questionposter

Well I suppose if the universe could not operate without imaginary numbers, then that would satisfy their purpose, but otherwise they just seem to be a byproduct of the fact that math is just our interpretation of patterns found in nature, not nature itself. .

That's what I mean, not on normal graphs, but even in a complex plane they still don't represent real values which is why you never see them when you graph a function on a Cartesian graph.

People would still have a problem even with a new name because you can't see them on normal graphs. They don't represent real quantities no matter what you call them. What I would really find strange though, is if you "needed" an actual non existent value in order to have this universe itself, although I suppose scientists could easily just call that "an unknown particle". Le'ts call them "transformative-reality numbers" Then someone asks "Hey, why don't transformative reality numbers appear on graphs?" And then someone answers "Because they don't actually exist, they are essentially imaginary."

I don't know how much geometry you've taken, but it seems like your only starting to learn geometry. You can still easily use 2D objects to calculate parts of a 3D object. The height is a line right? Well that's just one dimension, and what does a triangle have? 2. It's made up off lines. So what you do is you draw a right triangle inside the cone which consists of the slant height as the hypotenuse, the radius of the base as a leg, and the actual height as the other leg, and in order to get the height you need to know the slant height or radius along with an angle, or use Pythagorean theorem if you know two of the 3 sides of the triangle. So if you know the radius, here's what you do: In an advanced calculator like a scientific or graphing one, you can type "tan" and in the parentheses put the angle which is between the hypotenuse and the radius of the base. tan(angle)=height/radius and then re-arrange the equation to make tan(angle)*radius=height And if you know the angle and slant height which is the same as the hypotenuse sin(angle)=height/hypotenuse then re-arrange it to make sin(angle)*hypotenuse=height and there you go. And there is definitely a relationship between the slant height and the actual height and it's because a cone does have inherent triangular properties about it. The only way they could be related is because of this triangle thing I'm talking about, because the height and slant height are connected at the same point, and can be connected by a straight line after a specific distance which will form a certain set of angles.

Which part of a cross-section of a cone are you defining as the hypotenuse of the triangle? Because you can use the side as either a slant height or the hypotenuse. The general way to find the volume or surface area of a cone already uses trigonometry, or just 1/3 that of the cylinder it would make, so if there's some kind of angle you'd probably just use a trigonometric function to find a side length and that's about it. Depending on how you arrange the equation for a cone you can get the different parts of it.

But I mean, there still just imaginary, there just a by product. And with wave functions even those are real things, it's just that they oscillate. If I make a ripple in the water, is there really some imaginary point outside of the pool of water that's rippling? Not really, there's some water who's position is now below and above where water would be if it was stagnant, and even then, the level of water where it's stagnant exists in the middle of the ripples. I guess it seems like they don't have a purpose in reality, they are just a by product of math is more of what I'm getting at. Like they aren't really a part of nature, and yet all these mathematical equations we developed use them.

I guess its really just a by product of how our math works, but If I swing on the swing and I graphed the position off the ground, not over time, just distance from the ground, it would be a parabola with an exact equation, but no matter what, I would never actually be at 0 distance from the ground yet I could still get imaginary numbers for 0s. And then another problem with it is you can generate real numbers from imaginary numbers by raising them to an exponent, or perhaps there actually is something multiplied by itself to give a quantity that is less than 0 that we don't know of.

Oh wait, I didn't notice that the dashed line represents an asymptote. If that's the cause, it's definitely not a cubic function, it looks like a tangent function although I can't say that for sure because it's zoomed in so much, so it's still possible it's an inverse function. Although you need 3 sides to make a triangle, so how could one side actually be 0? I guess it's just where math and nature don't match up.

Well obviously a quintic is going to cross the x axis at some point, so there has to be 0s. There has to be something going one which causes the process of y being equal to an x value, and the way that happens is you use y to solve for x. If x is equal to y, then in some way or another, y has to be equal to x, and since y can be 0, x has to equal something at that point. But that's number theory; its indisputable that if ...x...=...y..., then ...y...=...x..., but otherwise I'm not quite sure why having something like a 5th root means I'm not actually seeing real 0s on my calculator when I see the curve cross the x axis. http://en.wikipedia....Ruffini_theorem "It does not assert that higher-degree polynomial equations are unsolvable." There's no way that after thousands of years that there wouldn't be a way to figure out the 0s of a mere 5th or even 6th degree equation, even the quadratic formula was developed during the ancient Greece era.

