Dendrite tips as elliptical paraboloids

D V Alexandrov1, E A Titova2, P K Galenko1,3

  • 1Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Ekaterinburg 620000, Russia.

Related Concept Videos

Centroid for the Paraboloid of Revolution01:16

Centroid for the Paraboloid of Revolution

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.
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...
698
Reflective Property of Parabolas01:26

Reflective Property of Parabolas

A parabola is a basic type of conic section that results from the intersection of a plane with a double-napped cone in a direction parallel to one of the cone's sides. This U-shaped curve has a distinctive reflective property: all incoming rays parallel to its axis of symmetry are directed toward a single point, known as the focus. This property is widely utilized in optical and communication technologies that require precise signal concentration.In analytic geometry, a parabola is defined as...
9
Parabolas01:30

Parabolas

A parabola is a fundamental curve in the family of conic sections arising from the intersection of a plane with a double-napped cone when the plane is parallel to the cone’s slant height. This geometric condition yields a unique open curve defined by its equidistance from a fixed point, the focus, and a fixed line, the directrix.A parabola is mathematically defined as the locus of all points in a plane that are equidistant from the focus and the directrix. In Cartesian coordinates, the...
14
Neurons: The Cell Body and the Dendrites01:23

Neurons: The Cell Body and the Dendrites

A typical nerve cell comprises three main components: the cell body, dendrites, and the axon. The cell body, also known as the soma or perikaryon, serves as the central biosynthetic hub housing a nucleus surrounded by cytoplasm containing organelles commonly found in most cells. Notably, Nissl bodies, clusters of the rough endoplasmic reticulum and free ribosomes responsible for protein synthesis, are distinctive features of the neuronal cell body. As neurons age, aggregates of a brown pigment...
5.1K
Ellipses01:30

Ellipses

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest...
17
Hyperbolas01:30

Hyperbolas

A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse...
24