Mathematics-Formula-Calculator.cpp

#include<iostream.h>
#include<conio.h>
#include<math.h>

struct formulae
{
 int r;
 int i;
 float x;
 float y;
 float z;
};
  formulae c1,c2,c3,p1,p2,p3,p4;
void main()
{
 clrscr();
 cout<<"                         \n\nFORMULAE LIST:\n\n";
 cout<<"1 for ADDITION OF COMPLEX NUMBERS \n";
 cout<<"2 for ROOTS OF QUADRATIC EQUATION\n";
 cout<<"3 for FACTORIAL OF A NUMBER\n";
 cout<<"4 for ARITHMETIC AND GEOMETRIC PROGRESSION\n";
 cout<<"5 for SLOPE OF A LINE\n";
 cout<<"6 for COLLINEARITY OF THREE POINTS\n";
 cout<<"7 for 3 - D GEOMETRY\n\n";
 cout<<"Enter the number of chapter you want to solve using formulae - ";
 int ch;
 cin>>ch;
 clrscr();

 if(ch==1)
{
 cout<<"                         \n\nADDITION OF COMPLEX NUMBERS\n\n";
 cout<<"Enter the real and imaginary part of 1st number\n";
 cin>>c1.r>>c1.i;
 cout<<"Enter the real and imaginary part of 2nd number\n";
 cin>>c2.r>>c2.i;
 c3.r=c1.r+c2.r;
 c3.i=c1.i+c2.i;
 cout<<"Result = "<<c3.r<<" + i"<<c3.i;
}


 else if(ch==2)
{
 int a,b,c,x,y;
 cout<<"                         \n\nROOTS OF QUADRATIC EQUATION\n";
 cout<<"Enter the coefficient of ax^2 + bx+ c from the equation \n";
 cin>>a>>b>>c;
 x=(-b+(sqrt((b*b)-4*a*c)))/(2*a);
 y=(-b-(sqrt((b*b)-4*a*c)))/(2*a);
 cout<<"Value of x = "<<x<<" and "<<y;
}


 else if(ch==3)
{
 cout<<"                         \n\nFACTORIAL OF A NUMBER\n\n";
 cout<<"Enter a number to find factorial \n";
 int n,i,fact=1;
 cin>>n;
 i=n;
 while(n)
{
 fact*=n;
 --n;
}
 cout<<"The factorial of "<<i<<" is "<<fact<<"\n";
}


