Interesting Use Of Pigeonhole Principle

[bhobba]

Check this one out about the number of hairs on a person's head, if not behind a paywall (I can't tell because I subscribe to Scientific American). Let me know if it is, and I will post a precis.

https://www.scientificamerican.com/...-have-the-same-number-of-hairs-on-their-head/

Thanks
Bill

 

[martinbn]

It opens for me, it must be free. The example is fairly well known. I've seen it more than once since I was a child.

 

[Klystron]

The SA article opened fine for me. I do not recall human head hairiness as a sage example of teaching the pigeonhole principle.

I do recall a teacher using using this premise to discuss boundary value problems and limits, as in how does one define the hairiness counting space, do facial hairs count, neck hairs, etc. Lively discussion ensued before the class delved into Dirichlet problem, Green's function and general boundary conditions. Perhaps I simply do not remember a pigeonhole reference.

Most striking for me was learning the pigeonhole principle at my first college adjacent to the Old Mission in Santa Barbara, CA. Mud swallows had colonized the eaves, building small spherical nests with distinctive round openings. Our geometry/stats teacher had us delineate a nesting section then attempt to count the birds returning from insect hunts entering the nests.

While not a precise exercise, we learned a practical lesson.

Picture of swallow nests from Mission San Juan Capistrano in California.