coronal plane
(noun)
Any vertical plane that divides the body into anterior and posterior (belly and back) sections.
Examples of coronal plane in the following topics:
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Body Planes and Sections
- There are three basic reference planes used in anatomy: the sagittal plane, the coronal plane, and the transverse plane.
- The coronal plane (frontal or Y-X plane) divides the body into dorsal and ventral (back and front) portions.
- The coronal plane, the sagittal plane, and the parasaggital planes are examples of longitudinal planes.
- For example, during human embryonic development the coronal plane is horizontal, but becomes vertical as the embryo develops into a fetus.
- There are three basic planes in zoological anatomy: sagittal, coronal, and transverse.
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Animal Body Planes and Cavities
- A sagittal plane divides the body into right and left portions.
- A frontal plane (also called a coronal plane) separates the front (ventral) from the back (dorsal).
- A transverse plane (or, horizontal plane) divides the animal into upper and lower portions.
- Shown are the planes of a quadruped goat and a bipedal human.
- The frontal plane divides the front and back, while the transverse plane divides the body into upper and lower portions.
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Movement at Synovial Joints
- Protraction is the anterior movement of a bone in the horizontal plane.
- (a)–(b) Flexion and extension motions are in the sagittal (anterior–posterior) plane of motion.
- (e) Abduction and adduction are motions of the limbs, hand, fingers, or toes in the coronal (medial–lateral) plane of movement.
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Spherical and Plane Waves
- Spherical waves come from point source in a spherical pattern; plane waves are infinite parallel planes normal to the phase velocity vector.
- A plane wave is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector .
- It is not possible in practice to have a true plane wave; only a plane wave of infinite extent will propagate as a plane wave.
- However, many waves are approximately plane waves in a localized region of space.
- Plane waves are an infinite number of wavefronts normal to the direction of the propogation.
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Vectors in the Plane
- Vectors are needed in order to describe a plane and can give the direction of all dimensions in one vector equation.
- Planes in a three dimensional space can be described mathematically using a point in the plane and a vector to indicate its "inclination".
- As such, the equation that describes the plane is given by:
- which we call the point-normal equation of the plane and is the general equation we use to describe the plane.
- This plane may be described parametrically as the set of all points of the form$\mathbf R = \mathbf {R}_0 + s \mathbf{V} + t \mathbf{W}$, where $s$ and $t$ range over all real numbers, $\mathbf{V}$ and $\mathbf{W}$ are given linearly independent vectors defining the plane, and $\mathbf{R_0}$ is the vector representing the position of an arbitrary (but fixed) point on the plane.
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Equations of Lines and Planes
- A line is a vector which connects two points on a plane and the direction and magnitude of a line determine the plane on which it lies.
- A line is essentially a representation of a cross section of a plane, or a two dimensional version of a plane which is a three dimensional object.
- The components of equations of lines and planes are as follows:
- This direction is described by a vector, $\mathbf{v}$, which is parallel to plane and $P$ is the arbitrary point on plane $M$.
- where $t$ represents the location of vector $\mathbf{r}$ on plane $M$.
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Tangent Planes and Linear Approximations
- The tangent plane to a surface at a given point is the plane that "just touches" the surface at that point.
- Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point.
- Note the similarity of the equations for tangent line and tangent plane.
- Since a tangent plane is the best approximation of the surface near the point where the two meet, tangent plane can be used to approximate the surface near the point.
- The tangent plane to a surface at a given point is the plane that "just touches" the surface at that point.
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The Coronation of 800 CE
- [Pope Leo III and Charlemagne], like their predecessors, held the Roman Empire to be one and indivisible, and proposed by the coronation of [Charlemagne] not to proclaim a severance of the East and West.
- Charlemagne's coronation as Emperor, though intended to represent the continuation of the unbroken line of Emperors from Augustus to Constantine VI, had the effect of setting up two separate (and often opposing) Empires and two separate claims to imperial authority.
- In support of Charlemagne's coronation, some argued that the Imperial position was actually vacant, deeming a woman (Irene) unfit to be Emperor.
- Whether he actually desired a coronation at all, remains controversial - his biographer Einhard related that Charlemagne had been surprised by the Pope - but Byzantium felt its role as the sole heir of the Roman Empire threatened and began to emphasize its superiority and its Roman identity.
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Rise of the Holy Roman Empire
- The formation of the Holy Roman Empire was initiated by Charlemagne's coronation as "Emperor of the Romans" in 800, and consolidated by Otto I when he was crowned Emperor in 962 by Pope John XII.
- Some historians refer to the coronation of Charlemagne as the origin of the empire, while others prefer the coronation of Otto I as its beginning.
- Following the example of Charlemagne's coronation as "Emperor of the Romans" in 800, Otto was crowned Emperor in 962 by Pope John XII in Rome, thus intertwining the affairs of the German kingdom with those of Italy and the Papacy.
- Otto's coronation as Emperor marked the German kings as successors to the Empire of Charlemagne, which through the concept of translatio imperii, also made them consider themselves as successors to Ancient Rome.
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Graphing Inequalities
- A straight line drawn through the plane divides the plane into two half-planes, as shown in the diagram below.
- This a true statement, so shade the half-plane containing $(0, 0). $
- The boundary line shown above divides the plane into two half-planes
- All points lying on the line and in the shaded half-plane are solutions.
- Graph an inequality by shading the correct section of the plane