 else if(ch==4)
{
 cout<<"                         \n\nARITHMETIC AND GEOMETRIC PROGRESSION\n\n";
 cout<<"Enter A to find nth term of an A.P\n";
 cout<<"Enter B to find sum of n terms in A.P.\n";
 cout<<"Enter C to find arithmetic mean in an A.P.\n";
 cout<<"Enter D to find nth term of a G.P.\n";
 cout<<"Enter E to find sum of n terms in G.P.\n";
 cout<<"Enter F to find geometric mean in G.P.\n";
 char c;
 cin>>c;
 clrscr();
 if(c=='A')
{
 cout<<"                         \n\nnth TERM OF AN A.P.\n\n";
 cout<<"Enter value of a from the given A.P. - ";
 int a;
 cin>>a;
 cout<<"\nEnter value of n - ";
 int n;
 cin>>n;
 cout<<"\nEnter balue of d - ";
 int d;
 cin>>d;
 int an=a+(n-1)*d;
 cout<<n<<" term is "<<an;
}
 else if(c=='B')
{
 cout<<"                         \n\nSUM OF n TERMS IN A.P.\n\n";
 cout<<"Enter value of a - ";
 int a;
 cin>>a;
 cout<<"Enter value of n - ";
 int n;
 cin>>n;
 cout<<"Enter value of d - ";
 int d;
 cin>>d;
 int p=n/2;
 int q=2*a;
 int r=n-1;
 int s=r*d;
 int sn=p*(q+s);
 cout<<"Sum of "<<n<<" terms of the A.P. is "<<sn;
}
 else if(c=='C')
{
 cout<<"                         \n\nARITHMETIC MEAN IN AN A.P.\n\n";
 cout<<"Enter 2 numbers a and b to find their Arithmetic mean\n";
 int a,b;
 cin>>a>>b;
 int am=(a+b)/2;
 cout<<"Arithmetic mean of "<<a<<" & "<<b<<" is "<<am<<endl;
 cout<<"Thus A.P. constructed is "<<a<<", "<<am<<", "<<b;
}
 else if(c=='D')
{
 cout<<"                         \n\nnth TERM IN A G.P\n\n";
 cout<<"Enter value of a for the G.P. - ";
 int a;
 cin>>a;
 cout<<"Enter value of r - ";
 int r;
 cin>>r;
 cout<<"Enter value of n - ";
 int n;
 cin>>n;
 int x=n-1;
 int y=pow(r,x);
 int an=a*y;
 cout<<n<<" term of the G.P. is "<<an;
}
 else if(c=='E')
{
 cout<<"                         \n\nSUM OF n TERMS IN G.P.\n\n";
 cout<<"Enter value of a - ";
 int a;
 cin>>a;
 cout<<"Enter value of r - ";
 int r;
 cin>>r;
 cout<<"Enter value of n - ";
 int n;
 cin>>n;
 int p=pow(r,n);
 int q=1-p;
 int t=1-r;
 int sn=(a*q)/t;
 cout<<"Sum of "<<n<<" terms of the G.P. is "<<sn;
}
 else if(c=='F')
{
 cout<<"                         \n\nGEOMETRIC MEAN IN G.P.\n\n";
 cout<<"Enter two numbers a and b to find their geometric mean\n";
 int a,b;
 cin>>a>>b;
 float gm=sqrt(a*b);
 cout<<"Geometric mean of "<<a<<" and "<<b<<" is "<<gm<<endl;
 cout<<"Thus "<<a<<", "<<gm<<", "<<b<<" are consecutive terms of a G.P.";
}
}


 else if(ch==5)
{
 cout<<"                         \n\nSLOPE OF A LINE\n\n";
 cout<<"Enter x and y coordinates of 1st point\n";
 cin>>p1.x>>p1.y;
 cout<<"Enter x and y coordinates of 2nd point\n";
 cin>>p2.x>>p2.y;
 int a=p2.y-p1.y;
 int b=p2.x-p1.x;
 cout<<"Slope of the line = "<<a<<" / "<<b;
}


 else if(ch==6)
{
 cout<<"                         \n\nCOLLINEARITY OF THREE POINTS\n\n";
 cout<<"Enter x and y coordinates of 1st point\n";
 cin>>p1.x>>p1.y;
 cout<<"Emter x and y coordinates of 2nd point\n";
 cin>>p2.x>>p2.y;
 cout<<"Enter x and y coordinates of 3rd point\n";
 cin>>p3.x>>p3.y;
 float a=p2.y-p1.y;
 float b=p2.x-p1.x;
 float m1=a/b;
 float c=p3.y-p2.y;
 float d=p3.x-p2.x;
 float m2=c/d;
 if(m1==m2)
 cout<<"The points are collinear ";
 else
 cout<<"The points are not collinear";
}


