Tangent Graph Theory

A tangent graph looks (kinda) like:


| | | | | | |
/ / / / / / /
----|----|----|----|----|----|----
/ / / / / / /
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Yeh? But the top of one line never meets the bottom of the next...

What about if you took the graph, wrapped it around the outside of a cylinder with an infinate diameter... would the tops and bottoms meet?

[SteveCRM]

a cylinder with an infinite diameter would be like a flat wall...that doesn't seem like it helps you much

:confused:

[Sam Finch]

what you're looking at is something called an Asymptote, in the tangent graph this is the line x = (2N-1)*pi / 2 where N is an integer, ie the vertical lines at the points where tan(x) is undefined. what happens at these points is unknown, maths makes some increadible attmts to ignore these points, if tan(pi/2) is required we have to use various(very complicated) theories about limits to determine its value (in the simple case it's infinite, but if tan(pi/s) comes up in more complicated expressions the value of the whole expression can be calculated, eg x(tan(pi/2 - x) ) where x = 0 can be shown to be 0 (I think, i didn't do it very rigorously) as a rule in this case we look at what happens when we get very close to the undefined limit, an do not consider what it would look like, it's fair to say if you imagined a cylider whith an infinite radius, viewed from far enough away that it looked like a cylider with a finite radius (this is wierd idea, which I don't think is formalised in maths, but can be imagined) then it would look like a cylinder with bands around it.

In my opinion nobody has yet come to any decant theory about infinity yet in maths (a guy called Georg Cantor came close but I don't like his ideas, they lead to too many contradictions which are easily dismissed just by saying that nobody can understand the infinite, But they conflict too much with intuitive, and correct ideas in linear algebra)

As I say the trick in maths in dealing with the infinite is not to think about it, and I hope someone comes up with a usable theory, but until then we have to avoid the subject.

Steve...that didn't ever occur to me, but my idea still stands (with a little modification!)...assume the wall has an infinate height...at its top and bottom (yeah I know these wouldn't even exist, but what the hell!! :) ) would the top of one curve be vertically above the bottom of the next?

Sam...your new "signiture" is spelt wrong. :D
Unfortunately I already have thought of it... a few years ago in pure maths and the idea has been with me ever since.

if you imagined a cylider whith an infinite radius, viewed from far enough away...it would look like a cylinder with bands around it.Score!!!!! :D (Assuming these are complete bands wich actually join up...as bands usually do :) )

[paulw]

I think that your idea of an infinitely wide cylinder does not really help. The value of Tan as it approaches (2n-1)pi/2 is either infinitely positive or infinitely negative depending on which side you approach from. At (2n-1)pi/2 itself Tan is Infinity (which is all we can say). The concept of +ve or -ve loses its relevance.

There are branches of mathematics that deal with infinities of infinity (pico maths from memory) but in general terms infinite states are not well defined. The concept of above or below has no relevance in infinity so the basic question is invalid.

States can change catastophically and you can be 'flipped from one point to another discontinuously. Mechanical failure is a good example. If a component is stressed to breaking point, trying to measure the stress forces at the point of breakage becomes nonsensical.

Interesting though.

P.

Ah! I see my mistake! :)
I'm trying to describe it to people who know what they're talking about!!! :)

Someone who failed their A-Level maths (like me :( ) would understand and agree with me instantly!! :D

[paulw]

Unfortunately I have a degree in Mathematics so that must be my problem:D

Cheers,

P.

I expected that you meant infinite height of the cylinder. The plan is that the tangent curve never converges with the asymptote. In fact, the very definition of asymptote.

[kedaman]

that would even go for a cylinder with null height:
------o------o------o------o------

Careful, Kedaman... the direction your sig is taking it will be running straight back to gaol!!! :)

[kedaman]

heh

[morgan868]

How do circles relate to the tan graph, and why circles have a greater area than polygons of the same perimeter.
ANY HELP ASAP IS GOOD PLEASE!!!!!!!!!!!!!!!!!!!

[kedaman]

How do circles relate to the tan graph, and why circles have a greater area than polygons of the same perimeter.
ANY HELP ASAP IS GOOD PLEASE!!!!!!!!!!!!!!!!!!!What you get on the tan graph is the point where the vertical line, the tangent of the unit circle (circle with radius 1), intersects with the line trough the center of the circle, at angle a.

I don't have a proof, but intuitively, a circle has the most area/permiter quotient because its the most convex object you can make with a curve (assuming polygons are curves). Balloons, soap bubbles, the shape of earth, all conform to a perfect sphere for a similar reason, to conserve energy, and if I remember correctly the proof involved surface energy tensors.

[moeur]

What about if you took the graph, wrapped it around the outside of a cylinder with an infinate diameter... would the tops and bottoms meet?
The answer to this question is yes.
1. At infinity, the lines will be at their asymptotes which are all parallel lines
2. At infinity, parallel lines meet

So, all the tops will meet and all the bottoms will meet.