In class, we've talked about how the location of a buried treasure can be described by using a displacement vector. If a treasure hunter knew where to start (the origin) and the displacement vector, he or she would be able to find the treasure.
What about other coordinate systems? Suppose instead of a displacement vector, the treasure hunter knew exactly how far the treasure was away from two fixed points. If this were the case, would he or she be able to dig up the treasure on the first try? How many possible locations for the treasure would there be?
If someone were to use two fixed points instead of the displacement of a vector, it would be more difficult to find the treasure. Using displacement, there is an angle and a distance to go off of. Using two points, there would be more math to do to find the exact spot the treasure would be. Plus, this method leaves more room for human error.
ReplyDeleteAs goat said displacement would be more accurate. There would be no error. Not only does it give you length it also gives you angle measures.
ReplyDeletethere would be two possible locations the treasure could be. Inroder to determin the location of the treasure the hunter would draw two circle using the known points as the origin and the distance the treasure is from that point as the radius of the circle. the two locations the circles intersect at would mark the possible locations of the treasure
ReplyDeletei agree that displacement would be a more efficient method because it does give a distance and also and angle, which seems like it would be more accurate than guessing between two known points
ReplyDeleteIt wouldn't necessarily have two possible locations. If the distance given between the two points was the midpoint of a line drawn between them, there would only be one. If, for instance, point A was at (3,5), and B was at (7,5), and the distance from each of the points was 2, there is only one possible location: (5,5). So there can be an instance where there is only one location. However, as Anonymous said, there could be instances where two possible locations would exist.
ReplyDeleteVery insightful comments, roseDesire and Anonymous! However, you are both thinking of both points and the treasure as all being in the same plane... ... After all, aren't most treasures buried? Does thinking in three dimensions change anything?
ReplyDeleteIt seems like we agree that in two dimensions, we're looking that how two circles might intersect. What is the 3D analog of this?
Thanks for the comments this week!
ReplyDeletethe 3D analog of this is where two spheres intersect. If you are considering 3 domensions then there are an infinite number of possible locations i believe. However most treasure hunters follow a map to guide them to the X, which is just 2D.
ReplyDelete