Question about perspective and which mountain is taller

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Discussion Overview

The discussion revolves around the perception of mountain heights from a specific viewpoint, particularly focusing on which mountain appears taller to an observer named Simon. Participants explore the implications of distance and relative height in their reasoning, with references to a specific question from a linked document. The scope includes conceptual understanding and mathematical reasoning related to visual perception.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Debate/contested

Main Points Raised

  • Some participants suggest that the mountain furthest away from Simon is Don, which is perceived as smaller due to distance.
  • Others argue that Bob appears tallest to Simon because it is the nearest mountain.
  • It is proposed that Mount Bart looks taller than Homer based on its proximity, despite the actual heights of the mountains.
  • One participant notes that Don, while being the tallest, appears shortest from Simon's perspective due to its distance.
  • There is a suggestion that the order of mountains from closest to farthest is Bob, Col, Axe, and Don, based on their perceived heights.
  • Another participant agrees with the order but emphasizes the importance of relative heights in perception, correcting their earlier reasoning.
  • One participant introduces a mathematical comparison involving Mount Bart, suggesting it looks taller based on a ratio of heights.

Areas of Agreement / Disagreement

Participants express differing views on the order of the mountains and their perceived heights, indicating that multiple competing views remain. The discussion does not reach a consensus on the correct order or the interpretation of the visual perception involved.

Contextual Notes

Participants acknowledge the complexity of the problem, noting that assumptions about height perception and distance may influence their conclusions. There are unresolved mathematical steps in the reasoning presented.

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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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.
 
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. :)
 
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.
 
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
 
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.
 
For part 3, I say that Mount Bart looks taller since $\displaystyle \frac{30}{20}<\frac{1500}{1200}$.
 

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