TheYorks Posted July 2, 2002 Share Posted July 2, 2002 Hello. Stumbled across this site last week and thought it looked like a great excuse to play with my GPS. The family and I found our first three caches this past weekend. Now we're hooked! We have started working on a couple of the more challenging ones that require triangulation and figuring out points from the area of circles and that sort of thing. Math was never one of my strong subjects, although I did relatively well in geometry. I know some of the basics of how circles can be used to find points, enough so I can use Topo USA to draw objects and figure out the location anyway. Some of the more complicated things have me scratching my head though. I'd like to learn the math involved so I can figure these things out "in the field" if necessary. Perhaps somebody can point me to a web site or other reference that explains the formulas commonly required here and how to use them. I tried doing a web search, but it's hard to find something when you don't really know what you're lookikng for. I found some sites that will calculate triangulations for you, but so far none that really explain the formulas. Thanks for any help. Quote Link to comment
+welch Posted July 3, 2002 Share Posted July 3, 2002 which cache(s) are you having trouble with? Quote Link to comment
TheYorks Posted July 3, 2002 Author Share Posted July 3, 2002 Well, I'm not really having trouble so much as just wanting to know the math behind the answers. Like I said, I've been able to figure them out so far using Topo USA. A couple examples would be Another Clue from Dewey and Pies Are Square. I can get the answers using software, but if someone asked me to figure it out with a paper and pencil, I wouldn't even know where to start. Quote Link to comment
+ApK Posted July 3, 2002 Share Posted July 3, 2002 With the standard cache icons, I'd feel sorry for those intrepid soles who don't read clues or descriptions. quote:Originally posted by TheYorks: Well, I'm not really having trouble so much as just wanting to know the math behind the answers. Like I said, I've been able to figure them out so far using Topo USA. A couple examples would be http://www.geocaching.com/seek/cache_details.asp?ID=18530 and http://www.geocaching.com/seek/cache_details.asp?ID=26750. I can get the answers using software, but if someone asked me to figure it out with a paper and pencil, I wouldn't even know where to start. Quote Link to comment
+sbell111 Posted July 3, 2002 Share Posted July 3, 2002 You might have some luck starting at this site: http://www.math2.org/index.xml Quote Link to comment
+MrGigabyte Posted July 3, 2002 Share Posted July 3, 2002 quote:Originally posted by TheYorks: A couple examples would be ... http://www.geocaching.com/seek/cache_details.asp?ID=26750. if someone asked me to figure it out with a paper and pencil, I wouldn't even know where to start. First step is to convert the given coordinates to UTM. This will allow you to work with straight distances, rather than arc distances. You can do this conversion right in your GPSr simply be entering the lat and long of each point in the given format, then change your GPSr position format settings to UTM. NOTE: the lat & long given on the cache page are in decimal degrees, NOT minutes.decimal minutes. For each point, you need to solve the distances to the other 2 points. Subtract 2 northing values and the corresponding easting values to obtain a dY and dX for each course. Use Pythagoras to solve the distance point to point. Do this for all 3 pairs. Hint: d^2 = dX^2 + dY^2 You also will need the bearing of this course. Hint: arctan(dY/dX) Now, To find the distance from each given point, you need to solve the radius of a circle knowing the area. Hint: Area = PI * R^2 Knowing the 3 distances to the cache from the known points and the 3 distances between the given points, you can now solve the coordinates of the cache. This problem is over-determined. that is, you only need two distances from known points to solve a 2D location. However, a 2 point solution is ambiguous as there are two possible solutions. Depending on which 2 points you choose to use, you may be able to tell which solution is correct as one may fall in a inaccessible location. I would suggest you solve all three as this is a good check. You need to do a distance-distance intersection from 2 of the known points and using the radii distances. Solve the angles at each known point that are subtended by the cache course and the other known point course. Hint: a^2 = b^2 + c^2 -2bc cos(A) Apply the angle to the known bearing from the two known points to solve the bearing to cache. Solve the coordinates of using this bearing and the previously solved radius distance. Hint dY = sin(A)*R, dX = cos(A) * R Apply these dY and dX values to the known northing and easting of the known point used to solve the coordinates of the cache Repeat for all three points to ensure you have the non-ambiguous solution and also that you have not made any errors. All three should result in the same coordinates. Enter these UTM values into your GPSr as a new waypoint, then change your position format from UTM back to ddd mm.mmm That's, it... your ready to hunt Quote Link to comment
+parkrrrr Posted July 3, 2002 Share Posted July 3, 2002 quote:Originally posted by ApK:With the standard cache icons, I'd feel sorry for those intrepid soles who don't read clues or descriptions. Unfortunately, there's no icon for "puzzle multicache" so someone had to choose which icon to use for one of those caches. In fact, there's not an icon for a puzzle cache of any sort: the "?" icon description says "Unknown Cache For whatever reason, this cache either does not have a designation or is a surprise to the hunter." though I've seen it used to mean a puzzle cache. Quote Link to comment
