What is the value of e^\pi - \pi?

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Discussion Overview

The discussion revolves around the expression eπ - π and whether it equals 20. Participants explore the mathematical implications and interpretations of this expression, including its approximate value and related concepts.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant questions the validity of the claim that eπ - π equals 20 and seeks further clarification on how to approach the problem.
  • Another participant suggests that the claim may have originated from an engineer, noting that the actual difference is approximately 9.00021 x 10-4, indicating it is not a true equality.
  • A third participant refers to the expression as an "almost integer" and mentions that there are other similar expressions documented in Mathworld.
  • A later reply identifies a comic as the source of the misunderstanding regarding the expression, indicating a misinterpretation of its meaning.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the claim that eπ - π equals 20, with multiple viewpoints presented regarding its approximate value and interpretation.

Contextual Notes

There are unresolved assumptions regarding the definitions and interpretations of "almost integers" and the context in which the original claim was made.

rohanprabhu
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I read somewhere that [itex]e^\pi - \pi = 20[/itex].

1. Is it true?
2. I tried finding out.. but all I've reached till is:

[tex] e^{\pi} = \cos{(i \pi)} - i \sin{(i \pi)}[/tex]

what do i do from here on>
 
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Probably it was an engineer who told you :smile:
The difference with 20 is about 9.00021 x 10-4. So it's an approximate equality (which is, for a mathematician, of course not an equality).
 
It's a nice example of an "almost integer". Mathworld has a nice on them, its got many other expressions that are "almost integers" like yours.
 

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