## sâmbătă, 18 octombrie 2008

### Uitasem cat de complicat este

Parca era mai simplu la geometrie, in clasa a noua.

Damn it. Pana nici tangentele nu mai sunt ce'au fost odata...

:) :p

Suppose M is a Ck manifold (k ≥ 1) and x is a point in M. Pick a chart φ : U → Rn where U is an open subset of M containing x. Suppose two curves γ1 : (-1,1) → M and γ2 : (-1,1) → M with γ1(0) = γ2(0) = x are given such that φ o γ1 and φ o γ2 are both differentiable at 0. Then γ1 and γ2 are called tangent at 0 if the ordinary derivatives of φ o γ1 and φ o γ2 at 0 coincide. This defines an equivalence relation on such curves, and the equivalence classes are known as the tangent vectors of M at x. The equivalence class of the curve γ is written as γ'(0). The tangent space of M at x, denoted by TxM, is defined as the set of all tangent vectors; it does not depend on the choice of chart φ.

#### 2 comentarii:

Anonim spunea...

Te-ai gandit cum poti defini notiunea de tangenta la o parabola, de exemplu, unor elevi de liceu, fara a utiliza vreo formula? Nu te grabi sa-mi spui ca e dreapta care intersecteaza curba intr-un singur punct ca axa de simetrie a parabolei exact asta face si nu e tangenta.

Anonim spunea...

Pai, sa zica bunul matematician depresiv, ca pe mine, cu matematica de Poli, anul I, ma depasheshte.