section
(noun)
The middle level in Boundless' three-level book structure. Each chapter contains at least one.
Examples of section in the following topics:
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MLA: The Works Cited Section
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APA: The References Section
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Chicago/Turabian: The Bibliography Section
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Ellipses as Conic Sections
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Hyperbolas as Conic Sections
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What Are Conic Sections?
- A focus is a point about which the conic section is constructed.
- These properties that the conic sections share are often presented as the following definition, which will be developed further in the following section.
- Each type of conic section is described in greater detail below.
- The nappes and the four conic sections.
- Describe the parts of a conic section and how conic sections can be thought of as cross-sections of a double-cone
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Conic Sections
- Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse.
- In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section—though it may be degenerate—and all conic sections arise in this way.
- Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.
- There are three types of conic sections: 1.Parabola; 2.
- Identify conic sections as curves obtained from the intersection of a cone with a plane
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Conic Sections in Polar Coordinates
- Conic sections are sections of cones and can be represented by polar coordinates.
- 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.
- 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 such sufficient interest in its own right that it is sometimes called the fourth type of conic section.
- In polar coordinates, a conic section with one focus at the origin is given by the following equation:
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Table of Contents
- Boundless' content is organized into a three-tiered hierarchy: chapters, sections, and concepts.
- Each chapter is comprised of several sections.
- For example, a section in the Founding a Nation chapter is "A New Constitution,” numbered Section 7.2.
- Within each section is a number of concepts.
- History, demonstrating the chapter-section-concept structure and numbering.
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Eccentricity
- The eccentricity, denoted $e$, is a parameter associated with every conic section.
- The value of $e$ is constant for any conic section.
- The value of $e$ can be used to determine the type of conic section as well:
- Below, each type of conic section is graphed with a focus and directrix.
- Explain how the eccentricity of a conic section describes its behavior