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

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In summary, the conversation discussed the mathematical expression e^\pi - \pi = 20 and its accuracy as an approximation of an integer. The conversation also referenced a comic from XKCD that illustrates the concept of "almost integers."
  • #1
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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  • #2
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).
 
  • #3
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.
 
  • #4

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

What is "Exp[π] - π"?

"Exp[π] - π" is a mathematical expression that represents the difference between the value of the mathematical constant e raised to the power of π (approximately 23.14) and the value of the constant π (approximately 3.14).

Why is "Exp[π] - π" significant?

The expression "Exp[π] - π" is significant because it is an example of a transcendental number, meaning it cannot be expressed as a finite decimal or fraction. It is also closely related to the famous Euler's identity, e^(iπ) + 1 = 0, which connects five of the most important mathematical constants: e, π, i, 1, and 0.

How is "Exp[π] - π" calculated?

"Exp[π] - π" is calculated by first finding the value of e^(π) and then subtracting the value of π. This can be done using a scientific calculator or by using a computer program such as Python or Mathematica.

What is the approximate value of "Exp[π] - π"?

The approximate value of "Exp[π] - π" is 19.14. This value is significant because it is an irrational number, meaning it cannot be expressed as a finite decimal or fraction.

What are some real-world applications of "Exp[π] - π"?

One real-world application of "Exp[π] - π" is in the field of computer science, specifically in the study of algorithms and data structures. The number is also relevant in physics and engineering, particularly in the study of waves and oscillations. Additionally, it has been used in the development of encryption algorithms for computer security.

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