Taxicab Geometry
... To every point of the line there corresponds exactly one real number. B. To every real number there corresponds exactly one point of the line, and C. The distance between two distinct points is the absolute value of the difference of the corresponding real numbers. ...
... To every point of the line there corresponds exactly one real number. B. To every real number there corresponds exactly one point of the line, and C. The distance between two distinct points is the absolute value of the difference of the corresponding real numbers. ...
Chapter 1 PowerPoint Slides File
... Point think of as a location. It has no size. It is represented by a small dot and is named by a capital letter. Space the set of all points. Line a series of points that extends in two opposite directions without end. You can name a line by any two points on the line or with a single lowercas ...
... Point think of as a location. It has no size. It is represented by a small dot and is named by a capital letter. Space the set of all points. Line a series of points that extends in two opposite directions without end. You can name a line by any two points on the line or with a single lowercas ...
Taxicab Geometry
... DEFINING TAXICAB DISTANCE Consider the coordinate plane as city blocks. Taxicab may only travel along the city streets. Distance is found by counting how many units one must travel to get from one point to another, moving only horizontally and vertically. ...
... DEFINING TAXICAB DISTANCE Consider the coordinate plane as city blocks. Taxicab may only travel along the city streets. Distance is found by counting how many units one must travel to get from one point to another, moving only horizontally and vertically. ...
Chapter 1 Study Guide
... 3. When two rays intersect with a common endpoint a(n) ________________ is formed. 4. The ________________ is the point located halfway between the endpoints of a segment. 5. ___________________ are nonadjacent angles formed by the intersection of two lines. 6. A(n) ________________ divides an angle ...
... 3. When two rays intersect with a common endpoint a(n) ________________ is formed. 4. The ________________ is the point located halfway between the endpoints of a segment. 5. ___________________ are nonadjacent angles formed by the intersection of two lines. 6. A(n) ________________ divides an angle ...
INTERSECTION THEORY IN ALGEBRAIC GEOMETRY: COUNTING
... We can now pose our two keynote questions. The term general means that the answer should hold for “most” configurations in a way that will be defined later. (1) Given four general lines in P3 , how many lines meet all four? (2) How many lines in P3 are secant to (intersect at least twice) two genera ...
... We can now pose our two keynote questions. The term general means that the answer should hold for “most” configurations in a way that will be defined later. (1) Given four general lines in P3 , how many lines meet all four? (2) How many lines in P3 are secant to (intersect at least twice) two genera ...
Chapter 3
... Remark: In an algebraic context equivalence classes are often called cosets. For example, lines and planes in Euclidean geometry (affine subspaces) are cosets of the underlying linear algebra, the equivalence relation on the vectors being that their difference belongs to the true subspace (line or p ...
... Remark: In an algebraic context equivalence classes are often called cosets. For example, lines and planes in Euclidean geometry (affine subspaces) are cosets of the underlying linear algebra, the equivalence relation on the vectors being that their difference belongs to the true subspace (line or p ...
Conic section
In mathematics, a conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2, and as a quadric of dimension 1. There are a number of other geometric definitions possible. One of the most useful, in that it involves only the plane, is that a non-circular conic consists of those points whose distances to some point, called a focus, and some line, called a directrix, are in a fixed ratio, called the eccentricity.Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section. The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas. In the focus-directrix definition of a conic the circle is a limiting case with eccentricity 0. In modern geometry certain degenerate cases, such as the union of two lines, are included as conics as well.The conic sections have been named and studied at least since 200 BC, when Apollonius of Perga undertook a systematic study of their properties.