Comments on: An airport-inspired puzzle

By: ybing81

ybing81 — Fri, 03 May 2013 23:40:08 +0000

Such a model seems to be somewhat similar to the charge transportation in semiconductors, where concepts like “trap” and “mean free path” may find analogues in this ingenious puzzle.

By: Anonymous

Anonymous — Mon, 11 Feb 2013 22:22:20 +0000

Your situations are only correct if the walkway stretches until ten end of the terminal. As soon as the walkway ends before your arrival point the advantage you gained starts disappearing.

So it is not as easy as you believe..it depends on how long are the walkways and how long the distance between them, and if the point b is just at the end of a walkway or not…

By: An introduction to special relativity for a high school math circle « What’s new

Sat, 22 Dec 2012 22:40:31 +0000

[...] relativity per se, such as spacetime diagrams, the Doppler shift effect, and an analysis of my airport puzzle. This will be my first time doing something of this sort (in which I will be spending as much [...]

By: Assorted free entertainment #1 « Unabashed Naïveté

Assorted free entertainment #1 « Unabashed Naïveté — Sun, 29 Jul 2012 04:18:55 +0000

[...] finally another one from Terry Tao: this time a little puzzle. Share this:TwitterFacebookMoreLike this:LikeBe the first to like [...]

By: Some Miscellaneous Awesomeness « Research in Practice

Some Miscellaneous Awesomeness « Research in Practice — Wed, 18 Jul 2012 04:39:08 +0000

[...] Terry Tao’s airport puzzle. If you have to get from one end of the airport to the other to catch a plane, but you really need to stop for a minute to tie your shoe, is it best to do it while you’re on the moving walkway or not? (I learned this problem from Tim Gowers’ blog.) [...]

By: A trip to Watford Grammar School for Boys « Gowers's Weblog

A trip to Watford Grammar School for Boys « Gowers's Weblog — Fri, 06 Jul 2012 23:09:26 +0000

[...] was a short break — not that it is too important. Anyhow, at some point round now I described Terence Tao’s airport-inspired puzzle, which is the following question. You want to get from one end of an airport to the other and your [...]

By: How should mathematics be taught to non-mathematicians? « Gowers's Weblog

How should mathematics be taught to non-mathematicians? « Gowers's Weblog — Fri, 08 Jun 2012 15:53:55 +0000

[...] question comes from a blog post of Terence Tao, and the response to it provides us with strong empirical evidence that people find it [...]

By: Lori

Lori — Fri, 25 May 2012 10:21:12 +0000

Above diagram again (some of the symbols were interpreted as html tags):

Newton                             SR

T                                  T
                  T'                                T'
|               /                  |               /
|              +             T''   |_             X             T''
|             /|           _/      | \_          /|           _/
|            / |         _/        |   \_ u     / |         _/
|           /  |       _/          |     \_    /  |       _/
|          /   |T2   _/            |       \_ /   |T2'' _/
|         /    |   _/              |         X_ v |   _/
|   u    /  V  | _/                |        /| \_ | _/         
|-------+------+/                  |       / |   \X/           
|      /|    _/                    |      /  |  _/             
|     / |  _/                      |     /T1'|_/               
|    /T1|_/                        |    /   _X                 
|   /  _+                          |   /  _/                   
|  / _/                            |  / _/                    
| /_/                              | /_/                      
|//___________________ X           |//____________________

By: Lori

Lori — Fri, 25 May 2012 10:15:34 +0000

Nice puzzle. I realise this is a late response but I didn't see an intuitive explanation to all three parts without significant algebra manipulations. One possibility is to use a displacement-time (Minkowski) diagram to compare the time taken to cover a given distance at different speeds as shown below (which I hope comes out OK!). Define: T1(u;v)=net additional time when speed is decreased to u by an amount v T2(u;v)=net time reduction when speed is increased from u by an amount v The first diagram shows the Newtonian case in which times in all frames of reference are equal. The three lines T,T' and T'' represent stationary, slower and faster frames of reference respectively. It's clear that for fixed v, T1(u;v) is increasing in u and T2(u;v) is decreasing in u which implies the answers to parts 1 & 2 respectively. In the second diagram, time and displacement are now relative to frame of reference and so the X axis label has been omitted. The line segments u and v are orthogonal to the lines T' or T'' for the corresponding times T1' or T2'' respectively (these two cases are actually distinct but have been combined for economy). The T-intercept represents the time dilation for a unit of time in the moving frame T' or T''. Changing u and holding v fixed in the reference frame T' or T'' implies the slope of the line segments u and v change orthogonal to the lines T' or T'' but the same relationships apply as in the Newtonian case hence the answer to part 3.

Newton                             SR

T                                  T
                  T'                                T'
|               /                  |               /
|              +             T''   |_             X             T''
|             /|           _/      | \_          /|           _/
|            / |         _/        |   \_ u     / |         _/
|           /  |       _/          |     \_    /  |       _/
|          /   |T2   _/            |       \_ /   |T2'' _/
|         /    |   _/              |  X_ v |   _/
|   u    /  V  | _/                |        /| \_ | _/         
|+------+/                  |       / |   \X/           
|      /|    _/                    |      /  |  _/             
|     / |  _/                      |     /T1'|_/               
|    /T1|_/                        |    /   _X                 
|   /  _+                          |   /  _/                   
|  / _/                            |  / _/                    
| /_/                              | /_/                      
|//___________________ X           |//____________________

By: lhm

lhm — Mon, 24 Oct 2011 06:23:46 +0000

The optimal strategy of pausing on moving walkways and running between walkways can be seen as a consequence of unit-elasticity. The slope of a tangent to the “isodisplacement” curves gives the time change for a unit change in velocity. this is greater at lower speeds than higher ones due to the convex shape.

In the relativistic case one can draw a similar picture by replacing the velocity v with the rapidity r = atanh v/c. The isodisplacement curves are also convex but are relative to half the rapidity r. To see this let v’->v in the equation from TT’s comment so that dT/dv = -T/v√(1-v²/c²) and solve for r to find T tanh r/2 = const.