Geometric Fields

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Abstract Algebra › Geometric Fields

Questions 1 - 4

Identify the following definition.

Given that lives in the Euclidean plane $\mathbb{R}^2$ . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.

Line in

Circle in

Plane

Angle

Subfield

Explanation

By definition, given that lives in the Euclidean plane $\mathbb{R}^2$ . When elements , , and in the subfield , form a straight line who's equation form is , is known as a line in .

Identify the following definition.

Given that lives in the Euclidean plane $\mathbb{R}^2$ . Elements , , and in the subfield that form a straight line who's equation form is , is known as a__________.

Line in

Circle in

Plane

Angle

Subfield

Explanation

By definition, given that lives in the Euclidean plane $\mathbb{R}^2$ . When elements , , and in the subfield , form a straight line who's equation form is , is known as a line in .

Identify the following definition.

For some subfield of $\mathbb{R}$ , in the Euclidean plane $\mathbb{R}^2$ , the set of all points that belong to that said subfield is called the __________.

Plane

Line

Constructible Line

Angle

None of the answers.

Explanation

By definition, when is a subfield of $\mathbb{R}$ , in the Euclidean plane $\mathbb{R}^2$ , the set of all points that belong to is called the plane of .

Identify the following definition.

If a line segment has length and is constructed using a straightedge and compass, then the real number is a __________.

Constructible Number

Plane

Straight Line

Angle

Magnitude

Explanation

By definition if a line segment has length and it is constructed using a straightedge and compass then the real number is a known as a constructible number.

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