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Surface, Curves And Equations

If we talk in mathematical terms, the surface Geometry deals with the plane and smooth surfaces. “Carl Friedrich Gauss” gave this concept. In this field the vital role has been played by the Lie groups. Lie groups define many essential elements of the surfaces and also enable us to know about its properties.

A curve is a figure which is not straight like line. Curve geometry may be two-dimensional like Plane Curve and can be three-dimensional like space curve. The meaning of curve basically depends on the context in which it is explained.

Parabola is an example of curve and arc is the segment of curve which is made  by two distinct points on the curve. 

Those equations which are required to find out the area, volume, surface area of the various mathematical figures are called geometry equations. Some of the formulas are shown below:

Area of Square = m 2; where ‘m’ is its side.

Area of Rectangle = mn; where ‘m’ is length and ‘n’ is breadth.

Area of triangle = (1/2) mn; where ‘m’ is its base and ‘n’ is its height.

Volume of Cube = m 3; where ‘m’ is its sides.

Volume of cylinder = ∏s2 t; where‘s’ is its base and t is its height.

Volume of cone = (1/3) ∏r 2 t; where ‘r’ is its radius and t is its lateral height.

Volume of Sphere = (4/3) (22/7)r 3; where ‘r’ is its radius.

Surface area of cube = 6t 2;where ‘t’ is its side.

Surface area of sphere = 4∏ r 2 ; where ‘r’ is its radius.

 

Topics Covered in Surface, Curves And Equations

Equation of a surface

In day to day life, we see different types of shapes some of them are round some are Square and many more. Here we will talk about some of the shapes which are present in the Geometry. In the mathematical geometry there are many shapes which are Circle, cone, cylinder, sphere, and pyramid and so on. Here we will see what these shapes actually are and how to find...Read More

Equation of a curve

In our day to day life we deal with many types of shapes and figures like lines, circles, ellipses, curve and many more. They all come under the curves in Geometry. A Geometry curve can be defined as a line which is not a Straight Line. There are two types of curve which are as follows:-
1. Open curve: - In open curve, we consider those curves whose close Point do n...Read More

Cones

In Geometry, cone is a three dimensional surface which has circular base and also one vertex. In other word, we can say that it is has flat base, and one side is curved surface of a cone. Cones are not polyhedral because it has a curved surface.
Let’s see some formulas related to the cone. Suppose we want to calculate the surface area of base then the formula is given by:
 Surfa...Read More

Cylinders

In cone, base of a cone is always perpendicular to its sides. If a line joining the center of Circle of a given cylinder is perpendicular to the base then the cylinder is a Right Circular Cylinder. Let’s see some formulas and properties of cylinder. 
If length and radius and length or height is defined for then cylinder then volume of a right circular cylinder is given by:
 ...Read More

Plane and straight line

In mathematical Geometry, a plane is a two dimensional surface and it is used to show two dimensional shapes like Circle, triangle, line etc. The angle lie in between two intersecting plane is a dihedral angle.
A line which is not in the form of a curve is known as Straight Line. As we know, equation of a straight line is given by:
 Y = mx + b; or,
 Y = mx + c...Read More

Loci in Space

When a common characteristic exists between a Set of coordinates, they are said to define a locus. The locus of points is defined such that all points will have a constant distance from a given straight line, figure, or equality. For example, boundary of Circle can be considered as collection of points that lie at a fixed distance from the Center of Circle. This fixed dist...Read More

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