Bignose

That's what I got from the pictures, too. But, Flak, you have to very careful with your terminology there. 4 points cannot "create a plane" 4 points can all lie on a plane, but all 4 have to satisfy the equation of the plane. It takes 3 points to define a plane, and then all you have to do is check to see if the 4th also satisfies the equation that describes the plane the first 3 points are on. Otherwise, as your picture showed, it will take two different planes to describe all 4 points. I think that you really should drop calling it a "4-plane" or "quad plane" because that terminology really isn't correct unless you want to start talking about 4 dimensions. Even then, the terminology usually is to call it a hyperplane. That wikipedia link I posted earlier, http://en.wikipedia.org/wiki/Plane_(mathematics) has a formula for calculating a distance from a point to a plane, so you can use that to see how far you have to move a point to get back aligned with the plane of the first three points.

Ok, you are wrong. Never mind the infinity adding and subtracting that is indeterminate... but why would all the terms on your right hand side become additions just from removing the parentheses? 5 + (6 - 7) does not in any way equal 5 + 6 + 7, which is what you posted.

As a lifetime resident of the Midwest, that list sounds just about right to me. I have lived in MO, MI, IN, and am in the process now of moving to IA. Looking back, now, I need to spread out.

Yes, sorry for the sloppy terminology. I also agree that it doesn't have any asymptotes, but since it looked like a homework problem, I didn't want to say that. I wanted the OP to do their own work -- since this really looked like a homework problem.

I'm glad HallsofIvy asked, because it still isn't making sense. That is, can you explain in great detail what you mean by "quad plane" Because, if you want to locate a point on a plane, once you've established that plane, you have the equation. ax + by + cz = d. Given three points, you can establish what a,b,c are. (see http://en.wikipedia.org/wiki/Plane_(mathematics) ). Then, any other point that solves that equation is also on the plane. Any point that doesn't solve that equation, isn't on the plane. It's a simple as that.

Besides what i_a said, which is good stuff, I think that a good place to start is a fluid mechanics text. If you aren't technically trained, a book like Steven Vogel's Life in Moving Fluids is very good. It is a fluid mechanics book for biology majors, but as someone who has studied a lot of fluid mechanics, I thought it was very well done. Chapter 11 is called "Lift, Airfoils, Gliding, and Soaring" and Chapter 12 is entitled "The Thrust of Flying and Swimming" If you are technically trained, there are many, many good fluids books out there.

I know, I was showing fattyjwoods, in response to his question "well if you minus infinty by infinity isnt it zero." That it isn't zero. I'm not trying to answer every case, I'm not trying to explore all possibilities, just trying to give some simple examples that show that infinity isn't just a "regular" number.

I didn't say that they were different. Just that infinity minus infinity doesn't necessarily equal zero, and I gave an example of that.

No, that's pretty much the point of this thread. Again, look at some of the examples I gave. The best one for this is probably to compare [math]x^3[/math] and [math]e^x[/math] again. As x goes to infinity, [math]e^x[/math] goes to infinity much faster. Both terms go to infinity, but in the limit as x goes to infinity, [math]e^x - x^3[/math], would still be infinity. Infinity - Infinity = Infinity, in this case. Look what I mean: [math]x[/math]..........[math]x^3[/math]..........[math]e^x[/math] 1..........1.........2.72 5.........125.........148.4 10.........1000.........22026 20.........8000.........4.85*10^8 40..........64000.........2.35*10^17 You can clearly see how the [math]e^x[/math] terms starts to completely and totally dominate there after a while. It goes to infinity faster, and you can see that even though [math]x^3[/math] still goes to infinity, at x=40, the [math]e^x[/math] term is changed less than 0.000 000 000 005 percent if you would subtract the [math]x^3[/math] term.

