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        riddles >> general problem-solving / chatting / whatever >> Photo quiz
        
(Message started by: BenVitale on Sep 19^th, 2010, 5:15pm)

Title: Photo quiz
Post by BenVitale on Sep 19^th, 2010, 5:15pm

http://i.imgur.com/1nT6a.jpg

Do you think this relates to a Fib sequence or to something else?

The beginning of an exponential sequence?
The beginning of a polynomial sequence?
Something else?

Title: Re: Fibonacci sequence or not?
Post by Noke Lieu on Sep 20^th, 2010, 12:10am

Either way, it's awesome!

Title: Re: Fibonacci sequence or not?
Post by towr on Sep 20^th, 2010, 2:03am

Here's the approximate numerical sequence (pixel x-coordinates): 35, 43, 55, 70, 85, 107, 127, 157, 191, 235, 283, 382, 574

If we discard the last pigeon, exponential fits slightly better than quadratic; including the last pigeon neither fit very well.

Best fit is a twelve degree polynomial ::)

Title: Re: Photo quiz
Post by BenVitale on Sep 20^th, 2010, 2:57pm

Okay, towr.

Here's another photo quiz: a parabola or a hyperbola?

http://maa.org/FoundMath/10week37.html

Title: Re: Photo quiz
Post by towr on Sep 20^th, 2010, 3:07pm

I'd go with elipse.
Although it might be something else still. But assuming it is a circle in perspective (it does say it's a circular overpass, after all), then it is not a parabola or hyperbola (it should be a closed curve ... probably).

Title: Re: Photo quiz
Post by Grimbal on Sep 23^rd, 2010, 2:48pm

Any true* perspective projection of a circle gives a conic (circle, ellipse, parabola or hyperbola). The curve is not closed if the circle passes behind the camera.

The one on the picture looks like a hyperbola.

*A fish-eye lens would not produce a true projection as it does not preserve straight lines. It would give other curves.

Title: Re: Photo quiz
Post by BenVitale on Sep 25^th, 2010, 2:47pm

on 09/23/10 at 14:48:54, Grimbal wrote:

The one on the picture looks like a hyperbola.

So, it could be a parabola.

What's the one thing we would need in the photo to make it....
(a) a hyperbola, or
(b) a parabola

Quote:

*A fish-eye lens would not produce a true projection as it does not preserve straight lines. It would give other curves.

Title: Re: Photo quiz
Post by BenVitale on Oct 8^th, 2010, 1:46pm

How to Slice a Bagel into Two Linked Halves (http://www.georgehart.com/bagel/bagel.html)

Topology problem: Modify the cut so the cutting surface is a one-twist Mobius strip.
(You can still get cream cheese into the cut, but it doesn't separate into two parts.)

Calculus problem: What is the ratio of the surface area of this linked cut to the surface area of the usual planar bagel slice?