Swedish Math problem i got. Seems to be easy. but not quite ?

  • Thread starter Cyrus1
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In summary, the conversation is about a math problem involving finding the best viewing angle in a movie theater. The person chose what they thought would be an easy problem but it turned out to be difficult. They have a method but the answer seems unrealistic and they are seeking help. There is some discussion about using a formula and drawing a sketch. One person suggests using a circle and the other person suggests a different approach using a diagram. The conversation ends with the person still unsure about the solution.
  • #1
Cyrus1
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Swedish Math problem i got. Seems to be easy. but not quite...?

This is a problem i chose because i thought it would be interesting as well as easy, however, i should have known better than to choose the last question in my maths book as my "essay" question. I have done it and i can't see how my method is wrong in any way. The answer i get is not realistic hence, something must be wrong. I will not show my calculations as it would take too long.

Question:
You are in a movie theatre. The screen is 8 m high and 2 meters from the ground as well as 3 meters from the first row of seats. All the seats are on an incline att an angle of 22 degrees. When you sit on a chair your eyes are 1 meter from the incline. Where on the incline are you to sit so that you will have the best viewing angle?
This is how it looks like and how i have thought a bit!
https://docs.google.com/drawings/d/1Ry5s05KkhwvfF1u8S2aAqYmMrkE92XgxNOYC-W7fS44/edit

The text translates to "what value of "h" will give the best possible viewing angle? i.e how far upp the incline must you walk?"
Answer i got was 2.56 meters. Any help would be appreciated.
 
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  • #2
Would you not want your eye to be level with the centre of the screen?
 
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  • #3
That seems reasonable. However i would need to prove that having the eye level at the centre gives the highest angle, something which i have no clue how to do. Should i use a^2=b^2+c^2 - 2bc(cos(A)) ?
 
  • #4
Cyrus1 said:
Should i use a^2=b^2+c^2 - 2bc(cos(A)) ?
That formula could be useful in some way but first you have to find out what you want to calculate.

Did you draw a sketch?

Jilang said:
Would you not want your eye to be level with the centre of the screen?
In the real world, probably. Here, not.
 
  • #5
mfb said:
That formula could be useful in some way but first you have to find out what you want to calculate.

Did you draw a sketch?

I want to calculate the highest possible value for Z, which you can see here. I differentiated a bit at the end when i got a function of h. I probably forgot to mention that it is necessary to have a function f(h)=Z
https://docs.google.com/drawings/d/1Ry5s05KkhwvfF1u8S2aAqYmMrkE92XgxNOYC-W7fS44/edit
 
  • #6
mfb said:
That formula could be useful in some way but first you have to find out what you want to calculate.

Did you draw a sketch?

In the real world, probably. Here, not.
Mfb, please remind me never go and see a movie with you, lest I end up with a stiff neck, lol!
 
  • #7
Cyrus1 said:
I want to calculate the highest possible value for Z, which you can see here. I differentiated a bit at the end when i got a function of h. I probably forgot to mention that it is necessary to have a function f(h)=Z
https://docs.google.com/drawings/d/1Ry5s05KkhwvfF1u8S2aAqYmMrkE92XgxNOYC-W7fS44/edit

If we are allowed stiff necks then...
Call the distance below the centre of the screen a, split z into z1 and z2 above and below the horizontal axis, derive expressions for z1 and z2. Then use...
Tan z = tan z1 + tan z2/(1-tan z1tan z2)
Then I would Differentiate to find the maximum of tan z.
Is that what you did?
 
  • #8
Jilang said:
If we are allowed stiff necks then...
Call the distance below the centre of the screen a, split z into z1 and z2 above and below the horizontal axis, derive expressions for z1 and z2. Then use...
Tan z = tan z1 + tan z2/(1-tan z1tan z2)
Then I would Differentiate to find the maximum of tan z.
Is that what you did?

This is not what i did. Interesting, i will try it out and get back to you. Thanks!
 
  • #9
Jilang said:
If we are allowed stiff necks then...
Call the distance below the centre of the screen a, split z into z1 and z2 above and below the horizontal axis, derive expressions for z1 and z2. Then use...
Tan z = tan z1 + tan z2/(1-tan z1tan z2)
Then I would Differentiate to find the maximum of tan z.
Is that what you did?

Ok i am lost. I have no idea what you did there.
 
  • #10
Jilang said:
Would you not want your eye to be level with the centre of the screen?

I doubt this is what is wanted. They probably want the position where the screen subtends the greatest angle at the eye.
 
  • #11
haruspex said:
I doubt this is what is wanted. They probably want the position where the screen subtends the greatest angle at the eye.


Exactly! Any ideas?
 
  • #12
Cyrus1 said:
Exactly! Any ideas?

What do you know about angles subtended by chords of a circle?
 
  • #13
I know the basics. I might post my method tomorrow as i just can't figure out what is wrong with it, but i am interested to know how you are thinking!
 
  • #14
Cyrus1 said:
I know the basics. I might post my method tomorrow as i just can't figure out what is wrong with it, but i am interested to know how you are thinking!
Draw a circle passing through the top and bottom of the screen and through a position on the seating ramp. What position maximises the angle?
 
  • #15
I drew it all very detailed and the problem is that the circle only touches a part at the bottom of the extended hypotenuse!
 
  • #16
I got that the eye level needs to be 63 cm lower than the bottom of the screen. We must be looking for a seat really near the front, less than 4m away from the screen. Stiff neck and nausea!
 
  • #18
Jilang said:
Sorry the description wasn't great. I have made a diagram.
http://tinypic.com/view.php?pic=igdb28&s=8#.UzmpDDK9KSM

Now i understand! Very nice, thanks ! however, i don't see how this works if the triangle in red is representing the angle of sight. in my head none of the equations would work out. Would appreciate an explanation! THANKS!
 
  • #19
Ah, yes that occurred to me too, but I think the tan(a+b) formula must still hold for negative angles. The blue lines are what I drew initially setting up the problem and the red line are the solution I got by maximising tan (a+b).
 

1. What is the Swedish Math problem and why is it difficult?

The Swedish Math problem is a commonly used term to refer to a mathematical problem that was created by a Swedish mathematician. It is known for its deceptively simple appearance, but its solution requires a complex understanding of mathematical concepts. Many people find it difficult because it challenges their assumptions and requires creative thinking.

2. How is the Swedish Math problem typically presented?

The problem is typically presented as a simple equation or set of numbers that seem to have an obvious solution. However, upon closer examination, the problem may involve hidden patterns or require unconventional methods to solve.

3. What makes the Swedish Math problem a popular topic in the mathematical community?

The Swedish Math problem is popular because it showcases the beauty and complexity of mathematics. It also encourages critical thinking and problem-solving skills, which are important in the field of science.

4. Are there any strategies or tips for solving the Swedish Math problem?

There is no one specific strategy for solving the Swedish Math problem, as each problem is unique. However, some tips include breaking the problem down into smaller parts, looking for patterns and connections, and thinking outside the box.

5. Can anyone solve the Swedish Math problem or is it only for experts?

The Swedish Math problem can be solved by anyone with a basic understanding of math, but it may take more time and effort for some. It is a great exercise for people of all skill levels to improve their mathematical thinking skills.

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