculations, as well as those exploring unconventional theoretical approaches in mathematics and physics.

phibonacci
What is the required knowledge to generate a trig table?
 
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A Taylor expansion of the function you want to look at will let you calculate it to arbitrary precision by taking enough terms. Then you just need to be able to add and multiply (and either a computer, or a lot of time!).
 
You can also calculate it by repeated application of the angle addition formulas, and a known triangle.
 
Last edited:
I prefer the nondetermanistic "many worlds" approach:
1. I write down random digits, hoping they're correct.
2. If they're wrong, the universe is destroyed.
We continue to exist only in those universes where I write the correct results.

This approach is especially effective for constants like Chaitlin's [tex]\Omega[/tex] where there's no easy way to calculate it. Of course, I haven't actually managed to implement step 2 yet. Research continues (see the IEDAB's methods for destroying the Earth for the foremost research).
 

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