What are the E, pi, phi constants relations

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Discussion Overview

The discussion centers around the relationships and identities involving the mathematical constants e, π (pi), and φ (phi). Participants explore various mathematical identities, series, and properties related to these constants, as well as their significance in mathematics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether constants like π and e have any significant relationships, suggesting that any perceived connections might be more mystical than mathematical.
  • Others present mathematical identities such as \( e^{i\pi} = -1 \) and discuss its implications, noting its relation to fundamental numbers in mathematics.
  • Power series for π and e are shared, with participants discussing their derivations and computational methods, including the use of scripts for calculations.
  • There is a discussion about the golden ratio φ, its definition, and its appearance in various mathematical contexts, including its relation to the Fibonacci sequence.
  • Participants explore the conditions for summations in the power series and express curiosity about formulas for calculating decimal places of π and e.
  • Some participants express uncertainty about the significance of certain equations and seek clarification on the derivation of constants and their relationships.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the significance of the relationships between the constants. Multiple competing views and interpretations remain throughout the discussion.

Contextual Notes

Some mathematical identities and series presented depend on specific conditions and assumptions that are not fully resolved in the discussion. The exploration of the golden ratio and Fibonacci sequence also introduces additional complexity that is not universally agreed upon.

  • #61
TTT is an aesthetic thing

Matt,

Your feedback of my TTT paper is appreciated. I'm always glad to have a "math smart" person give it gander. Forgive me as I realize it is a poorly done paper full of too much extranious opnion.. what can I say, I'm an artist/musician and my approach to math is aesthetic. I never claimed to be a mathematician or even "good" at math for that matter, fact is, I pretty well suck at math.

end of apology...

I didn't set out in the TTT to solve a problem. Mathematicians do that, I am not one of them. I found a ratio in the outer geometry of the Pyramid ie. (the e proportion). And there was no denying that it was there. I thought it was interesting. I looked at the Pi and Phi proportions and had long been awed by their coincidental occurrence in the Pyramid. Yes, I do know that coincedence is a reality. When I started playing with the angles I began substituting terms and ended up with an equation that was true. How could it be not true? My method was elementary and I was only dealing with identities and those identities led to an overall identity as opposed to a solution to a problem.

In the end I was looking at an equation with three unique angles embedded in it such that the equation was equal to "1". If the three angles in the equation could be anything else than what they are for the thing to equal "1" then I'd be interested to know what they would be.

That's all it is, just a curious correlation of three independent right triangles living together in a simple equation. But (and this is the kicker) three right triangles that are very nearly congruent.. only ever so slightly different in shape.. and that is aesthetic if nothing else.

Rick
 
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  • #62
wow... so if i spot that things are accurate to some completely artificial level of accuracy that makes it note worthy in such eulogising prose? the square root of two is 14 tenths, if you accept certain tolerances...
 
  • #63
I don't know how to respond to you Matt because I don't understand your thinking. Good luck in your endevours.

Rick
 
  • #64
but the number of days in a week divided by the number of fingers (and thumb) on one hand is almost equal to the square root of two, doesn't that suggest something to you about the people who set the number of days in a week?
 
  • #65
I know that you're not going to like this, but you brought it up so I'm going to say it anyway.

Take the number of fingers (and thumbs) most people have, and divide it by the number of days in a week.

10/7 = 1.4286

Also as you said

7/5 = 1.4

But get this, find the mid-point between the two, and you get even closer:

(10/7 - 7/5)/2 + 7/5 = 1.4143

It turns out than now you're only 7.215 * 10-5 out! Spooky! :biggrin:
 
  • #66
Or, the error is VERY NEARLY equal to:

(no. of days in week)/[(no. of fingers on both hands) ^ (no. of fingers on one hand)]

Oooooooooh !
 

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