B Interesting Use Of Pigeonhole Principle

AI Thread Summary
The discussion centers around an article from Scientific American that explores the pigeonhole principle using the example of hair count on human heads, suggesting that 8,000 people globally share the same number of hairs. Participants confirm that the article is accessible without a paywall and acknowledge the example as a common teaching tool. The conversation shifts to personal experiences with the pigeonhole principle, including its application in boundary value problems and practical lessons learned in a college setting. One participant recalls a memorable exercise involving mud swallows and their nests that illustrated the principle in a real-world context. Overall, the thread highlights the educational value of the pigeonhole principle through various examples and discussions.
Mathematics news on Phys.org
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.
 
  • Like
Likes bhobba and FactChecker
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.

ent%2Fuploads%2F2012%2F09%2FSan-Juan-swallow-nests.jpg


Picture of swallow nests from Mission San Juan Capistrano in California.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top