A Hairy Problem (and a Feathery Solution) - Numberphile

More links & stuff in full description below ↓↓↓

Includes The Pigeon Hole Principle.

NUMBERPHILE

Videos by Brady Haran

#melscience #melchemistry #melphysics #melkids

[davidgillies]

The Pigeonhole Principle is surprisingly powerful in a lot of areas, from compression algorithms to number theory.

[enbyennui]

Glad Ben mentioned the birthday paradox, as I based my initial guess (almost certain) on having heard of that. Didn't occur to me to consider that it could be 100% though! Small correction, you need a minimum of 367 people to know for certain that at least two must share a birthday (29th Feb babies always throw a spanner in the works).

[_abdul]

That reminds me, I need a Haircut for my Interview Tomorrow.
Numberphile is helping me in ways I couldn't Imagine.

[wardycruyff]

I think numberphile should do a series in core maths to help average mathematical people like myself be better at using maths in every day life .

[thipoktham]

I still remember vividly when I read to proof Fermat's little theorem using pigeonhole during my midterm exam. The sad part is, I have completely forgotten the proof, even though I read them right before the exam start

[theanimatedchemist]

As a chemistry educator, I always try to impart the idea of "number sense" or being able to describe a mathematical relationship between properties (say Pressure, Volume, and Temperature with respect to gases). It may not always catch on with everyone but I know some students have fixed mistakes after they get an answer they realize is nonsensical.

I am well aware that "gas laws" will not apply in their every day life that often but if I can increase a student's number sense or general confidence with mathematics then I'll take it too!

[neatodd]

Not for the first time, watching this, I wish that I had had access to all these brilliant Numberphile videos when I was a schoolboy

[NoIce]

10:13 was the first take, wasn't it? :D

[MelindaGreen]

Very glad to hear the UK teaches estimation and other highly practical math skills. Also glad to know I nailed the answer, but largely because the pigeonhole problem came up early in my CS training.

[ScienceHippie]

The tenth pigeon's embarrassment touched my heart profoundly.

[RegularCody]

Ben is definitely my favourite person on Numberphile

[ggtt]

Damn that started out as trivial and ended up amazing! Bravo!! Thank you for the video! It truly is a great ad for "core maths" at school. Maybe you should send it to your politicians!

[johnchessant]

An example of a "profound" result proved by the pigeonhole principle: Dirichlet's approximation theorem states that any irrational number x is approximated well by infinitely many rational numbers p/q, in the sense that x differs from p/q by at most 1/q^2.

[mettanotation]

Fantastic job in choosing the topic and in delivery! The more you learn, the more you learn how easily our intuition can be wrong. Over and over again.

[PaulMJohnson]

I love that qualification - what a great idea.

At work, the ability to sense check numbers, by estimating whether or not something you've been told "feels right", is so useful.

[invictus]

As soon as you asked this question, I started thinking about it as if it were Fermi's paradox' calculation. So I was VERY much on the mark, and I'm very happy cus this is a rare numberphile video where I was not only right, but on the right track!

[fyukfy]

This was actually a great breakdown. All around very high quality video and even the average person can feel that "eureka!" feeling I assume mathematicians feel when they figure something out

[infrabread]

"If you have 366 people, you're guaranteed to share a birthday". You are forgetting about leap years, sir!

[rainerausdemspring]

Another question: It is easy to see that there are always two different places on earth with the same temperature or two different places with the same air pressure. Of course, we assume that both are continuously dependant on the location.
Now estimate the probability that there are two different points on the sphere that have the same temperature AND air pressure.

[EnriqueDominguezProfile]

Everybody assumes that you're putting pigeons in holes, but it also works if you're carving holes in pigeons.