[Guille]

Originally Posted by AntonioLao

In any kind of game, somebody wins and somebody loses but there is always a next game to hope for and next time the losing team might win.

Actually real madrid won the match. But it only won 2-1 in home, against a greek team (and although greeks were great thinkers, they are terrible football players (by the way, you call it soccer, right?)).

Originally Posted by AntonioLao

About the Riemann, it is just like Pythagoras, except for the middle term
Pythagoras is x²+y² but Riemann is x²+2xy+y². Note the middle term 2xy for the Riemann. As for Gauss it's like this x²-y². Note the minus sign replaces the plus sign.

ok, thanks for these, now I can go and tell my teacher I have discovered two new types of geometries and their own mayor theorem over a night....Then he will tell me they are already discovered, but will be impresse dby me! lol!

[AntonioLao]

Originally Posted by GUILLE

you call it soccer, right?

That's correct. In order to distinguish the other more nationalized football established by the National Football League (NFL) divided into the American Football Conference (AFC) and the National Football Conference (NFC). Most of the U. S. states have a represented team, while some richer states have more than one team. These teams are usually sponsored by major cities. Those that can afford to build high tech capacity stadium.

Originally Posted by GUILLE

two new types of geometries

The more formal names are Riemann's elliptic geometry and Gauss' hyperbolic geometry. Both of these require the study of differential geometry. The traditional and more practical one is still the Euclidean geometry.

[Guille]

Originally Posted by AntonioLao

That's correct. In order to distinguish the other more nationalize football established by the National Football League (NFL) divided into the American Football Coference and the National Football Coference. Most of the U. S. states have a represented team, while some richer states have more than one team.
The more formal names are Riemann's elliptic geometry and Gauss' hyperbolic geometry. Both of these require the study of differential geometry.

Oh yes, I remeber I looked at the links that you gave me in www.mathworld.wolfram.com on differential geometry, so that I could apply it to my photogravitational process. But I find it quite dificult. What is it about, basically?

[AntonioLao]

Originally Posted by GUILLE

What is it about, basically?

The application of differential calculus (derivatives and partial derivatives) to geometry. One of the basic theorem is that the tangent vector along a differential curve is always perpendicular to the path vector. For example, circle in the plane can be defined as the curve γ where the vector γ(t) is always perpendicular to the tangent vector γ‘(t). Or written as an inner product

[Guille]

Originally Posted by AntonioLao

The application of differential calculus (derivatives and partial derivatives) to geometry. One of the basic theorem is that the tangent vector along a differential curve is always perpendicular to the path vector. For example, circle in the plane can be defined as the curve γ where the vector γ(t) is always perpendicular to the tangent vector γ‘(t). Or written as an inner product

That's what made it dificutl for me!

I don't know calculus. Well, I mean, my teacher helps me in reading all the papers you send me, etz...

But we haven't done calculus in math yet. Maybe we will start it this year. Actualy, you know what, I'm going to tell my teacher to teach me calculus, then I will understand much more things.

[AntonioLao]

I started learning calculus when I attended the university majoring in engineering then switch to physics in order to learn more about theories (physics) instead of learning more about applications (engineering).

[Guille]

Originally Posted by AntonioLao

I started learning calculus when I attended the university majoring in engineering then switch to physics in order to learn more about theories (physics) instead of learning more about applications (engineering).

Is calculus that much advanced as to start it in unviersity? Do you think I could still manage it now (to the basic terms at least)?

I actually find engineering very boaring and heavy. Theoretical physics, on the other had, gives you thi opportunity to start developing things yourself, but big things, not like those things that engineers develop, which are good, but indeed just about things in particular, whiles theoretical physis is about things in general, and, we hope, soon it will be about all things in general, i.e. everything.

[AntonioLao]

Originally Posted by GUILLE

I actually find engineering very boaring and heavy. Theoretical physics,

Hardly many theoretical physicists became rich doing what they do. However, engineers can become multi-billionaire like Bill Gate.

The prerequisites for calculus are good background base in geometry, algebra, trigonometry, and analytic geometry.

[AntonioLao]

When the time axis and the space axis are disconnected at their intersection then the worldline generated becomes discontinuous as shown below

[AntonioLao]

When the time axis is detached from the space axis, the degrees of freedom for both become unbounded. Although unbounded time remains uniform, bounded time is the province of special relativity. Moreover, bounded time becomes more and more prominence as the system evolves from simple to complex or from quantum mechanics into classical mechanics (this includes special and general relativity). The unboundedness of time allows its vector property to emerge such that it is possible to talk about directional time, which is describable in a Feynman diagram. However, time axes are then free to choose each own direction. The complete integration of these infinite chosen directions becomes an invariant loop. If this loop is linked to the space loop then two distinct invariant loops are formed (see the image of post#1).