There’s no paradox, there no such thing as “infinity” in reality.
Infinity is an unreal mathematical concept like “i” (imaginary numbers that are the square root of a negative number).
Useful in calculations but really it’s just a placeholder for our lack of understanding about how the universe works (or a simplistic lie to evade giving a difficult, long, and incomplete explanation) , it’s not something found in nature.

Why not a mobius toroid? …or maybe a multidimensional toroid that’s (somehow) a donut in every direction? …or maybe both at once? Have some imagination, physicists. Don’t limit yourself to only the dimensions you perceive or how you see them
Time/space could be something like this and we only perceive the point where all 3 axis converge….

I would never down vote a video like this simply because it offends my knowledge of math and logic and irritates the hell out of me. These kind of problems have been coming my way on facebook repeatedly and they do get huge numbers of comments with wildly different solutions. Actually out of the 500,000 comments claimed for this one probably half of them give 42 as the answer. My problem comes from the assumption that an algebraic variable represented by a symbol (an image of a boot) bears some inherent relationship to a different symbol (two boots). Even if you make that leap that two boots is two separate variables, if there is no operand between them they should be multiplied, not added. In algebra a term such as 3AB equals 3 times A times B not 3+A+B. Unfortunately in this problem with two horseshoes equaling 4 it works either way but if two boots equals 2 then one should equal the square root of two and the correct solution would be 21.414.

Yup, != not equal (in programming) sometimes written as <> but less people know that one.

Rules are you don't have to use all numbers but you can't reuse numbers and it has to be just * / + - (I think square root isn't allowed)

>> ^brycewi19:

That's an absolute thing of mechanical beauty.
Too bad it seems limited to just the multiplication function.


It can very obviously do addition. Every crank adds the number on the side to the number on the top, so just by changing the side between cranks, you've got an adding machine.

Less obvious is subtraction, not shown here. The hand crank on top pops up for subtraction. There's a red or silver ring on the crank that's exposed to make it obvious which mode you're in. Doing this engages an alternate gear set causing the number on the side to be subtracted from the total rather than added.

Multiplication, as demonstrated, is just adding repeatedly.

Division can be done by clever use of multiplication and subtraction. See http://www.isi.edu/~finn/curta/curta.html.

See the following video for a demonstration (but with no real explanation) of finding a square root:
http://www.youtube.com/watch?v=haaCoVrGd6k

>> ^dannym3141:

@GeeSussFreeK i don't like it either, but it's one of those things you have to accept is true - just like quantum mechanics Your mind's desire to slot it into a jigsaw puzzle will have to go unsatiated.


Refusing to accept received "truths" is exactly how science advances. The Ancient Greeks thought infinities and infinitesimals were dumb and irrational numbers, well, properly irrational. Now we "know" they're just numbers like every other number. Same thing with the square root of minus one. Ultimately though, they are just tools and we will use them until they no longer suit our purposes. There are already many number systems in which 0.(9) doesn't equal 1. Who knows when they'll be useful.

But I think the real question is, what of the transfinites? No one ever thinks about the transfinites.

>> ^bamdrew:

... what the hell was all of that nonsense?


My title is sort of misleading. If you weren't being ironic (and/or too lazy to google) the quadratic formula (not equation) is one of those nasty cornerstones of calculus that you just "need to know" or at least need to be able recognize and when to apply it. It's "(-B +- the square root of B squared -4AC) divided by 2A"

Its what you use to find X in a complicated equation that uses X squared, such as "A times X squared + B times X + C = 0"
Example:

34X^2+45X+21=0

Plug those bastards (34,45,21) into the QF as respectively (A,B,C) and you'll find out what X is.

This video basically shows you why that works.

EDIT: more correctly , you'll find 2 X's one for the positive and one for the negative solution, representing the 2 points where the line f(x) crosses the X line

A nice looking woman rubbing all over him, on film, in his boxer shorts.

He's trying to figure out the square root of 1764 in his head.

>> ^quantumushroom:

Poor guy looks terrified.
I'm jealous.

>> ^notarobot:

Magnets? How do they work?


I think you missed a "fu&king" in there somewhere.

Can someone tell me how an integral, derivative, trigonometry, algebra, geometry, division, multiplication, adding, subtraction works and what these constants are (the ones I keep hearing about)? I've figured out the square root of -4 so no issues there.

We should cut these things out of school. THEY NEVER HELP YOU!!1!

/extreme sarcasm...

Whoah.. That last bit is interesting. Taking the square root of the E⁴ equation allows for negative energy, purely by simple mathematics. And then it turns out that there IS such a thing as negative energy by way of positrons.

One question they didn't really answer in this bit: why is the factor the speed of light squared? Besides it being a result of the maths, what does that relationship actually mean?

Danny, it's kind of like Pi. The Square root of 2 and Pi have both been troubling Mathmaticians for a long long long time. They are irrational numbers. You can write logical proofs to show that they should exist, or why the exist, but pinning an exact number on them isn't likely.

http://en.wikipedia.org/wiki/Square_root_of_2

http://en.wikipedia.org/wiki/Pi

Well, that was the original challenge.

Hell, i wasn't aware it was POSSIBLE to run out of decimal places that i could go to. I thought EVENTUALLY i'd get there. Perhaps the sun would have burned out and life on earth lost/moved on by then, and possibly the numbers would get beyond the range of human comprehension, and the scope of "accuracy" would be something i could only argue with god himself, but ...?

I mean, my main aim was to say you could do root 2 using a calculator without having a root button. If you take what i did, feed it into a pc and loop it you'd end up with pretty much a calculator for getting the square root of 2, even if it kept going for a squillion years.

As for proving the exact square root of 2 exists, to be fair, i've not been taught any maths beyond a-level yet. This is all just me working stuff out. It doesn't make sense to me that i could ever run out of decimal places and thus be proved wrong that my method would eventually provide the answer. But there are many things that can only be explained mathematically, so perhaps that is the case afterall.

Edit:
Apparently (and then of course) the square root of 2 is exactly the length of the diagonal of a square with side length 1. How can such a thing not have an exact length?

You still haven't proved that the square root actually exists. Because the square root of 2 is an irrational number, you can repeat this process indefinitely and never get to a decimal number that gives 2 if squared. All you have shown us is that if it exists, it lies between 1 and 2 in value.

>> ^dannym3141: 1.4x1.4 = 1.96
1.45x1.45 = 2.1025
1.425....... and so on and so forth.

>> ^thinker247:
I'll give you a calculator that doesn't have a square root button. Have at it, Mr. Smartypants.


Now ok, i couldn't work out exactly what the value was, but i could tell you without thinking for a matter of miliseconds that the square root of 2 was between 1 and 2.... I just worked out in my head that..

1.5x1.5 = 2.25
k, lower it bit by bit and you'll get 2.. I mean if i had a calculator without a square root button, easy as pie..

1.4x1.4 = 1.96
1.45x1.45 = 2.1025
1.425....... and so on and so forth.

Do i win something? Or is this as easy as i thought it was? You learned THIS at university?

I'll give you a calculator that doesn't have a square root button. Have at it, Mr. Smartypants.
>> ^jimnms:
Give me a calculator and in 2 seconds I could have told you that.

We did this in our first year Analysis course actually, it was terribly tedious but not too bad all in all.

Try proving that the square root of two exists - now THAT was hell.

I think it took 12 hours of lectures to show it existed and was between 1 and 2 in value.