Think Differently
ltlprints.com
ltlprints.com
Сказка ложь да в ней намек
Добрым молодцам урок.
Tale of sense, if not of truth!
Food for thought to honest youth.
http://journal.petajinnathandersen.com/2008/03/fairy-tale-fr...I gave a very elegant non-constructive proof which showed that a solution existed without giving any hint of what the solution was -- but the instructor expected students to provide a solution. I ended up deciding that it wasn't worth the effort of formally appealing the grade, but I still think that I should have gotten the marks -- it wasn't my fault that the exam didn't ask the question the instructor intended to ask.
I had good math professors. Too bad I wasn't a good math student.
If the question actually asked to demonstrate that a solution existed, any professor worth her salt will give you credit for doing that if you point it out to her. It's quite possible you weren't given full marks because your exam was one of hundreds that needed to be graded that week.
- http://www.overcomingbias.com/2007/10/outside-the-box.html
Deleted comment
PV = nRT; n = m/M
PV = mRT/M; V = m/(rho)
p*m/(rho) = mRT/M
p/(rho) = RT/M
(rho) = pM/RT
p + (dp) = p + (rho)g(dh)
(dp) = (rho)g(dh)
(dp) = pMg(dh)/RT
(dp)/p = Mg(dh)/RT
integrate 0 to p (dp)/p = integrate h to 0 [Mg(dh)/RT]
ln(p) = -Mgh/RT + c
take h = 0 at bottom of building, then
ln(p_at_h=0) = c => read c from barometer to get constant
now, at height h we will read p_at_h=height from barometer, then:
ln(p_at_h=height) = -Mgh/RT + ln(p_at_h=0)
Mgh/RT = -ln(p_at_h=height) + ln(p_at_h=0)
Mgh = -RTln(p_at_h=height) + RTln(p_at_h=0)
-----------------------------------------------------------------------------
| height = -RTln(p_at_h=height)/Mg + RTln(p_at_h=0)/Mg =
| = RT/Mg(ln(p_at_h=0) - ln(p_at_h=height)) =
| = RT/Mg(ln(p_at_h=0/p_at_h=height))
-----------------------------------------------------------------------------
p in Pascals
g = 9.81
R = 8.31
T = temperature in absolute units
M = 28.97
I hope i did it right ;)
And also by years and years of meticulous surveying,
The Great Arc by John Keay tells the story of how the height of the world's tallest peak was measured.
Hint: You start from zero and work your way up :-)