parallel lines

Examples of parallel lines in the following topics:

• Parallel and Perpendicular Lines

  • Two lines in a plane that do not intersect or touch at a point are called parallel lines.
  • For example, given two lines: $f(x)=m_{1}x+b_{1}$and $g(x)=m_{2}x+b_{2}$, writing $f(x)$ $\parallel$ $g(x)$ states that the two lines are parallel to each other.  
  • In 2D, two lines are parallel if they have the same slope.
  • Given two parallel lines $f(x)$ and $g(x)$, the following is true:
  • Write equations for lines that are parallel and lines that are perpendicular

• Hatching and Cross-Hatching

  • Hatching and cross-hatching are artistic techniques used to create tonal, shading, and textural effects by drawing closely spaced parallel lines.
  • Hatching and cross-hatching are artistic techniques used to create tonal, shading and textural effects by drawing closely spaced parallel lines.
  • Artists use the technique with varying lengths, angles, closeness, and quality of line to achieve their desired image.
  • Hatch lines are defined as parallel lines which are repeated short intervals and drawn in a single direction.
  • Contoured hatching refers to hatching using curved lines in order to describe light and form of contours.

• Qualities of Line

  • Quality of line refers to the character that is embedded in the way a line presents itself.
  • Hard-edged, jagged lines present a staccato visual movement, while sinuous, flowing lines create a more comfortable feeling.
  • Horizontal, diagonal, and vertical lines describe a line's orientation.
  • Contour lines define the outer edges of an object.
  • Hatch lines are defined as parallel lines which are repeated short intervals generally in one direction.

• Linear and Quadratic Functions

  • Linear and quadratic functions make lines and parabola, respectively, when graphed.
  • Although affine functions make lines when graphed, they do not satisfy the properties of linearity.
  • An affine transformation (from the Latin, affinis, "connected with") is a transformation which preserves straight lines (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of distances between points lying on a straight line (e.g., the midpoint of a line segment remains the midpoint after transformation).
  • It does not necessarily preserve angles or lengths, but does have the property that sets of parallel lines will remain parallel to each other after an affine transformation.
  • The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis .

• Constant Velocity Produces a Straight-Line

  • If a charged particle's velocity is parallel to the magnetic field, there is no net force and the particle moves in a straight line.
  • If the magnetic field and the velocity are parallel (or antiparallel), then sinθ equals zero and there is no force.
  • If is between 0 and 90 degrees, then the component of v parallel to B remains unchanged.
  • In the case above the magnetic force is zero because the velocity is parallel to the magnetic field lines.
  • Identify conditions required for the particle to move in a straight line in the magnetic field

• Parallel-Plate Capacitor

  • A parallel-plate capacitor is an electrical component used to store energy in an electric field between two charged, flat surfaces.
  • For the purpose of this atom, we will focus on parallel-plate capacitors .
  • For a parallel-plate capacitor, capacitance (C) is related to dielectric permittivity (ε), surface area (A), and separation between the plates (d):
  • A brief overview of parallel plates and equipotential lines from the viewpoint of electrostatics.
  • Charges in the dielectric material line up to oppose the charges of each plate of the capacitor.

• Lines of Cleavage and Surgery

  • Langer's lines, sometimes called cleavage lines, are topological lines drawn on a map of the human body .
  • Incisions made parallel to Langer's lines may heal better and produce less scarring than those that cut across.
  • Kraissl's lines differ from Langer's lines in that while Langer's lines were defined in cadavers, Kraissl's lines have been defined in living individuals.
  • The lines described by Kraissl differ in some ways from Langer's lines, particularly on the face.
  • Tension lines of the human skin.

• 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 described by a point on the line and its angle of inclination, or slope.
  • Every line lies in a plane which is determined by both the direction and slope of the line.
  • This direction is described by a vector, $\mathbf{v}$, which is parallel to plane and $P$ is the arbitrary point on plane $M$.
  • Vectors $\mathbf{a}$ and $\mathbf{v}$ are parallel to each other.

• Parallel-Plate Capacitor

  • The parallel-plate capacitor is one that includes two conductor plates, each connected to wires, separated from one another by a thin space.
  • One of the most commonly used capacitors in industry and in the academic setting is the parallel-plate capacitor .
  • The purpose of a capacitor is to store charge, and in a parallel-plate capacitor one plate will take on an excess of positive charge while the other becomes more negative.
  • Potential (V) between the plates can be calculated from the line integral of the electric field (E):

• Serial and Parallel Processing

  • Serial memory processing compares a memory to a target stimulus, while parallel processing carries out multiple operations simultaneously.
  • Serial memory processing is the act of attending to and processing one item at a time, while parallel memory processing is the act of attending to and processing all items simultaneously.
  • Parallel processing is the ability to carry out multiple operations or tasks simultaneously.
  • In parallel processing, the brain simultaneously processes incoming stimuli of differing quality.
  • This line graph depicts both positive and negative self-terminating search, comparing length of list to mean reaction time recall.