parabola

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Trajectory of a projectile

A paraboloid reflector

Graph of a functionPart A illustrates the general idea of graphing any function: choose a value for the independent variable, t, calculate the corresponding value for f(t), and repeat this process until the general shape of the graph is apparent. (In practice, various techniques are available to reduce the number of values needed to determine the graph's basic shape.) In part B a specific function, the parabola f(t) = t2, is graphed for further illustration.

Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape.

Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP.

Archimedes' parabolic segment calculation

path of projectile

Figure 7: Parabola (see text).

Discover

Small, white rat (genus Rattus) on a glass table. (rodent, laboratory, experiment)

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African Americans demonstrating for voting rights in front of the White House as police and others watch, March 12, 1965. One sign reads, "We demand the right to vote everywhere." Voting Rights Act, civil rights.

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Ahura Mazda - relief of the Zoroastrian god Ahura Mazda at the ancient ruins of Persepolis in Iran. Also known as Ormazd Zoroastrianism,

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Battle of the Alamo from "Texas: An Epitome of Texas History from the Filibustering and Revolutionary Eras to the Independence of the Republic, 1897. Texas Revolution, Texas revolt, Texas independence, Texas history.

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Lusitania sinking, illustration from The War of the Nations (New York), December 31, 1919. World War I, WWI. This image is one of three on the page. (See source file for the other two.)

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New Zealand. Political/Physical map. Includes locator.

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Entrants falling and tumbling over while chasing the cheese at the 2016 'Cheese Rolling' held at Cooper's Hill, in the Cotswolds, Brockworth England

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Photos

Trajectory of a projectile

A paraboloid reflector

Graph of a functionPart A illustrates the general idea of graphing any function: choose a value for the independent variable, t, calculate the corresponding value for f(t), and repeat this process until the general shape of the graph is apparent. (In practice, various techniques are available to reduce the number of values needed to determine the graph's basic shape.) In part B a specific function, the parabola f(t) = t2, is graphed for further illustration.

Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape.

Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP.

Archimedes' parabolic segment calculation

path of projectile

Figure 7: Parabola (see text).

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Topics

conic section Fermat’s parabola parabolic equation parabolic antenna parabolic microphone ellipse hyperbola circle

Quiz

Equations written on blackboard

Numbers and Mathematics