How many lines on a cubic surface?

27 lines
It illustrates a remarkable fact: any smooth cubic surface contains 27 lines.

How do u work out the surface area of a cube?

A cube has 6 faces. The area of each face is found by squaring the length of the side. Multiply the area of one face by the number of faces to get the total surface area of the cube.

Is projective space Compact?

A (finite dimensional) projective space is compact. For every point P of S, the restriction of π to a neighborhood of P is a homeomorphism onto its image, provided that the neighborhood is small enough for not containing any pair of antipodal points.

Why is algebraic geometry useful?

Algebraic geometry is useful to many geometry problems. Some Geometric patterns which are hard to visualise can be turned into algebraic equations and solved analytically.

Is algebraic geometry abstract algebra?

Algebraic geometry is a branch of mathematics studying polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.

What is the surface area of a cube 3x3x3?

As you already know, a cube has six square faces. If each of those faces is 3 inches by 3 inches, then the area of each face is 3 × 3 = 9 square inches. And since there are six of them, the total surface area is 9 + 9 + 9 + 9 + 9 + 9 = 54 square inches.

What is a ray in Hilbert space?

The equivalence classes of for the relation. are also called rays or projective rays. This is the usual construction of projectivization, applied to a complex Hilbert space.

Is the real projective plane Contractible?

Infinite real projective space , which is contractible. The infinite projective space is therefore the Eilenberg–MacLane space K(Z2, 1).

Is algebraic geometry algebra or geometry?

In a sentence, algebraic geometry is the study of solutions to algebraic equations. People learning it for the first time, would see a lot of algebra, but not much geometry. But it is there. The picture above depicts a resolution of the singular curve y2=x3.