Question about perspective and which mountain is taller

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In summary, the conversation on page 10 of the provided link discusses a question about the perception of the height of different mountains by an observer named Simon. The last part of the question asks for an explanation of how the answer was reached. The conversation includes various responses discussing the relationship between distance and perception of object size, as well as the order of the mountains from closest to farthest. The final conclusion is that the order goes from closest to farthest as follows: Col, Bob, Axe, Don.
  • #1
Galux
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The question is on page 10 of this link http://www.educationaldesigner.org/ed/volume1/issue3/article9/pdf/burkhardt_09_fig3.pdf
It is the question about the mountain. In particular I would like help with the last part about which mountain appears taller to Simon. Could you please explain how you came up with the answer as this is a revision question for my exam so I will need to be able to know how to do it by myself.
Thank You
 
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  • #2
I'm not sure how mathematical this answer could be, but I'm guided by my intuition.

The mountain furthest away from Simon is Don, because it is the smaller one. Objects tend to be perceived as smaller than they actually are the farther you are from them.

The nearest mountain is Bob, because it looks the tallest.

Since mount Bart is the closest, Simon observes it as a taller object than Homer, thus it's the one that looks taller in comparison.

Someone please do correct if my intuition is flawed.
 
  • #3
Fantini said:
I'm not sure how mathematical this answer could be, but I'm guided by my intuition.

The mountain furthest away from Simon is Don, because it is the smaller one. Objects tend to be perceived as smaller than they actually are the farther you are from them.

I agree, but would add that the answer follows from the fact that Don is the tallest mountain but appears the shortest to the observer of the four. If Don were in front of any of the other mountains, from this vantage point, then it would appear taller than the mountains behind it. So it's a combination of two things.

It seems to me that Bob is closest as well. Axe is taller but appears smaller so it Axe cannot be in front of Col. Also, Bob and Axe have equal heights so Bob must be in front of Axe since it appears taller.

This is a headache to keep track of but I think the order goes: Bob, Col, Axe, Don.

Could be wrong as well. Would like verification. :)
 
  • #4
Yes, you're right in adding the explanation. In terms of distance, they would be, from closest to farther, as follows:

Bob,
Col,
Axe,
Don.
 
  • #5
Hm...I get that Col must be closer than Bob since Col is 1/2 the height of Bob but appears more than 1/2 the height of Bob.

I get the order as:

Col
Bob
Axe
Don
 
  • #6
MarkFL said:
Hm...I get that Col must be closer than Bob since Col is 1/2 the height of Bob but appears more than 1/2 the height of Bob.

I get the order as:

Col
Bob
Axe
Don

Nice catch. I didn't consider how much taller or shorter the peaks were, just taller or shorter than the true height. I agree completely with your reasoning though and stand corrected.
 
  • #7
For part 3, I say that Mount Bart looks taller since $\displaystyle \frac{30}{20}<\frac{1500}{1200}$.
 

FAQ: Question about perspective and which mountain is taller

What is perspective and how does it affect the perception of the height of a mountain?

Perspective is the way in which an object or scene is perceived, based on the viewpoint of the observer. In terms of a mountain's height, perspective can greatly influence how tall it appears to be. For example, if a mountain is viewed from a distance, it may appear smaller due to the surrounding landscape, whereas if it is viewed up close, it may seem much taller.

How is the height of a mountain measured?

The height of a mountain is typically measured from its base to its highest point, also known as its summit. This is usually done using tools such as a theodolite or GPS, which can accurately determine the elevation of a specific point on the mountain.

What is the tallest mountain in the world?

Mount Everest, located in the Himalayas on the border of Nepal and Tibet, is considered the tallest mountain in the world with a height of 8,848 meters (29,029 feet) above sea level.

Can two mountains be the same height?

Yes, it is possible for two mountains to have the same height. For example, Mount Everest and K2 both have a height of 8,848 meters (29,029 feet) above sea level, making them both the tallest mountains in the world.

How does the height of a mountain affect its climate?

The height of a mountain can greatly influence its climate, as higher elevations often have cooler temperatures and more precipitation. This is because as air rises up a mountain, it cools and condenses, leading to cloud formation and precipitation. This can result in a variety of climates on different sides of the same mountain, depending on factors such as wind patterns and proximity to bodies of water.

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