# Numb3rs Challenge

I am by no means a mathmatician. I guess you could say that I am a mathematically inclined individual, but never made anything of it until I was in my 30's and became a software engineer. Although I've never taken the math classes that I should have, the concepts still fascinate me, and I have a question.

I was watching an episode of Numb3rs and they stated what seemed like a fairly simple geometry/trigonometry question that I just could not wrap my brain around entirely.

They stated that with a few photos of the same location, by looking at the shadows caused by the sun, and knowing 1 distance in the pics and knowing the "exact" time stamp of the images, that they could calculate the exact (within a hundredth of a degree) location of the photos.

As I said before, I am no math expert, but wouldn't you also need 1 angle? Is what they said accurate? Could you calculate the angle based on the timestamps and the shadows given the height of the object that made the shadow?

Edit: I'm curious, If I posted 4 pictures (15 min apart, with accurate timestamps) with at least 1 item that was a known length, would some one take me up on the challenge of locating where the photos were taken?

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The sun moves over the time and its relative movement is different considering different places on earth. You can easily extract an angle if you know a distance from the picture too. –  Listing Jul 9 '11 at 12:22
There exists a book Devlin K., Lorden G. The numbers behind NUMB3RS books.google.com/books?id=Wm6SCRVby0kC Although I do not think that htey deal with this particular question, it might be interesting for you, if you're a fan of that series. –  Martin Sleziak Jul 9 '11 at 13:28
It's a modern twist on the Sherlock Holmes story ‘The Musgrave Ritual –  Gareth Rees Jul 9 '11 at 20:40

Two minor points: If the accuracy is supposed to be within one hundredth of a degree, you'll probably have to take into account that the Earth is a geoid, not a sphere, since the ellipticity is about $1/300$. And you need to be able to figure out at what angle the picture was taken relative to gravity, not relative to the ground, which might be sloped; that's going to be more difficult and might require the picture to contain liquid surfaces or plumblines :-) –  joriki Jul 9 '11 at 15:51