TheYorks Posted July 3, 2002 Author Share Posted July 3, 2002 Ok, I asked for it I guess. It's gonna take me a while to digest all that. I'm gonna have to dig out the old scientific calculator I see... Been a long time since I was in high school. That's probably the last time I saw any of this. Thanks for and explanation - and the link. Quote Link to comment
TheYorks Posted July 3, 2002 Author Share Posted July 3, 2002 Ok, I asked for it I guess. It's gonna take me a while to digest all that. I'm gonna have to dig out the old scientific calculator I see... Been a long time since I was in high school. That's probably the last time I saw any of this. Thanks for and explanation - and the link. Quote Link to comment
+scoobydum Posted July 3, 2002 Share Posted July 3, 2002 Pi aren't square! Cornbread are square... Pi are round!! Couldn't resist. m Mike "mighkel" Underwood ------------------------ STURGEON GENERAL WARNING: Fishing can decrease the risk of long-term employment, a meaningful relationship, and any chance of financial independence... Oh well. Quote Link to comment
+scoobydum Posted July 3, 2002 Share Posted July 3, 2002 Pi aren't square! Cornbread are square... Pi are round!! Couldn't resist. m Mike "mighkel" Underwood ------------------------ STURGEON GENERAL WARNING: Fishing can decrease the risk of long-term employment, a meaningful relationship, and any chance of financial independence... Oh well. Quote Link to comment
+ApK Posted July 5, 2002 Share Posted July 5, 2002 quote:Originally posted by Warm Fuzzies - Fuzzy: quote:Originally posted by ApK:With the standard cache icons, I'd feel sorry for those intrepid soles who don't read clues or descriptions. Unfortunately, there's no icon for "puzzle multicache" so someone had to choose which icon to use for one of those caches. In fact, there's not an icon for a puzzle cache of any sort: the "?" icon description says "__Unknown Cache_ For whatever reason, this cache either does not have a designation or is a surprise to the hunter._" though I've seen it used to mean a puzzle cache. http://216.202.195.127/warm.gif Yeah, it's the ? icon I was thinking of. Perhaps there should be some other sort of indication feature that this is a "math cache" or otherwise not at the given coords? Quote Link to comment
HangGlider Posted July 5, 2002 Share Posted July 5, 2002 quote:Originally posted by TheYorks: A couple examples would be ... http://www.geocaching.com/seek/cache_details.asp?ID=26750. if someone asked me to figure it out with a paper and pencil, I wouldn't even know where to start. Try your local community college - and don't be afraid to start with one level of math lower than what you feel comfortable with. When I started back to college I started w/ bonehead algebra - and I'm 48 ! I'm clear through Linear algebra and Differential Equations now! If I can do it ( I flunked High school algebra)- so can you! Good luck! HangGlider [This message was edited by HangGlider on July 06, 2002 at 10:10 AM.] Quote Link to comment
HangGlider Posted July 5, 2002 Share Posted July 5, 2002 quote:Originally posted by TheYorks: A couple examples would be ... http://www.geocaching.com/seek/cache_details.asp?ID=26750. if someone asked me to figure it out with a paper and pencil, I wouldn't even know where to start. Try your local community college - and don't be afraid to start with one level of math lower than what you feel comfortable with. When I started back to college I started w/ bonehead algebra - and I'm 48 ! I'm clear through Linear algebra and Differential Equations now! If I can do it ( I flunked High school algebra)- so can you! Good luck! HangGlider [This message was edited by HangGlider on July 06, 2002 at 10:10 AM.] Quote Link to comment
+majicman Posted July 8, 2002 Share Posted July 8, 2002 Yeah, when you get done with that little math puzzle, you might try mine "Seven Signs on SE 29th" (hehehehe): http://www.geocaching.com/seek/cache_details.asp?ID=22739 --majicman (Always trade UP in both quantity and quality and Geocaches will be both self-sustaining and self-improving!) Quote Link to comment
+Lil Devil Posted July 8, 2002 Share Posted July 8, 2002 quote:Originally posted by majicman:Yeah, when you get done with that little math puzzle, you might try mine "Seven Signs on SE 29th" (hehehehe): http://www.geocaching.com/seek/cache_details.asp?ID=22739 Is it just me, or is logging a "find" on ones own cache a bit unethical? Seems like a sneaky way to inflate ones score. Lil Devil Quote Link to comment
+OzzieSan Posted July 8, 2002 Share Posted July 8, 2002 Found all mine also (didnt even need GPS). Quote Link to comment
+OzzieSan Posted July 8, 2002 Share Posted July 8, 2002 Found all mine also (didnt even need GPS). Quote Link to comment
+ApK Posted July 9, 2002 Share Posted July 9, 2002 Who's keeping score? I wasn't aware of a competition. BTW, LilDevil, I see you only have 11 posts on the forums...I'm beating you! quote:Originally posted by LilDevil: [ Is it just me, or is logging a "find" on ones own cache a bit unethical? Seems like a sneaky way to inflate ones score. Quote Link to comment
+ApK Posted July 9, 2002 Share Posted July 9, 2002 Who's keeping score? I wasn't aware of a competition. BTW, LilDevil, I see you only have 11 posts on the forums...I'm beating you! quote:Originally posted by LilDevil: [ Is it just me, or is logging a "find" on ones own cache a bit unethical? Seems like a sneaky way to inflate ones score. Quote Link to comment
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