From an ordinary phenomenon in daily life——how to keep a chair stable,by establishing a mathematical model through mathematical tools to prove the fact,we can work out four-point coplanar theorem in a closed circle of smooth continuous curve space.

The analysis calculation method for circular plates subjected to distribution load which is continuous and derivable and axial symmetry;

It also discuss how to create a smooth curve which passes a serial of present point.

In order to print out the record as a smooth curve, the data should be fitted or interpolated.

In like manner, adefinition of smooth curved surface is also proposed.

In the computer geographic mapping,the tension spline interpolation is an effective method to realize the smoothing curve.

that a class of discontinuity points are distributed over limited smooth curves and that bounded bivar function in bounded closed region has the nature of integrability,by the use of the property that a smooth curve s area is zero.