Easy Questions?

[beagle]

Because the perceived height at the eye is proportional to the angle between a ray from the top of the object to the eye and a ray from the bottom of the object to the eye. Close, big objects can be almost 180 degrees but when far enough away will drop down to (eventually) 0 degrees. Width works the same way.

Looking up a description of perspective will probably give the best insight into how it works (and how long it took artists to work out how it works  ).


P.S., Good to see you back.

[Gloria The Camel]

Aren't these supposed to be for children to understand?!

[Swatopluk]

But the angle is not strictly proportional to the distance necessarily. There is that classic math problem a professor invented beacsue his students complained about lack of applicability of analysis:
A student walks behind a pretty short-skirted girl. The lower end of the skirt is at 60 cm above ground and his eyes are at 170 cm above ground. At what distance can the student see the legs under the largest angle? For the moralists: the answer is not zero. And for the hopeful student: it is not infinite 
That's actually quite tricky until you find the right way to solve it (then it's very easy).

[beagle]

I suppose the sledgehammer approach is finding the turning points of

(pi/2)-ATAN(distance/170)-ATAN(110/distance)
by differentiating WRT distance?

Is the easier one to recognize that the maximum of the required angle will occur for the minimum of the sum of the above two ATANed angles, and that in the first quadrant that will occur at the distance giving the minimum of the tan of the sum of the two angles, and then use the trigonometric tan(A+B) identity to eliminate most of the nastiness before differentiation to find the minima?

Anywhere near the right track?

[Swatopluk]

The easiest solution I found is indeed minimizing the sum of the adjacent angles. I think I did it over the sin not the tan but I did not check. (wasn't there a thumbs-up smiley?)

[beagle]

Has your professor been locked up by the political correctness police yet? Did "I was just measuring for a trigonometry question" cut it as an excuse?

Who was the famous mathematician who was horrified to find his work actually had a use?  G.H. Hardy probably I suppose.

[Swatopluk]

It was not my professor, I got that anecdote from a book.
About the shame of applicability I think it was somebody in connection with matrix calculations.

[Sibling Zono (anon1mat0)]

Ok, new 'easy' question: Why is the moon perceived as bigger when it is close to the horizon than when it is on the zenith where it is likely to be closer to earth?

[beagle]

I can't believe you've not heard of the oculomotor micropsia/macropsia theory . Don't they teach anything in U.S./Colombian High School? .

(OK. So I bunked off school that day too). And according to this it doesn't explain it anyway. The Beagle solution is to howl at it until it goes away.

[Griffin NoName]

Quote wiki - For over 100 years, research on the Moon illusion has been conducted by vision scientists who invariably have been psychologists

Quote wiki - It must also be kept in mind that people differ in how they experience the illusion (and some have no Moon illusion)


Begs another Easy Question:

Where is the entry in the DSM for this disease ?    (Absence of Moon Illusion)

we always knew Beagle was barking mad

[beagle]

we always knew Beagle was barking mad

I'm told one is judged by the company one keeps. And why are we whispering?

[Swatopluk]

Question from an area we did not cover yet:

Is there a linguistic/etymological connection between fascination and fascism or is the word similarity coincidental?
I know that the latter is derived from the bundle of rods (fasces) that was part of the insignia of the Roman lictors

[beagle]

Exhaustive research (Ok, Google) suggests that the root of fascination is "An attractive binding secret", so maybe it's the ribbon holding the rods together that is significant.

[Swatopluk]

And what about fashion?  Is that about wearing ribbons?

[Griffin NoName]

The aerial cable to the TV roof aerial is unplugged. IE. there is no connection to the roof aerial at present.

My TV, without the aerial cable plugged into it, has the expected fuzzy pic and sounds.

My TV with the aerial cable plugged into it, has good pic and sound.

How can this be, when the cable is not actually connected to the aerial?