I would just like to point out, again, that science is indeed receptive to new ideas. Sometimes, occasionally, rarely, the scientist, because they are a human being, will let his emotions cloud his judgment. If a significant part of your life's work has just been proven inaccurate or a dead end, you're probably going to be somewhat sentimental about it, too. However, the entire community of scientists is usually very dispassionate, objective, and is really only seeking one thing: Better theories. Again, like I said above, bring a theory that describes everything the old theory does better or describes more than the old theory can, and the new theory wins out. It is as simple as that. If these "wild" ideas you speak of can do the job scientifically better than the old ideas, then they win. But, not every "wild" idea has to be treated equally. Just because you have a "wild" idea, doesn't mean it is right, no matter how passionately or firmly you believe in it. There has to be proof. There has to be scientific tests. It has to perform in the crucible that is modern science. This is all that is needed to displace the old theory and bring in the new. So, whatever new theory you have, go ahead and post it, but don't expect scientists to embrace it unless you can back it up with loads and loads and loads of evidence to support it. Again, this is the hill that creationism has to climb. Because there are mountains upon mountains of data that support evolution at the moment, and to become the mainstream theory, creationism has to scientifically demonstrate that is can explain as much as evolution better or explain more than evolution. And the key word in there is scientifically.

Did you even attempt to look at a single reference Phi for All listed above in post #42? Those are papers that report on actual factual happenings, unless you think that the authors are lying?

yourdad, I wasn't trying to get too technical, just showing that not all infinities are equal.

Here is a good example of how two infinties are not equal. Consider two functions: [math]f(x) = \frac{1}{x}[/math] and [math]g(x) = \frac{1}{x^2}[/math]. In the limit as x goes to zero, both of these will go to infinity. But what about the limit of f(x)/g(x)? Even though both the numerator and the denominator go to infinity as x approaches 0, the limit of f/g goes to zero, a finite number. Same sort of thing on the other direction. [math]e^x[/math] goes to infinity faster than [math]x^3[/math] as x goes to infinity. Nature may not have any infinities, but the concept of infinity sure is useful. We say that things are infinitely far away all the time. In order to completely 100% accurately calculate how far I hit a golf ball, the gravitational pull of every single atom in the universe should go into that calculation. Do we really calculate anything like that? No. For the purposes of this example, the Andromeda galaxy, Venus, and the moon are all infinitely far away and have no influence on the flight of the ball. In the same way, the fluid dynamic effects of the air going around every single tree on the planet have some effect -- but again, they are all infinitely far away.

I don't have much to add, the previous posters pretty much cleared up a lot of Sandman's objections to fossils. My only comment is that, sure, fossils aren't perfect. But the experts who study fossils can learn quite a lot from them, determine which ones are good and which ones are bad or fakes or unusable. And the fossil record is the best we have. If we throw away all data from anything that is imperfect, we'd have almost no data on anything. We don't throw out the data from the Mars rovers just because we lost a few packets of information as it got transmitted. We don't throw out the temperature reading you take when you think you have fever just because it is only accurate to 1 degree, and not to tenths, or hundredths, or thousandths. We didn't ignore intercepted communiques between Japan and Germany during WWII just because we didn't get the entire message or could only decode part of it. The simple truth is that pretty much all real-world data has some errors and incompleteness in it -- there is an entire branch of mathematics devoted to studying these errors and getting the most out of incomplete and erroneous data. The same thing has to be said about the fossil record. Sure, it's incomplete, and rarely fossils get mixed up or mislabeled or misidentified. But, overall the quality is really quite amazing -- again, do try to plan to go to a good museum. Chicago's Field House museum has quite a collection. I am sure that London's Natural History Museum's collection is going to be excellent. Almost any city of any size has some kind of natural history museum and probably some significant collection of fossils on display.

