
YC Applicants: What did you put for the "surprising/amusing question"? - rrhoover
I'm referring to this question, asked at the end of the application:<p>Please tell us something surprising or amusing that one of you has discovered. (The answer need not be related to your project.)
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btilly
I'm not an applicant, but I know what I'd put. (And the fact that I'd put this
probably makes it good that I'm not an applicant!)

In grad school I proved the following:

 _A polynomial that is symmetric in the roots of two other polynomials is a
polynomial in the coefficients of the other two polynomials._

As an example it is easy to construct a polynomial with integer coefficients
that has sqrt(2) + sqrt(3) as a root. Just take the polynomial
(x-sqrt(2)-sqrt(3))(x-sqrt(2)+sqrt(3))(x+sqrt(2)-sqrt(3))(x+sqrt(2)+sqrt(3)),
multiply it out, and you'll get your answer. (In this case, x^4-2x+1.)

Kind of a cute result. So I took it to multiple mathematicians. None had heard
of it until I talked to an old mathematician who told me that it sounded like
a very old approach, and he encouraged me to look for an introductory algebra
book from the 1800s.

I did, and lo and behold! It was once well-known, and a standard part of the
undergraduate curriculum. Even better, two of the mathematicians who had not
known the result worked in areas of math that STARTED with that observation!
(One worked with the algebraic integers - that construction was how
mathematicians first proved they formed a ring, and the other worked with
symmetric polynomials - and that construction was the original reason why they
were studied.)

This incident opened my eyes to the truth of how easily knowledge gets lost,
and how little attention mathematicians pay to their own history.

~~~
keiferski
Wow, that's impressive. Well, at least it sounds impressive to someone without
a lot of math knowledge.

Which has me puzzled. I can't think of anything offhand that I "discovered". I
suppose you don't need to have been the first to discover it; it merely needs
to be relatively unknown to most people? If that's the case, then nevermind:
I'm full of obscure knowledge.

I've actually "invented" an impressive device, but I'm not sure if "something
you invented" is what they're looking for.

Of course, I'm probably reading into this a little too much.

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malandrew
When I was a child I discovered that band-aid wrappers exhibit
triboluminescence when opened. I happened upon that by accident and only
learned the term for that now as an adult.

~~~
petervandijck
<http://en.wikipedia.org/wiki/Triboluminescence>

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JoshKalkbrenner
CoinStar does not accept 1943 5 cent nickels!

But it does help identify $80 nickels.

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cperciva
When I applied to YC a few years ago, I believe I put down that the
quadrillionth bit of Pi is zero.

~~~
bartonfink
Another interesting fact is that the last bit of Pi is 1. It's not difficult
to see why when you stop and think about it, but if you tell that fact without
the usual mathematical disclaimers (e.g. - Pi doesn't have a last digit in any
base), it tends to put people into a funny "how the hell did you figure that
out" state.

~~~
ssp
I don't get it. What does it mean that the last bit of Pi is 1 when there is
no last digit?

~~~
bartonfink
The clincher is that rightmost 0's after a decimal point are insignificant and
can be discarded similarly to leftmost 0's before a decimal point. 00045.26030
= 45.2603 - the extra 0's are simply noise. In binary, the only non-0 digit is
1. This means that, if Pi does in fact terminate, its binary representation
must terminate in a 1 - any 0's to the right of the last 1 carry no value.

Now, that's a pretty big "if", but this isn't meant to be serious mathematics.
It's just an interesting consequence of binary representation and the
assumption that Pi might terminate, and is enough to make people do a bit of a
double take when you phrase it along the lines of "the last bit of Pi [if it
has one] is a 1".

~~~
cperciva
_rightmost 0's_

... which Pi doesn't have, since it has no rightmost bits at all...

 _the last bit of Pi [if it has one] is a 1_

This is true; it's also true that the last bit of Pi [if it has one] is a
forty-two. A falsehood implies everything.

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sim0n
"We've discovered that even owls don't stay up as late as developers." We
tried to go for something simple yet slightly amusing. Not sure if we'll
change it before the 20th or not.

~~~
petervandijck
Did you actually discover that?

Or is this more like trying to answer "what is your greatest weakness"
(terrible question!) with "I tend to work too hard"? :)

~~~
sim0n
It's more of a humorous remark more than something we've really discovered
(though spending all day and all night hacking away isn't something that's
uncommon for us) which is why I'm not 100% sure we'll be keeping it as our
final answer to the question :-)

~~~
petervandijck
I'd change it :)

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alexl
I posted my entire application here:
<http://news.ycombinator.com/item?id=2361753>

