Natural Length is the length when the spring is not under any kind of tension or compression. Equilibrium length is the is the length when the spring is under a load. Natural length depicts that it is under no circumstances encountering force.

Natural unemployment is the minimum unemployment rate resulting from real or voluntary economic forces. It represents the number of people unemployed due to the structure of the labor force, including those replaced by technology or those who lack the skills necessary to get hired.

The minus sign in F = -kx is there by convention; we think of F as the restoring force. When the spring is compressed, a positive force is required to extend it, and when it is extended, a negative force is required to shorten it, or restore it to its natural length.

The economy is considered to be at full employment when the actual unemployment rate is equal to the natural rate. When the economy is at full employment, real GDP is equal to potential real GDP.

The natural length of the spring is its length with no mass attached. We assume that the spring obeys Hooke’s law: If the length of the spring is changed by an amount ΔL from its natural length, then the spring exerts a force Fs=kΔL, where k is a positive number called the spring constant.

Overall length = Pickup length + Pre-load length + Working extension + (Inside diameter x 3.14 x 1.5).

A ideal spring has an equilibrium length. It is a measure of the spring’s stiffness. When a spring is stretched or compressed, so that its length changes by an amount x from its equilibrium length, then it exerts a force F = -kx in a direction towards its equilibrium position.

In modern notation the equation of the spiral is r = aeθ cot b, in which r is the radius of each turn of the spiral, a and b are constants that depend on the particular spiral, θ is the angle of rotation as the curve spirals, and e is the base of the natural logarithm.

One of the key parameters to characterize the morphology of spiral galaxies is the pitch angle. The pitch angle is the angle between the tangents to a spiral arm and a perfect circle, which measures how tightly the spiral arms are wound.

The main difference between Helix and Spiral is that the Helix is a smooth space curve and Spiral is a curve which emanates from a point, moving farther away as it revolves around the point. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis.

The double helix DNA turns after every 10 base pairs at a distance of 3.4 nm. This distance is called pitch. The distance between two base pairs is 0.34 nm.

Definition – What does Helicoid mean? The shape of a helicoid is defined by its pitch, its inside diameter, whether it turns to the left or to the right around the drill string and the thickness of the material from which it’s made.

1 : forming or arranged in a spiral. 2 : having the form of a flat coil or flattened spiral helicoid snail shell.

The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo 1986).

: a helicoid with generating line perpendicular to its axis.

You can create a helicoid by dipping a wire wound into a helix with a wire running along its axis into a container of bubble solution. A helicoid is a minimal surface.

A parametrized surface is a mapping by a function Φ:R2→R3 (confused?) of a planar region D onto a surface floating in three dimensions. To calculate the area of this surface, we chop up the region D into small rectangles, as displayed below for the function Φ(u,v)=(ucosv,usinv,v).

A parametrized surface is the image of the uv-map. The domain of the uv-map is called the parameter do- main. If we keep the first parameter u constant, then v ↦→ r(u, v) is a curve on the surface. Similarly, if v is constant, then u ↦→ r(u, v) traces a curve the surface.

The area of the parallelogram is simply the magnitude of the cross product of those two vectors ΔA=∥∂Φ∂u×∂Φ∂v∥ΔuΔv. The total surface area is approximated by a Riemann sum of such terms.

Edit: The surface integral of the constant function 1 over a surface S equals the surface area of S. In other words, surface area is just a special case of surface integrals. A similar thing happens for line integrals: the line integral of the constant function 1 over a curve equals the length of the curve.

If the vector field F represents the flow of a fluid, then the surface integral of F will represent the amount of fluid flowing through the surface (per unit time). The amount of the fluid flowing through the surface per unit time is also called the flux of fluid through the surface.

You can think about surface integrals the same way you think about double integrals:

1. Chop up the surface S into many small pieces.
2. Multiply the area of each tiny piece by the value of the function f on one of the points in that piece.
3. Add up those values.

So the dot product →v⋅d→S gives the amount of flow at each little “patch” of the surface, and can be positive, zero, or negative. The integral ∫→v⋅d→S carried out over the entire surface will give the net flow through the surface; if that sum is positive (negative), the net flow is “outward” (“inward”).

The circle on an integral generally means the integral is performed on a space which has lower dimension than the ambient space and is a “closed loop” which is informal language to say it’s compact (finite in size) and without boundary.