# I am looking for interesting physics/math or logic problems

1. Dec 5, 2015

Well, the tittle is self-explanatory. If anyone has an interesting problem or puzzle. I will be grateful if you could post it.

2. Dec 5, 2015

### Staff: Mentor

Why does a mirror change left and right but not up and down?

3. Dec 5, 2015

4. Dec 5, 2015

### OmCheeto

Why is it not possible to solve the equation: y = x - sin(x)?

Solving for y is simple, but solving for x, is, um, well, you asked for interesting math problems.

ps. I first asked this question, 30 years ago. And after 20 years of getting no answers, I offered a \$100 prize to anyone who could explain it to me. Fortunately, I ran into a mathematician one day, and he explained it, quite to my satisfaction. Can you do the same?
pps. Don't spend too much time on the problem, if you don't know the answer, as, it will consume many minutes of your life.

5. Dec 5, 2015

### CWatters

A cow stands in a circular field of radius R. It's tethered to a post on the boundary by a rope. How long is the rope if the cow can eat half the grass in the field? Ignore length of cow.

And no I don't have the answer.

6. Dec 6, 2015

I think I solved your problem. If you rearrange this equation you should get that r=(something)xd, where r is the radious of the field and d the length of the rope, that should be the relationship between the rope and the radius of the field. I hope I am right.

EDIT> Sorry there is a mistake on my work, I should post the correct solution tomorrow.

Last edited: Dec 6, 2015
7. Dec 6, 2015

8. Dec 7, 2015

9. Dec 7, 2015

### Mercy

Is it because they are linearly independent? Like how if you have y = sin(x) + cos(x) you can't isolate x?
In my head I just expand out the power series for sine and then you end up with an infinite degree polynomial which can't be reduced, not sure if that's the answer though

10. Dec 7, 2015

### Staff: Mentor

Or is it simply because $π$ is transcendent?

11. Dec 7, 2015

### OmCheeto

all bolding mine.

Perhaps you two should ask these questions in the "Maths" forum. I haven't spoken the language of maths in 30 years, so I have no idea what you two are talking about.
I've posted in the Maths forum about twice, in the last 8 years. Both times, I sensed that people thought that I didn't quite speak right, so I never went back.

12. Dec 7, 2015

### Staff: Mentor

Have you considered the fact that this might have been not your fault? I'm out for 20 years now and they leave nothing untried to shoot me down.

13. Dec 7, 2015

### Mercy

haha fair enough, do you remember what the answer you were satisfied with was?

14. Dec 7, 2015

### OmCheeto

It had something to do with taking the inverse of an infinite series.

If you solve for the first term of the sine series:

you get x

So y = x - sin(x) reduces to:

I was able to get that far.

Upon showing this to my acquaintance, he told me that taking the inverse of an infinite series was uglier than the original infinite series.
I checked that out, and he was correct.

Now I'm not saying the equation is impossible to solve, but, well, 30 years, is 30 years.

15. Dec 7, 2015

### Staff: Mentor

So basically we agree on: "It's getting uglier and uglier the more you try." Guess that's something for number theorists. They love those expressions.

16. Dec 7, 2015

### Mercy

Ah I see, in math that is known as the power series of sin(x). When you expand the series it becomes:

$$\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ...$$

and that goes on to infinity. So when you take y = x - sin(x) it cancels out that first x term in the series and you're left with an infinite degree polynomial that can no longer be reduced to sin(x) (since that first x is gone). It's (in almost all cases) impossible to isolate x in an infinite degree polynomial, therefore it's impossible to isolate x in y = x - sin(x)

I think that's the answer to the question

17. Dec 7, 2015

### rootone

If you have a spherical surface and are asked to place 5 points on it which are all equidistant from each other, what would be the closest you can get to that.
(Apart from putting all the points at the same place!)

18. Dec 9, 2015

### electric jake

Should Integers exist when there is an infinite amount of decimal numbers between them. If so why?

19. Dec 9, 2015

### rcgldr

A physics problem that has been brought up a few times in the past, requires calculus. Two point masses, each with mass M, are in space free from any outside force and initially not moving with respect to each other, separated by distance R. How long before the two point masses collide due to gravity?

Thought problem, can a sailcraft out run the wind that propels it? Say a sand yatch is tacking downwind at some angle, can it's downwind component of speed exceed the wind speed? Or can a wind driven vehicle where it's wheels drive a propeller against the wind go faster directly downwind than the wind?

A flat mirror reverses forwards and backwards (along a line perpendicular to the surface of the mirror), not left and right or up and down.

20. Feb 9, 2016