But wait, what do I do if I have something like x^6+x+57? I can't use factoring of any kind, I can't use rational root theorem and synthetic division, and I don't know of a sextic formula, and say I don't have a graphing calculator, now what? Say I'm stranded on the island and I know the fuel in something decreases at a rate of x^6+x+57 but I have a big helicopter with full fuel, how do I figure out how far it could take me before the fuel runs to 0? I'm only saying this in case someone's not going to bother if they think x^6 never occurs in reality and therefore I shouldn't worry about it.

So in other words, its possible to have a formula for any degree of a polynomial equation, but you actually can't have a consistant pattern with the ways the formulas for them are written, you'd have to figure them out all of them by hand?

Synthetic division doesn't really work to get real roots because you need to use the rational root theorem in order to figure out what factors there are I guess. It kinda sucks, but the formulas for polynomials can still be used when you break the polynomial down into those types of products.

That's actually exactly what I mean. I formula for any polynomial that =0, which I would imagine would be very complex since it's so general. I don't see why there wouldn't be equations for like an octic polynomial, and then if we can get that far, where there isn't an equation to generate those formulas. I mean we have a formula for 5 different types of polynomials as far as I know, surely mathematicians have noticed the patterns in those by now.

I heard it's for some reason mathematically impossible to have a formula for a polynomial beyond a quartic for some reason, but its a consistant pattern as the degree goes up so I don't see why it wouldn't be possible. Basically I'm looking for a formula that generalizes polynomials and I hear that's impossible for some reason.

Yeah I suppose I'll just have to factor by grouping or use the quadratic formula if I can break it down into second degree factors

Couldn't I describe it as a "cubic" curve? There's probably some other Latin word for it, but it looks like a cubic equation where y≤a unless that line is there just to mark the exact integer of a.

Yet every time I've graphed an equation like the one I'm saying, they never crossed the x axis. I mean I can just do the constant and lead coefficient divided by x as separate equations to get a list of factors, and nothing seems to work, and there's only like 3 plusorminus whole numbers and they don't work, so what am I suppose to do with that? There's literally infinite possibilities for p/q and I really don't have a lot of time to test that many. Here's the equation. Maybe there's some step I'm missing, but synthetic division to get roots doesn't seem to work when using the rational root theorem. Isn't the rational root theorem and synthetic division suppose to work for complex numbers too? In fact I've gotten complex numbers before, but I've never used this process when all numbers were imaginary or complex, so what am I doing wrong by using the rational root theorem and synthetic division to find the factors? "x^4+0x^3+10x^2+0x+9" The original equation doesn't have the 0 Xs, but you need them for any polynomial division. And what's even stranger is I can just factor it by eye and see that its also (x^2+9)(x^2+1), yet stuff still doesn't work with the rational root theorem and synthetic division.

Ok, so I'm doing synthetic division for a polynomial and I have to show all my work, but no matter what number I use from the ration root theorem, nothing works, which means all the 0s are imaginary, but then how do I find out exactly which imaginary numbers there are? Because I couldn't find a "quartic" formula and I'm not always dealing with a polynomial where there's an automatic formula for it like a quadratic formula, so is there still some quick way I can do this? Preferably using synthetic division or should I just say in an equation like that where the highest degree is in x^n, there's n "i"s?

I guess that's kind of what I was talking about, but I was thinking more about finding the area of a random blob using some kind of infinite triangle theorem.

Newton devised some way to measure the area of a blob by using some infinite triangle theorem, but I have no idea what the theorem is right now.

The brain could not have consciousness unless individual cells had consciousness no matter how small it may be. This is an accepted fact that is even taught in schools.

A number divided by 0 is always undefined because there is nothing determining how many times something 0 actually goes into something or how. It's a permanent gray area. So you'd basically have one over undefined.

I thought an electron could pass harmlessly through the nucleus...

But as argued before, a brain couldn't have consciousness unless the individual cells had consciousness and worked individually with each other. Similarly, this is how the relationship between atoms and cells is being argued. There's also the matter of bacterium and single cells, because not every type of cell is a neuron, and not every single celled organism has a nucleus, yet they have consciousness.

Actually now that I think about it, how your assuming I'm thinking about it might actually be true. A bacterium doesn't have any neurons, or even a brain, so we say it doesn't have so much consciousness. Things like bugs have a brain, but they are pretty small, so we also say bugs don't have so much consciousness. Things that are larger are harder to determine, but with that it isn't necessarily a size issue, but its still a numbers issue, the number of connections between cells. A smaller brain can have more consciousnesses by having more connections per unit of volume. This is why we say people and dolphins and chimps have a lot of consciousnesses. There's probably other ways things can have consciousness besides connections since single celled organisms have consciousness themselves.