constructible point造句

The geometric definition of a constructible point is as follows.
In " The Continuum ", the constructible points exist as discrete entities.
I swear Compass and straightedge constructions # Constructible points and lengths is just as confusing as it was then.
This implies that the degree of the field extension generated by a constructible point must be a power of 2.
By the above paragraph, one can show that any constructible point can be obtained by such a sequence of extensions.
It's difficult to find constructible point in a sentence. 用constructible point造句挺难的

As a corollary of this, one finds that the degree of the minimal polynomial for a constructible point ( and therefore of any constructible length ) is a power of 2.
In particular, any constructible point ( or length ) is an algebraic number, though not every algebraic number is constructible; for example, } } is algebraic but not constructible.
Since the field of constructible points is closed under " square roots ", it contains all points that can be obtained by a finite sequence of quadratic extensions of the field of complex numbers with rational coefficients.
But this is not a power of 2, so by the above, } } is not the coordinate of a constructible point, and thus a line segment of } } cannot be constructed, and the cube cannot be doubled.
The numbers that can be constructed are called the origami or pythagorean numbers, if the distance between the two given points is 1 then the constructible points are all of the form ( \ alpha, \ beta ) where \ alpha and \ beta are Pythagorean numbers.