Sorry, you do not have access to this eBook
A subscription is required to access the full text content of this book.
Metrics
Views
113
In This Chapter
-
Analytic Geometry
- Points, Segments, and Coordinates on Line and Plane
- Coordinates on Line
- Coordinates on Plane
- Rectangular Cartesian coordinates on plane.
- Transformation of Cartesian coordinates under parallel translation of axes.
- Transformation of Cartesian coordinates under rotation of axes.
- Transformation of coordinates under translation and rotation of axes.
- Polar coordinates.
- Relationship between Cartesian and polar coordinates.
- Points and Segments on Plane
- Curves on Plane
- Curves and Their Equations
- Basic definitions.
- Equation of curve in Cartesian coordinate system.
- Special kinds of equations.
- Equation of curve in polar coordinate system.
- Parametric equations of a curve.
- Algebraic curves.
- Main Problems of Analytic Geometry for Curves
- Straight Lines and Points on Plane
- Equations of Straight Lines on Plane
- Slope-intercept equation of straight line.
- Point-slope equation of straight line.
- Equation of straight line passing through two given points.
- General equation of straight line on plane.
- General equation of straight line passing through given points on plane.
- Parametric equations of straight line on plane.
- Intercept-intercept equation of straight line.
- Normalized equation of straight line.
- Equation of straight line in polar coordinates.
- Equation of a pencil of straight lines.
- Mutual Arrangement of Points and Straight Lines
- Condition for three points to be collinear.
- Deviation of point from straight line.
- Distance from point to straight line.
- Angle between two straight lines.
- Point of intersection of straight hnes.
- Condition for straight hnes to be perpendicular.
- Condition for straight hnes to be parallel.
- Condition for straight lines to coincide.
- Distance between parallel lines.
- Condition for a straight line to separate points of plane.
- Second-Order Curves
- Circle
- Ellipse
- Definition and canonical equation of ellipse.
- Focal property of ellipse.
- Focus-directrix property of ellipse.
- Equation of tangent and optical property of ellipse.
- Diameters of ellipse.
- Ellipse in polar coordinate system.
- Hyperbola
- Definition and canonical equation of hyperbola.
- Focal properties of hyperbola.
- Focus-directrix property of hyperbola.
- Equation of tangent and optical property of hyperbola.
- Diameters of hyperbola.
- Hyperbola in polar coordinate system.
- Parabola
- Definition and canonical equation of parabola.
- Focal properties of parabola.
- Focus-directrix property of parabola.
- Equation of tangent and optical property of parabola.
- Diameters of parabola.
- Parabola with vertical axis.
- Parabola in polar coordinates.
- Transformation of Second-Order Curves to Canonical Form
- General equation of second-order curve.
- Nine canonical second-order curves.
- Invariants of second-order curves.
- Characteristic equation of second-order curves.
- Centers and diameters of second-order curves.
- Principal axes.
- Reduction of central second-order curves to canonical form.
- Reduction of noncentral second-order curves to canonical form.
- Geometric definition of nondegenerate second-order curve.
- Tangents and normals to second-order curves.
- Coordinates, Vectors, Curves, and Surfaces in Space
- Vectors. Cartesian Coordinate System
- Coordinate Systems
- Cartesian coordinate system.
- Transformation of Cartesian coordinates under parallel translation of axes.
- Transformation of Cartesian coordinates under rotation of axes.
- Transformation of coordinates under translation and rotation of axes.
- Cylindrical and spherical coordinates.
- Relationship between Cartesian, cylindrical, and spherical coordinates.
- Surfaces and curves in space.
- Vectors. Products of Vectors
- Scalar product of two vectors.
- Cross product of two vectors.
- Conditions for vectors to be parallel or perpendicular. A vector a is collinear to a vector b if
- Triple cross product.
- Scalar triple product of three vectors.
- Curves and Surfaces in Space
- Line and Plane in Space
- Plane in Space
- Equation of plane passing through point M 0 and perendicular to vector N.
- General equation of plane.
- Parametric equation of plane.
- Intercept equation of plane.
- Normalized equation of plane.
- Equation of plane passing through point and parallel to another plane.
- Equation of plane passing through three points.
- Equation of plane passing through two points and parallel to line.
- Equation of plane passing through point and parallel to two straight lines.
- Plane passing through two points and perpendicular to given plane.
- Plane passing through point and perpendicular to two planes.
- Equation of plane passing through line of intersection of planes.
- Line in Space
- Parametric equation of straight line.
- Canonical equation of straight line.
- General equation of straight line.
- Equation of line in projections.
- Equation of straight hne passing through two points.
- Equation of straight hne passing through point and perpendicular to plane.
- Mutual Arrangement of Points, Lines, and Planes
- Angles between lines in space.
- Conditions for two lines to be parallel.
- Conditions for two lines to be perendicular.
- Theorem on the arrangement of two lines in space.
- Angles between planes.
- Conditions for two planes to be parallel.
- Conditions for planes to coincide.
- Conditions for two planes to be perpendicular
- Intersection of three planes.
- Intersection of four planes.
- Angle between straight hne and plane.
- Conditions for line and plane to be parallel.
- Condition for line to be entirely contained in plane.
- Condition for line and plane to be perpendicular
- Intersection of line and plane.
- Distance from point to plane.
- Distance between two parallel planes.
- Distance from point to line.
- Distance between fines.
- Quadric Surfaces (Quadrics)
- References for Chapter 4
Abstract
A straight line on which a sense is chosen is called an axis. If an axis is given and a scale segment, i.e., a linear unit used to measure any segment of the axis, is indicated, then the segment length is defined (see Fig. 4.1).
Other ways to access this content:
Email to request access
Purchase this book
Related chapters
Search for more...
© Informa UK Limited, an Informa Group Company
Home | About RHO | Collections
| Free trial
| How to buy
| Promotions
| Contact us | Help & FAQs
Librarian resources
| Privacy policy
| Cookies
| Terms & conditions