 else if(ch==7)
{
 cout<<"                         \n\n3 - D GEOMETRY\n\n";
 cout<<"Enter A to find distance between 2 points\n";
 cout<<"Enter B to find coordinates of the point which divides the line segment internally\n";
 cout<<"Enter C to find coordinates of the point which divides the line segment externally\n";
 cout<<"Enter D to find coordinates of the mid-point of the line segment \n";
 cout<<"Enter E to find coordinates of the centroid of a triangle\n";
 char c;
 cin>>c;
 clrscr();
 if(c=='A')
{
 cout<<"                         \n\nDISTANCE BETWEEN TWO POINTS\n\n";
 cout<<"Enter x, y and z coordinates of 1st point\n";
 cin>>p1.x>>p1.y>>p1.z;
 cout<<"Enter x, y and z coordinates of 2nd point\n";
 cin>>p2.x>>p2.y>>p2.z;
 float a=(p2.x-p1.x)*(p2.x-p1.x);
 float b=(p2.y-p1.y)*(p2.y-p1.y);
 float c=(p2.z-p1.z)*(p2.z-p1.z);
 float d=a+b+c;
 float t=sqrt(d);
 cout<<"Distance between the point = "<<t<<"units";
}
 else if(c=='B')
{
 cout<<"                         \n\nCOORDINATES OF POINT DIVIDING A LINE SEGMENT INTERNALLY\n\n";
 cout<<"Enter x, y and z coordinates of 1st point\n";
 cin>>p1.x>>p1.y>>p1.z;
 cout<<"Enter x, y and z coordinates of 2nd point \n";
 cin>>p2.x>>p2.y>>p2.z;
 cout<<"Enter ratio \n";
 int m,n;
 cin>>m>>n;
 p3.x=((m*p2.x)+(n*p1.x))/(m+n);
 p3.y=((m*p2.y)+(n*p1.y))/(m+n);
 p3.z=((m*p2.z)+(n*p1.z))/(m+n);
 cout<<"Coordinate of the point is ("<<p3.x<<" , "<<p3.y<<" , "<<p3.z<<")";
}
 else if(c=='C')
{
 cout<<"                         \n\nCOORDINATES OF POINT DIVIDING A LINE SEGMENT EXTERNALLY\n\n";
 cout<<"Enter x, y and z coordinates of 1st point\n";
 cin>>p1.x>>p1.y>>p1.z;
 cout<<"Enter x, y and z coordinates of 2nd point\n";
 cin>>p2.x>>p2.y>>p2.z;
 cout<<"Enter ratio\n";
 int m,n;
 cin>>m>>n;
 p3.x=((m*p2.x)-(n*p1.x))/(m-n);
 p3.y=((m*p2.y)-(n*p1.y))/(m-n);
 p3.z=((m*p2.z)-(n*p1.z))/(m-n);
 cout<<"Coordinates of the point is ("<<p3.x<<" , "<<p3.y<<" , "<<p3.z<<")";
}
 else if(c=='D')
{
 cout<<"                         \n\nMID-POINT\n\n";
 cout<<"Enter x, y and z coordinates of 1st point\n";
 cin>>p1.x>>p1.y>>p1.z;
 cout<<"Enter x, y and z coordinates of 2nd point\n";
 cin>>p2.x>>p2.y>>p2.z;
 p3.x=(p1.x+p2.x)/2;
 p3.y=(p1.y+p2.y)/2;
 p3.z=(p1.z+p2.z)/2;
 cout<<"Coordinates of mid-point are ("<<p3.x<<" , "<<p3.y<<" , "<<p3.z<<")";
}
 else if(c=='E')
{
 cout<<"                         \n\nCENTROID OF A TRIANGLE\n\n";
 cout<<"Enter coordinates of 1st vertex of the triangle\n";
 cin>>p1.x>>p1.y>>p1.z;
 cout<<"Enter coordinates of 2nd vertex of the triangle\n";
 cin>>p2.x>>p2.y>>p2.z;
 cout<<"Enter coordinates of 3rd vertex of the triangle\n";
 cin>>p3.x>>p3.y>>p3.z;
 p4.x=(p1.x+p2.x+p3.x)/3;
 p4.y=(p1.y+p2.y+p3.y)/3;
 p4.z=(p1.z+p2.z+p3.z)/3;
 cout<<"Coordinates of the centroid of the triangle is ("<<p4.x<<" , "<<p4.y<<" , "<<p4.z<<")";
}
}
getch();
}