Incorrect Homework Statement: Identifying an Error in a Given Problem

  • Thread starter Thread starter -EquinoX-
  • Start date Start date
AI Thread Summary
The discussion centers around an incorrect homework statement regarding the value of pi. Participants clarify that while pi is often approximated as 3.14, it is actually an irrational number and cannot be expressed as a simple decimal. The distinction between approximation and exact value is emphasized, highlighting that pi is transcendental and has infinite, non-repeating digits. The conversation also references external resources for further understanding of pi. Accurate comprehension of pi is crucial for solving related mathematical problems correctly.
-EquinoX-
Messages
561
Reaction score
1

Homework Statement



http://img292.imageshack.us/img292/7638/capturedv5.jpg
http://g.imageshack.us/img292/capturedv5.jpg/1/

Homework Equations





The Attempt at a Solution


The one that I check marked is incorrect, am I missing something?
 
Last edited by a moderator:
Physics news on Phys.org
-EquinoX- said:
The one that I check marked is incorrect, am I missing something?
You might like to reconsider that statement about pi, Equi.
 
hmm.. isn't pi = 3.14?
 
-EquinoX- said:
hmm.. isn't pi = 3.14?

Pi is an irrational number, 3.14 is very much rational. What do you think?
 
-EquinoX- said:
hmm.. isn't pi = 3.14?

Pi is approximately 3.14 (to two decimal places), not equal to.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...

Similar threads

Back
Top