Leslie the gardener and equally watering each of her flower. A math Story Problem!?

The Gardener Leslie has a sprinkler that sprays water around in a circle. The Closer a flower is to the sprinkler the more water it gets.





To be sure that her flowers each get the same amount of water Leslie needs to place the sprinkler where it will be the same distance from each of the flowers.





What are her choices about where to put the sprinkler? Describe all the possiblilities. Remember the flowers are already in place and cannot be moved only the sprinkler can be moved.





1. Suppose Leslie was trying to water two flowers equally


* Now she's trying to water 3 flowers Equally


* Now she's trying to water 4 flowers Equally.


* Now she's trying to water 5 flowers Equally


* Now she's trying to water 6 flowers Equally .





For each number of flowers describe how Leslie can find the correct location (or locations) for the sprinkler.
Leslie the gardener and equally watering each of her flower. A math Story Problem!?
That's a pretty neat way to phase that problem. I'm not sure what control we have over the radius of the sprinkler, so I'll assume we can control that however we like.





The case of 2 flowers is pretty easy (you'd just put it at the midpoint - which is half way between the two of them).





For 3 flowers, you need a very special point called the circumcenter. Assuming the three points aren't all collinear (on the same line), then it's possible to find a circle that passes through all 3 points (flowers). This point is called the circumcenter, and if you placed the sprinkler there, would hit each of the flowers equally.





For 4-6, there are probably a variety of answers, so I'll leave that as a mental exercise for you to ponder.
Reply:For 2 flowers:


On any point of the line that is perpendicular to the one that connects the flowers and intersects it on the middle of their distance.





For 3 flowers:


If they are not collinear (on the same line) then you can find the circumcenter which is the center of the (imaginary) circle on which every flower is on.





For n%26gt;3 flowers:


If any three flowers are colinear then there is no point when you can place it.


In order to have a point where you can place it the flowers must be parts of a (imaginary) circle.


If there is no such circle you find ie the point that has minimum distance from the flowers: f(x,y)=dist((x,y),flower1)+dist((x,y),fl... and finding the point(s) where f gets the minimum value. Same you can find any other "good" points.affiliate reviews