## Surface

#### Hyperboloid

Hyperboloid is a quadric surface. It is characterized by not being a cone or a cylinder, having a center of symmetry, and intersecting many planes into hyperbolas.
One example of Hyperboloid is given by an equation This graph is shown in the first figure.
The nature of Hyperboloid is visualized below. #### Minimal surface

Minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature.
Plane surface and helicoid are example of minimal surface.

Another example of minimal surface is given by This graph is shown in the figure below. #### The helicoid

The helicoid is given by an equation Here, is rotational length and is height
This graph is shown in the figure below. #### Cone

Cone is a surface traced by a straight line being revolving around a fixed vector, about a given point.
The fixed vector is called axis
The straight line is called generator
The point is called vertex
Cone is given by a equation where v is height of the cone.
Here, The graph of a cone is given by  #### Cylinder

Cylinder is a surface traced by a straight line being parallel to a fixed vector.
The fixed vector is called axis
The straight line is called generator
Cylinder is given by a equation where a is radius and v is height of the cylinder.
Here, The graph of a cylinder is given by  #### Pseduo-sphere

The pseudosphere is a surface of constant negative Gaussian curvature. It is a surface of revolution generated by a tractrix about its asymptote. The parametric equation of pseudosphere is u;v∈(0,2π)
The coefficients of first fundamental form are
E=tan h2u, F=0, G=sec h2u
The coefficients of the second fundamental form are  1. Conoidal surface 2. Saddle surface 3. Saddle surface 4. Paraboloid #### Monge’s form  #### General surface of revolution  ## Set

The Venn-diagram below shows the result of a survey conducted at a City Hospital Kathmandu who were attended on a particular day. Set W represents those who complained of body weakness, set H those who complained for headache and set F those who complained of fever. a 1. Use the information in the Venn-diagram to find the number of people who complained
1. body weakness only
2. body weakness and fever only
3. headache
2. Calculate the percentage of those who complained of all the ailments.