Math Is Fun Forum

Well I guess we must assume a and b are constants. I don't think we can differentiate with more then two variables.

So I guess it would have to be with respect to the independant variable. But if they are constants then their derivatives are zero. That makes a differance. I just hope its not a false assumption.

in this case if we have to find the derivative of u = bx we have to multiply b by the derivitive of x which is 1. And x * the derivitive of b. But if b is a constant then its slope is 0.

Ok I'll try messing with that to see if I can rearrange it into the desired form. But how am I supposed to know b and a were constants?

Hmm... I'll have to review the chain rule. But isn't that what I did? The derivative of bx is b * the derivitive of x (which is 1) + x * the derivitive of b (which is also 1) so it should be e^u (x + b) right?

Thats not the answer. My book wants the answer only in terms of a and constants. You can't use x. The answer to the problem is: a^2 / (a-1)

Wierd huh?

[Sh]e's right! Technically we should say the slope of e^x when x equals two.

I think I see where the confusion is now, irspow, thanks.

"Math is the intelligence and order of the mind of God. This order enforced upon the world holds the physical word together. Without it, nothing could exist. God created the world, but first he created math, and built the world upon it." - Mikau

And btw, the idea of this thread is just to list lots of interesting philosophies about math. Not start a religious debate. If you do not believe in God, just ignore it, I'm not trying to preach or prove anything.

Ok heres the idea. As an object gets closer and closer, the angle from the viewer to the point gets closer and closer to 90 degree's. When its far away, changes of the distance and location of the object effect the angle at which the viewer see's it very little. This is the same reason why the sun or moon appears to follow you when your driving. Its so far away that proportionally small changes to your location hardly effect the angle at which you see it at all. As a point gets closer, the angle at which you see it begins to accelerate. Again, when your driving, it often appears nearby objects like telephone poles are moving a lot faster then the buildings far behind them. You know what I mean.

Anways, that acceleration is what makes objects go off screen when you get close or go past them. The angle to the object begins to accelerate towards 90 degrees and beyond. The viewing cone is 60 degree's wide at most so that disapears off screen.

Now when objects are far away, they vanish slower because the angles are not as abrupt. You  can see the basic shape of the functions graph below. The angle to the object gets closer and closer to 90 degree's and accelerates towards it as it gets close. It slows down a bit as it gets close but its already off screen at that point.

Anyways, when I first measured the Z distance to a point and added the constant B to it, this was indirectly shifting the graph b units to the left. The red line I drew is where the y axis would be in that case. This shows why that worked to shorten the vanishing points. The curve is much slower and flater there. But it also shows why objects did not go off the screen when they were behind you. They had to go much farther back before the angles would hit 90 degree's and accelerate off the edge of the screen.

Then I had an inspiration. All I need to do to lessen the steepness of the curve is multiply (Zd/Xd) by a positive constant. Since the slope is negative, if we multiply Xd/Zd by say... 2, then the curve will be half as steep in every place. I created a constant m which would indirectly multiply the curve by 2 or whatever constant I wanted, to lessen the steapness of the curve. I tried it and it worked. Everything vanished slower. But there was a problem. It was doing what it was supposed to, no glitches, but since objects vanished slower, objects that weren't so far away weren't much smaller, and thus, they were bigger and dissapeared off the screen pretty quickly. Therefore you could not see much onscreen unless they were pretty far away, which is equivilent to just having a more narrow viewing cone. Dang.

At this point I'm not sure what else to do. Every possible adjustment I thought would be usefull I've figured out how to make, they all worked in differant ways, but none that allowed at least a 60 degree viewing cone without distortions. I can think of no other adjustments to the perspective that are not self contradictory. Objects need to both vanish slower and faster.

My design thus far would work fine for third person games, but for a first person game, you would have to have a very narrow viewing cone. 30 or maybe 40 degree's at most. I've often noticed first person video games seem to have a pretty narrow view but I doubt its as little as 30 degree's. But I could be wrong. It may be a natural consequence that a 3d illusion on a 2d plane must be limited to a narrow viewing angle to work properly.   

Of course there is the possibility that certain adjustments must be made to compensate for the fact that we do not percieve a screen as a window to another world. If it were so, the objects are all in the exact locations they should be. (where we would see them through the glass) but since close and far objects are all on the same 2d plane (the screen) its more then a bit differant then just a glass window. So perhaps, adjustments must be made which in reality would be incorrect but tricks the brain into thinking it looks right. :-)

No problem. I don't believe in interplanetary discrimination.

it will make a differance al right. that will happen about 1/3 of the time, and when it does, the point will go to the switcher. So that 1/3 of the points that are missing, all go to the switcher. That brings the odds up to 2/3.

Think clearly! :-D

Why did you not get a total of 100 million? Instead your total is roughly 2/3 of 100 million. 1/3 of 100 million worked, 1/3 of 100 million did not work, what about the other third? If it goes to the switch then numb3rs WAS right.

What did you mean by "Makes sure the one reveiled was not the answer, if it was, the whole thing is discarded." Discarded? I'm not sure what you mean but just to make sure, after (for instance) door A is picked. The program should  check to see whats behind door B, if its a goat, then reveal it and switch the choice to door C. If you picked door A and door B has a car behind it, then B cannot be revealed so you reveal door C and switch your choice WHICH WILL WIN YOU THE CAR! If you simply quite the game if theres a car behind the door you want to reveal, then about 1/3 of the answers should be missing, and that third should go to the switch method.

Induction? I'd like a proof. It appears my mathbook assumes I know it. Must have been an updated version of a previous book I didn't know about.

Calculus is a kidney stone?

Ok, I never thought I'd say this but KIDNEY STONES ROXXOR TEH BIG ONEZ!!!111

So you going to pick it apart, MathIsFun or did I just do it for you?