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Related Concept Videos

Circles01:18

Circles

242
A circle in the coordinate plane is defined as the set of all points that lie at a constant distance, known as the radius, from a fixed point called the center. This relationship is captured using the distance formula. For a point (x, y) on the circle and a center (h, k), the distance between them equals the radius r. By squaring both sides of the distance formula, the equation of the circle is written in standard form:Constructing the Equation from Geometric InformationIf the center and the...
242
Mohr's Circle for Moments of Inertia: Problem Solving01:14

Mohr's Circle for Moments of Inertia: Problem Solving

3.2K
Mohr's circle is a graphical method for determining an area's principal moments by plotting the moments and product of inertia on a rectangular coordinate system. This circle can also be used to calculate the orientation of the principal axes.
Consider a rectangular beam. The moments of inertia of the beam about the x and y axis are 2.5(107) mm4 and 7.5(107) mm4, respectively. The product of inertia is 1.5(107) mm4. Determine the principal moments of inertia and the orientation of the major and...
3.2K
Mohr's Circle for Moments of Inertia01:10

Mohr's Circle for Moments of Inertia

1.2K
Mohr's circle is a graphical method to determine an area's principal moments of inertia by plotting the moments and product of inertia on a rectangular coordinate system.
1.2K
Mohr's Circle for Plane Stress01:23

Mohr's Circle for Plane Stress

1.3K
Mohr's circle is a graphical method for identifying the state of stress at a point in a material, making it easier to analyze stress transformations under plane stress conditions. This two-dimensional technique visualizes both normal and shearing stresses on an element.
Consider a set of Cartesian coordinates. The horizontal and vertical axes correspond to normal stress (σ) and shearing stress (τ), respectively. Two points, points A and B, are defined by the normal and shear...
1.3K
Mohr's Circle for Plane Strain01:18

Mohr's Circle for Plane Strain

1.2K
Mohr's circle is a crucial graphical method used to analyze plane strain by plotting strain on a set of cartesian coordinates, where the abscissa is normal strain ∈ and the ordinate is shear strain γ. Similarly to Mohr’s circle for plane stress, two points X and Y are plotted. Their coordinates are (∈x, -γXY) and (∈Y, γXY), respectively.
Mohr's circle visually represents the strain states under various conditions, which is essential for...
1.2K
Frost Circles for Different Conjugated Systems01:18

Frost Circles for Different Conjugated Systems

3.7K
The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.
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Related Experiment Video

Updated: Feb 2, 2026

Protocol for Isolating the Mouse Circle of Willis
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Protocol for Isolating the Mouse Circle of Willis

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Pixellated circle.

Colin J R Sheppard

    Applied Optics
    |November 22, 2018
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new parameter to measure how accurately digital circles and rings can be formed using pixel arrays in optical systems. It provides a method for optimizing pixelated circle generation.

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    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution
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    Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution

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    Area of Science:

    • Optics and Photonics
    • Digital Image Processing
    • Computer Graphics

    Background:

    • Representing circular apertures in pixellated digital systems is crucial for optical applications.
    • Existing methods for generating digital circles may lack objective measures of accuracy.

    Purpose of the Study:

    • To introduce an objective parameter for quantifying the quality of pixelated circle approximations.
    • To evaluate the generation of both filled circles (disks) and rings using square pixel arrays.
    • To explore the use of even-width pixel arrays for generating circular quadrants.

    Main Methods:

    • Development of a quantitative parameter to assess pixelated circle fidelity.
    • Analysis of filled circles and rings generated from square pixel grids.
    • Investigation of pixel array configurations, including even-width arrays for quadrants.

    Main Results:

    • An objective parameter was defined to measure the accuracy of pixelated circles.
    • Both filled circles and rings can be approximated using square pixel arrays.
    • Even-width pixel arrays facilitate the generation of circular quadrants, which can be combined.

    Conclusions:

    • The introduced parameter provides a valuable metric for evaluating digital circle approximations in optical systems.
    • The method allows for the optimized generation of pixelated circles and rings.
    • The technique is applicable to creating complete circles and quadrants from optimized ring and disk components.