Interesting Math Facts

http://www.businessinsider.com/the-most-controversial-math-problems-2013-3#-1

anyone who says the monty hall problem is an easy, simple problem is a pompous ass

not rly if you practice thinking things through sequentially.. it isn't an easy problem if you just rely on your fast response system 1 tho

Well there you have it mnj

I still struggle with the Monty Hall problem... blows the mind

Here's a problem. Car A vs Car B in a 1/4 mile drag race. Car A gets a running start and travels at a consistent speed of 225 mph. Car B is a top of the line dragster and is not allowed to take off until Car A is even with it. In other words, Car B is sitting on the track, Car A is behind it and comes driving past at 225 mph and Car B can start once the two cars are even. Who wins the race?

wut

The 225 mph car will make a 4 second pass which is faster than any dragster.

On March 29 2013 17:03 blackjacki2 wrote: Here's a problem. Car A vs Car B in a 1/4 mile drag race. Car A gets a running start and travels at a consistent speed of 225 mph. Car B is a top of the line dragster and is not allowed to take off until Car A is even with it. In other words, Car B is sitting on the track, Car A is behind it and comes driving past at 225 mph and Car B can start once the two cars are even. Who wins the race?

+ Show Spoiler +

On March 29 2013 17:03 blackjacki2 wrote: Here's a problem. Car A vs Car B in a 1/4 mile drag race. Car A gets a running start and travels at a consistent speed of 225 mph. Car B is a top of the line dragster and is not allowed to take off until Car A is even with it. In other words, Car B is sitting on the track, Car A is behind it and comes driving past at 225 mph and Car B can start once the two cars are even. Who wins the race?

Miles*((Seconds/hour)/(Miles/hour)
(1/4)(3600/225) = 4

It takes A 4 seconds to complete the entire track.

Top Fuel Dragster (TF/D). The rail dragsters, or "diggers", are the fastest class. Among the fastest-accelerating machines in the world, these cars can cover the dragstrip in less than 3.8 ­seconds and record trap speeds over 325 mph. Top Fuel cars are 25 feet long and weigh 2,320 pounds in race-ready trim. Methanol fuel mixed with up to 90% nitromethane is used.

The top level dragster if it is allowed proper traction and no wind.

my favorite math fact (formula) is e^(pi*i)+1=0 uses 5 of the most important numbers (or complex numbers ) in all of mathematics.


some other facts/proofs/formulas/random stuff i love:
-shapes can have finite volume and infinite surface area: fractals or gabriels horn are good examples

-cantor sets (http://en.wikipedia.org/wiki/Cantor_set): perfect sets that are nowhere dense, pretty amazing

-the proof of square root of 2 being irrational:
suppose root(2) is rational. that means it can be represented as integers a and b where a/b are not reducible. then (a/b)^2 = 2 or a^2=2b^2. this means that a^2 is even which implies that a is even. say a=2k. (2k)^2 = 4k^2 = 2b^2 or 2k^2=b^2, so b^2 is even which implies that b is even. so both a and b are divisible by 2 but we assumed they were not reducible. => <= contradiction, thus root(2) is irrational. very cool proof by contradiction showing that there existed numbers that could not be represented by fractions.

-transcendental numbers are numbers that are not roots of any polynomial equations with rational coefficients. aka they are not algebraic. its very hard to prove something is transcendental and we dont know of many transcendental numbers, but almost all of the real numbers are transcendental since they are an uncountable set while the algebraic numbers are countable.

-non transitive dice: this one is a bit tricky but really cool.
suppose there are 3 dice

die A: 1,1,4,4,9,9
die B: 2,2,6,6,8,8
die C: 3,3,5,5,7,7

there is a 20/36 chance that die A outrolls die B.
there is a 20/36 chance that die B outrolls die C.
there is a 20/36 chance that die C outrolls die A.


-Russell's paradox:

from wikipedia:

Let us call a set "abnormal" if it is a member of itself, and "normal" otherwise. For example, take the set of all geometrical squares. That set is not itself a square, and therefore is not a member of the set of all squares. So it is "normal". On the other hand, if we take the complementary set that contains all non-squares, that set is itself not a square and so should be one of its own members. It is "abnormal". Now we consider the set of all normal sets, R. Determining whether R is normal or abnormal is impossible: If R were a normal set, it would be contained in the set of normal sets (itself), and therefore be abnormal; and if R were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.

did lots of set theory in college so i always found them really interesting

oops, yeah top fuel dragsters can do a 1/4 mile faster than 4 seconds. Pretty fuckin sick

Why the conversation in this thread is still all about math and not about me and how I made an amazing contribution to this forum by finding this presentation and starting this thread here?

None of these are controversial. Imagine someone said it was controversial whether aces were the best nlhe hand to have and you can have a good idea how silly calling these controversial is

You can say what you want but I don't think the "monty python" problem is that abstract... I am by no means a mathematical genius and I solved the problem in highschool. I'm really not trying to brag either because i am very far from being genius.

DAUT, I ALWAYS WANTED TO KNOW MORE ABOUT E AND WHERE IT SHOWS UP IN NATURE.

NEVER COULD FIND EXAMPLES THOUGH

e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + ... = approx 2.7818

e is also used in finance. For instance, suppose I were to give you an interest rate of 100% (never going to happen, but for practical purposes). You put $1 in the bank and you will get $2 if compounded yearly. if we compound biyearly, we get
$1 x (1 + 1/2)^2 = $2.25
compounded quarterly
$1 x (1 + 1/4)^4 = $2.4414 approx
compounded monthly
$1 x (1 + 1/12)^12 = $2.613035 (do you see the pattern?)
compounded "n" periods
$1 x (1 + 1/n)^n
compounded continuously
lim n->infinity $1 x (1 + 1/n)^n = $2.7818 approx = e

This is why when you hear the term compounding continuously we use the formula e^rt where r = interest rate and t = time period to calculate how much money you will have after a certain period of time at a certain rate.

On March 30 2013 01:56 KoeBawlt wrote: None of these are controversial. Imagine someone said it was controversial whether aces were the best nlhe hand to have and you can have a good idea how silly calling these controversial is

That's not true. When the monty python example was first released to the public there were multiple debates from Ph.D mathematicians regarding the true solution to the problem. While the idea seems simple enough, the difficulty at the upper echelons of mathematics was to prove the answer as 2/3 always. You can repeat 10000 trials and realize it's always 2/3 but this is not a mathematical proof.

And as a person that has worked on many many problems similar to all of these out of entertainment, there as definitely been high scale debates over these topics at one point or another. Only thing in today's society is we have all the answers right in front of us. When you go back to when these problems were first contrived, there was much more heated debate.

When you multiply any number by 9, the sum of the resulting numbers added up will always be 9. Cool huh ?

On March 31 2013 09:05 brambolius wrote: When you multiply any number by 9, the sum of the resulting numbers added up will always be 9. Cool huh ?

This post led me to play with the calculator for a little bit. You sir, might be on to something