But, Sandman, you see, we actually do have those millions of years of observations -- it is in the fossil records. That's a primary basis for the theory of evolution, that we have all of these skeletons of creatures that sort of look like something modern, but not really. Where does each piece fit in? That's a lot of the modern research. Arguing over where each unique species belong in the evolutionary history, and where to dig for other fossils, to better fill in the puzzle. This is where most creationists cherry pick and say that evolution is crumbling. They like to think that just because not everyone agrees on where to put the latest fossil find, that means that the whole system is ready to fall down. Which, as previous posters in this thread have noted, couldn't be farther from the truth. If anything, each new fossil find continues to affirm the accuracy of the theory. That is, that life forms have adapted and changed over time. It has happened time and time again, and really it will happen again, but sometimes a new fossil discovery means a significant change in the knowledge of a species history. A new fossil may mean that a modern species evolved from a different path than had previously been thought. These are the debates that are carried on in the journals. The fossil record really is quite amazing. You'd do yourself a great service to go to a really good museum and look at them. Off the top of my head, I don't know of any good webpages, maybe someone else here can post a few up?

It's not a circle, nor a Pythagorean theorem, it is a 3-D curve. It is a parabolic "bowl" shaped curve that extends upward. Any slice taken along a constant value of z will be a circle, but the radius of the circle will increase as z increases. Anyway, amj, it does look like a homework problem and as such, the rules of this forum forbid us from giving you direct answers. However, we can give you suggestions, and help point out where you might have made mistakes. Do you know the definition of asymptotic? Basically, it means approaching a value or a curve arbitrarily closely as some sort of limit is taken. See this entry in mathworld: http://mathworld.wolfram.com/Asymptote.html and the others related to it.

Well, firstly, if the object on the floor started at rest, and then was at rest at the top of the 5 ft height, then no change in velocity, and hence no acceleration (acceleration is the derivative of velocity). But, also, you have to remember that gravity is accelerating objects downward, so to move accelerate it upward, just to counteract gravity. It is sort of counterintuitive idea that force is proportional to acceleration. For example, how do you make your bike go faster? You pedal harder. Daily occurrences make it seem like velocity is proportional to force. But, the bike really is accelerated more by pedaling harder, it is just that the equilibrium between forces changes when you put more force into the bike. I.e. the drag increases at the higher velocity. Re-adjusting your intuition to correspond with a physic-based analysis is a difficult skill, but worthwhile if your goal is to get a greater understanding of the physical world.

joey, the rules of this board are not to give you direct answers. If you give us your answers, and why you chose those answers, we will tell you where you made mistakes, if any. But, you won't learn a single thing if we just give you the answers, and this forum is here to help you learn, not just copy answers from.

Sandman, not to be too hackneyed here, and though part of me is loathe to say a cliche, but "close only counts in horseshoes and hand grenades." Meaning, the answer may have been close, but what does close really mean? If in the application, +- 10 m was okay, then, yes, your answer was fine. If you only had +- 1 m, your answer was exceptionally poor. Let me give you an example, let's say you were a scrap metal dealer and you were going to pay someone for this tower ... by your method you just overpaid someone for 8 m of metal that wasn't there. Finally, however, the question was about how to do a math problem. I could have guessed, and been "close" but how does that help the person trying to solve the math problem? I think that's precisely why math was invented, so that we wouldn't have to just guess. Math is very exact, and being close on a math problem usually isn't good enough. There was an exact correct way to do this problem, and your way wasn't it. Math is either right, or it's wrong. If I tried to say 2 + 2 = 4.03, I'd be wrong, even though I was "close". It's as simple as that. Edit: I don't want to add another post, so I'm just going to add this: I'm sorry if I misinterpreted your tone. I took your tone when you wrote "However, my answer was close..." as in it wasn't all THAT wrong, that it WAS close, that my method is NEARLY right, not in the tone you meant with your next post there.

Your LaTeX looks pretty good, this forum uses the [ math ] and [ / math ] tags (without spaces) to display LaTeX. change all those [tex] tags and I think that your post would be a lot easier to read -- and then I think I can help you with Stokes' theorem, too. let's see how that looks... probably more like you intended. Firstly, I don't think that you can ignore the y dependence, since the points go from (0,0,0) to (1,1,1). Secondly, I think that this is going to involve multiple line integrals, since you are going to want to go each point separately. I.e. the total line integral equals the line integral from (0,0,0) to (1,0,1) plus the line integral from (1,0,1) to (1,1,1) plus the other two. The nice thing about breaking it into each part is that you can calculate the normal to each line pretty easily.

