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Related Concept Videos

Area of a Surface of Revolution01:29

Area of a Surface of Revolution

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Surfaces of revolution are formed when a two-dimensional curve is rotated around an axis, producing a three-dimensional shape. This concept is used in engineering tasks like determining the surface area of a rocket nozzle, where precise calculations are critical for applying uniform heat-resistant coatings. When a curve is revolved about the x-axis, it sweeps out a continuous surface whose area must be calculated accurately to estimate material requirements.Approximating with Conical BandsTo...
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Volumes of Solids of Revolution01:29

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Volumes of irregularly shaped objects can be systematically determined using the concept of solids of revolution. This approach begins with a region defined by a curve in a two-dimensional plane. When this region is rotated about a fixed line, known as the axis of revolution, it generates a three-dimensional object with rotational symmetry. Such objects frequently arise in mathematical modeling, physics, and engineering applications.When the region being rotated lies directly against the axis...
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Centroid for the Paraboloid of Revolution01:16

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The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
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National Nursing Organizations I01:26

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Nursing organizations assume a significant role in consistently developing the nursing profession through education, research studies, establishing practice standards, and reforming health policies. Typically, nursing organizations operate at the regional, national, and international levels. For example, the International Council of Nurses (ICN) represents more than 28 million nurses worldwide. In contrast, the American Nurses Association (ANA) is a membership organization representing nurses...
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The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
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Related Experiment Video

Updated: Feb 15, 2026

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
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Empires, Nations, and Revolutions.

Jeremy Adelman

    Journal of the History of Ideas
    |February 6, 2018
    PubMed
    Summary

    The Age of Revolutions broadened political ideas and identities, challenging the traditional shift from empires to nation-states. It reveals how Iberian imperial crises spurred new political categories beyond the national mold.

    Area of Science:

    • Political Science
    • History
    • Sociology

    Background:

    • The Age of Revolutions is often viewed as a transition from old regimes to unitary nation-states.
    • Traditional historical narratives focus on the emergence of national identity as the primary outcome.

    Purpose of the Study:

    • To examine how the Age of Revolutions expanded political ideas and identities.
    • To challenge the conventional narrative of a simple shift to nation-states.
    • To explore the complex political transformations within the Iberian empires.

    Main Methods:

    • Historical analysis of political discourse and identity formation.
    • Examination of the political crisis within the Iberian empires.
    • Re-evaluation of traditional narratives on state formation.

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    Main Results:

    • The Age of Revolutions significantly broadened the range of political ideas and identities.
    • The political crisis in the Iberian empires led to the reinvention of existing categories like monarchy and empire.
    • New political categories emerged that did not conform to the nation-state model.

    Conclusions:

    • The Age of Revolutions fostered a more diverse political landscape than previously understood.
    • The Iberian imperial context produced unique political innovations that defy simple national categorization.
    • Understanding this period requires moving beyond the nation-state paradigm.