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Question about perspective and which mountain is taller

Galux

New member
Sep 23, 2012
1
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
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
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.
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,052
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. :)
 

Fantini

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
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.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,052
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.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
For part 3, I say that Mount Bart looks taller since $\displaystyle \frac{30}{20}<\frac{1500}{1200}$.