Solving an annoying equation

  • Thread starter Thread starter MexWave
  • Start date Start date
AI Thread Summary
Mark is attempting to convert pixel coordinates to geographical latitude and longitude in Microsoft's Virtual Earth but is struggling with the equation a = (1 + sinLatitude) / (1 - sinLatitude). He seeks assistance in expressing "sinLatitude" in terms of "a." A user responds with the solution, stating that sinLatitude = (a - 1) / (a + 1) appears to be correct after testing. Mark confirms that this solution works for his needs. The discussion highlights the challenge of mathematical conversions in programming.
MexWave
Messages
2
Reaction score
0
[SOLVED] Solving an annoying equation... please help

Hi,

I'm playing with the code used to convert between on-screen pixel co-ordinates and geographical lat-lon in Microsoft's Virtual Earth. They have a page that explains how to go one way (including example code) at http://msdn2.microsoft.com/en-us/library/bb259689.aspx" but it only explains how to get the pixel co-ordinate from a lat-lon and not the other way around.

I decided it shouldn't be too difficult to solve myself so I started on it. I'm now stuck at the following point:

a = (1 + sinLatitude) / (1 - sinLatitude)

I need to calculate "sinLatitude" in terms of "a" but I don't seem to be able to do it. Can anyone please give me some pointers, or do I need to approach the whole thing another way?

Many thanks,

Mark
 
Last edited by a moderator:
Mathematics news on Phys.org
Is sinLatitude = (a-1)/(a+1) the answer you are looking for?
 
After running a few tests, it certainly seems to be!

Many thanks for your help!

Mark
 
Last edited:
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top