touch point

Examples of touch point in the following topics:

• 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.
  • The tangent line (or simply the tangent) to a plane curve at a given point is the straight line that "just touches" the curve 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.
  • The approximation works well as long as the point $(x,y,z) $ under consideration is close enough to $(x_0,y_0,z_0)$, where the tangent plane touches the surface.
  • The tangent plane to a surface at a given point is the plane that "just touches" the surface at that point.

• The Derivative and Tangent Line Problem

  • The tangent line $t$ (or simply the tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
  • Informally, it is a line through a pair of infinitely close points on the curve.
  • To find the tangent line at the point $p = (a, f(a))$, consider another nearby point $q = (a + h, f(a + h))$ on the curve.
  • It barely touches the curve and shows the rate of change slope at the point.
  • Define a derivative as the slope of the tangent line to a point on a curve

• Derivatives and Rates of Change

  • Historically, the primary motivation for the study of differentiation was the tangent line problem, which is the task of, for a given curve, finding the slope of the straight line that is tangent to that curve at a given point.
  • The word tangent comes from the Latin word tangens, which means touching.
  • Thus, to solve the tangent line problem, we need to find the slope of a line that is "touching" a given curve at a given point, or, in modern language, that has the same slope.
  • If $x$ and $y$ are real numbers, and if the graph of $y$ is plotted against $x$, the derivative measures the slope of this graph at each point.
  • Describe the derivative as the change in $y$ over the change in $x$ at each point on a graph

• Spherical and Plane Waves

  • In 1678, he proposed that every point that a luminous disturbance touches becomes itself a source of a spherical wave; the sum of these secondary waves determines the form of the wave at any subsequent time.
  • Since the waves all come from one point source, the waves happen in a spherical pattern.
  • All the waves come from a single point source and are spherical .
  • Each point on the wave produces waves which interfere with each other either constructively or destructively.
  • When waves are produced from a point source, they are spherical waves.

• Assessing CNS Disorders

  • An example of a specific type of neurological test is a monofilament test which evaluates fine touch by applying pressure to the skin with a set of nylon filaments.
  • Sensory system testing involves provoking sensations of fine touch, pain, and temperature.
  • Fine touch can be evaluated with a monofilament test, touching various dermatomes with a nylon monofilament to detect any subjective absence of touch perception.

• Integration of Signals from Mechanoreceptors

  • The configuration of the different types of receptors working in concert in the human skin results in a very refined sense of touch .
  • The large mechanoreceptors (Pacinian corpuscles and Ruffini endings) are located in the lower layers and respond to deeper touch.
  • The subject reports if they feel one point or two points.
  • If the two points are felt as one point, it can be inferred that the two points are both in the receptive field of a single sensory receptor.
  • The points could then be moved closer and re-tested until the subject reports feeling only one point.

• Plant Responses to Wind and Touch

  • Plants respond to wind and touch by changing their direction of growth, movement, and shape.
  • These are examples of how plants respond to touch or wind.
  • A thigmonastic response is a touch response independent of the direction of stimulus.
  • Tendrils of a redvine produce auxin in response to touching a support stick and then transfer the auxin to non-touching cells.
  • The non-touching cells elongate faster to curl around the support stick.

• Capacitors with Dielectrics

  • A dielectric partially opposes a capacitor's electric field but can increase capacitance and prevent the capacitor's plates from touching.
  • Eventually every material has a "dielectric breakdown point," at which the potential difference becomes too high for it to insulate, and it ionizes and permits the passage of current.

• Animal Communication and Living in Groups

  • Animals communicate using signals, which can be chemical (pheromones), aural (sound), visual (courtship displays), or tactile (touch).
  • These signals are chemical (pheromones), aural (sound), visual (courtship and aggressive displays), or tactile (touch).
  • If at any point the display is performed incorrectly or a proper response is not given, the mating ritual is abandoned and the mating attempt will be unsuccessful.
  • Many animals, especially primates, communicate with other members in the group through touch.
  • Activities such as grooming, touching the shoulder or root of the tail, embracing, lip contact, and greeting ceremonies have all been observed in the Indian langur, an Old World monkey.

• Product Life-Cycle Curve

  • The two charts and demonstrate the break-even point reached during the product life cycle as well as sales and profits in general.
  • The iPod touch is currently in the mature phase of the product life cycle.
  • This is because the iPod touch is just an evolution of a product that has been around for long time.
  • Today, the iPod touch is more than just a music player; it plays videos, runs apps and can be used as an organizer.