Pain in the Ass Math

[Ralphis]

Hey everyone, I figured I'd post something sort of cool from my useless math book. You see, I'm taking IMP math and there are some problems that are seperate from class activities. In the back of the textbook are some challenging problems that we aren't required to do, but may do so if we want. Anyway, feel free to try and figure this out.

"Equally Wet"

1. Two delicate flowers were planted in a garden. The gardener, Lesie, 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 possibilities. (Reminder: The flowers are already in place, and Leslie needs to adjust the position of the sprinkler relative to the flowers.)

2. Now suppose Leslie plants three flowers and wants to know if it will still be possible to place the sprinkler the same distance from all three.

a. Determine which arrangements of the flowers (if any) will make this possible and which (if any) will make it impossible. (As in Question 1, Leslie will be looking for a place to put the sprinkler after the flowers have already been planted.)

b. For those arrangements for which it will be possible, describe how Leslie can find the correct location (or locations) for the sprinkler.

3. What about four flowers? Five flowers? Generalize as much as you can.

The task is to explain as fully as possible, for various cases, where Leslie can put the sprinkler in order to give the flowers the same amount of water.

I'm still trying to figure out how to explain this one. I'm curious to see what you guys come up with. Good luck!

If you guys try this and enjoy it, I'll post another.

[Grimm]

I'm guessing you should put the sprinkler in the center of the arrangement. Yeah.

[The Ultimate DooMer]

1. Between the two, exactly in the middle so they're the same distance from the sprinkler.

2/3. The text in question 2 suggests that she's already planted the two flowers from question 1, so all she has to do is turn on the sprinkler (making sure it only just reaches the 2 flowers), mark spots somewhere on the outside edge of the wet circle left by the water and plant all other flowers on them.

Or you could do it the conventional way and measure the distances.

[Grazza]

[Fredrik]Put the sprinkler so far from the flowers that no water reaches any of them. They then all get an equal amount of water, no matter how many of them there are. Problem solved.[/Fredrik]

[Sharessa]

Heh, that or plant them in a circular/equidistant arrangement. Thats the only way I can figure.

[Lüt]

Tell Leslie to quit being a lazy hag and use a garden hose herself.

[Sharessa]

Also, WTF is she doing planting just 2-3 flowers in her garden. Those better be pretty impressive or big flowers, or she's a retarded landscaper.

[Chopkinsca]

Buy plastic flowers.
QED

[Ichor]

Rain

[fraggle]

1. Two delicate flowers were planted in a garden. The gardener, Lesie, 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 possibilities. (Reminder: The flowers are already in place, and Leslie needs to adjust the position of the sprinkler relative to the flowers.)

Draw a locus of points equidistant from the two flowers. That is, draw a straight line between the two flowers. Find the midpoint. The locus is a line stretching "to infinity" at right angles to the first line and passing through the midpoint of the first line. You can place the sprinkler anywhere on the locus.

2. Now suppose Leslie plants three flowers and wants to know if it will still be possible to place the sprinkler the same distance from all three.

a. Determine which arrangements of the flowers (if any) will make this possible and which (if any) will make it impossible. (As in Question 1, Leslie will be looking for a place to put the sprinkler after the flowers have already been planted.)

b. For those arrangements for which it will be possible, describe how Leslie can find the correct location (or locations) for the sprinkler.

Draw a circle which passes through all the flowers and place the sprinkler at the midpoint. I think you can always do this, but I might be wrong.

3. What about four flowers? Five flowers? Generalize as much as you can.

For more than three, it is only possible if all flowers are on a circle, and the sprinkler can be placed at the center.

[DooMBoy]

Don't plant flowers, use the space where the flowers currently reside as a place to store the bodies of people you plan to kill in the future.

[Planky]

At least then you won't have to worry about compost

[Cyb]

Select a random point on the ground, call it x. Now plant every flower y units from point x in any direction (assuming level ground). Now place the sprinkler on point x (generalization for question 2 and 3).

fraggle got #1 right, of course :)

[Grazza]

Cyb said:

Select a random point on the ground, call it x. Now plant every flower y units from point x in any direction (assuming level ground).

But the original post stipulated:
(As in Question 1, Leslie will be looking for a place to put the sprinkler after the flowers have already been planted.)

Anyway, isn't it normally spelt Lesley when it's a girl's name?

fraggle said about the three-flower case:
Draw a circle which passes through all the flowers and place the sprinkler at the midpoint. I think you can always do this, but I might be wrong.

If "Leslie" has planted the three flowers in a straight line, then that midpoint will be at infinity, which brings us back to the Fredrik-style answer I gave earlier.

[Fredrik]

Yeah. This is trivial.

[fodders]

Put down 3" of concrete and sell the sprinkler.

[zark]

fodders said:

Put down 3" of concrete and sell the sprinkler.

Genius.

[fraggle]

Grazza said:

If "Leslie" has planted the three flowers in a straight line, then that midpoint will be at infinity, which brings us back to the Fredrik-style answer I gave earlier.

Quite right. Touche'.

[cycloid]

the locus answer given earlier also allows you to adjust the poisition of the sprinkler dependant on how much water you want the flowers to get. basically it's a triangle with the sprinkler at the corner closest to you and the flowers at the other two corners.

once you start adding more flowers then it starts to become a circular thing

[Cyb]

Grazza said:

But the original post stipulated:
(As in Question 1, Leslie will be looking for a place to put the sprinkler after the flowers have already been planted.)

I did that :P You plant the flowers and then choose point x to place the sprinkler :D

[Fredrik]

More advanced arrangements may still be possible if we are allowed to warp spacetime.

[Ralphis]

Cyb said:

Select a random point on the ground, call it x. Now plant every flower y units from point x in any direction (assuming level ground). Now place the sprinkler on point x (generalization for question 2 and 3).

fraggle got #1 right, of course :)

The flowers are already planted and their coords aren't specified. Anyway, Fraggle won

[Ichor]

Why is she using a circular sprinkler anyway? It should be one that sweeps back and forth over itself along a line. That way, they will all get the same amount of water, regardless of the arrangement (except at the very edges where the sprinkler stops for a moment before moving in the opposite direction).

[Sharessa]

Grazza said:

Anyway, isn't it normally spelt Lesley when it's a girl's name?

No.

[Kid Airbag]

This is a "challenge" problem?

It's common fucking sense!

[Fredrik]

Everything is easy if you know it.

[Sharessa]

Kid Airbag said:

This is a "challenge" problem?

It's common fucking sense!

Yeah really. I learned this stuff in math, and the farthest I got was Geometry.

[Ralphis]

Kid Airbag said:

This is a "challenge" problem?

It's common fucking sense!

The point was to prove how you knew. All cases aren't just 'in the middle'

[Grimm]

I believe they are. So long as the flowers are arranged in a regular polygon, just pretend said polygon is inscribed in a circle, and place sprinkler at midpoint of said circle . . . right?

But as Ichor said, an arc sprinkler would be best anyway.

[Cyb]

Ralphis said:

The flowers are already planted and their coords aren't specified. Anyway, Fraggle won

do I at least win the booby prize?


mmmm boobies