Sandman, it's okay to want to figure things out for yourself, but when you do figure them out, you have to check to make sure they are right. You cannot just assume that you didn't make any mistakes. And in this case, you had 2,000 years of people before you telling you you were wrong: http://en.wikipedia.org/wiki/History_of_trigonometric_functions After you get done figuring things out for yourself, you should check to make sure you did everything right.

Again, you have to remember that forces acting on an object are source/sinks in the "conservation of momentum." Let me give you a very simple example: hold an object, any object completely still some distance above the floor. Momentum ([math]\mathbf{p}[/math]) is [math]\mathbf{p} = m \mathbf{v}[/math] where m = mass of the object, [math]\mathbf{v}[/math] is the velocity. (p.s. Benjamin, this has to be exactly what was meant by momentum, or the teacher is teaching something that is not the otherwise common, accepted definition that is used by all other physicists everywhere.) So, that object is held still, which means that the velocity is zero, hence there is zero momentum. Drop that object. Obviously it gains speed before it hits the ground, so there is a non-zero velocity, which means that there is now some momentum. The object went from zero momentum to some momentum... did we create some? Did we violate the conservation of momentum? No, an outside force, gravity in this case, acted on the object. In this case a force is a source of momentum. Gravity can also be a sink of momentum, if you throw that object straight up, it has some momentum as it leaves your hand, but eventually gravity pulls it back down. There is some instant of time when its velocity is exactly zero... in this case the gravity force acted as a sink taking away momentum; the momentum the object had when it left your hand was reduced to zero when it reached its peak. So, yes, there is a conservation of momentum, but you have to remember that forces can change how much momentum an object has. The total momentum of a system is perfectly conserved if there are no forces. Such as perfectly elastic collisions (billiard balls on a frictionless table are a classic example, noble gas molecule collisions is a better one). Finally, I would personally say that the concept that the train loses momentum so that the raindrop's speed is that same as the train's is exactly the point of acting the problem. I think that it is a very important non-negligible point, but maybe I am getting ahead of myself. Again, I think that the key word here is that the train car is described as "open" which means that it collects the rain, rather than letting the rain roll off the back like what would happen on a closed car.

No, the train will lose some x velocity. The rain drop that falls into the train will need to be accelerated up to the speed of the train. The rain drop isn't just going to stand still and leave. (Now a rain drop on the top of your car's roof... it will slide off, but we're talking about a drop of rain that falls into an open container. That drop will have to be accelerated, which is done by the train. Since the train uses some of its momentum to accelerate the drop, the train's speed will drop.

I think in both cases you are neglecting forces. You have to remember that the conservation of momentum equation contain common source terms: forces such as gravity, friction, etc. Whereas the conservation of mass equation only has source terms in really exotic situations -- i.e. nuclear events. So, regarding your train and raindrop situation, when the rain falls and hit the car, it's vertical momentum is "used" to impart a force on the bottom of the car when the drop hits. Or, to think about it in an equal but opposite way, the bottom of the train imparts a force in the raindrop when the drop hits, and the net result of the train's upward force is a drop with zero velocity. Momentum cannot just change directions. Each component of the momentum, the vertical and horizontal momentum are basically independent. Without a force acting to turn an object's momentum from vertical to horizontal, it won't just happen. Which, coincidently, is what happens in the first case, the drop coming in has no horizontal momentum. The train will give up a little horizontal momentum by imparting a horizontal force on the drop of water so that the drop and the train will travel at the same speed. I am unsure if the pre-wetted train and the train with rain on it would still have the same momentum. Because the increasing mass and the decreasing velocity are multiplied together, I'm not sure if the two terms come back out. In the real world, there would be friction and inefficiencies of transfer that would definitely have lesser total momentum, but I am not sure about what could happen in a perfect frictionless 100% efficient world.

There is no simpler "form" for tangent. It is a defined function. Sandman, get out your ruler and protractor, and draw a triangle with a side of 100 centimeters, and the angle of 52 degree, and you will see that your answer is wrong. It is as simple as that.