Analytic Geometry- Lobachevski-Non-Euclidean Geometry
- Spherical Triangle
Definition of a Derivative- Matrices
- Binomial Coefficients
- Series
- Complex Numbers
- Indefinite Integrals
- Integrals
- Probability Theory
- Hyperbolic Functions
- Differential Equations
- Beta Function
Formulas from plane analytic geometry
DISTANCE d BETWEEN TWO POINTS P1(x1,y1) AND P2(x2,y2)
SLOPE m OF LINE JOINING TWO POINTS P1(x1,y1) AND
P2(x2,y2)
EQUATION OF LINE JOINING TWO POINTS P1(x1,y1) AND
P2(x2,y2)
y = mx + b
where 
is the intercept on the y axis, i.e. the y intercept.
EQUATION OF LINE IN TERMS OF x INTERCEPT a≠0 AND y INTERCEPT b≠O
NORMAL FORM FOR EQUATION OF LINE
xcosα + ysinα = p
where p = perpendicular distance from origin O to line
and α = angle of inclination of perpendicular with
positive x axis.
GENERAL EQUATION OF LINE
Ax + By + C = 0
DISTANCE FROM POINT (x1, y1) TO LINE Ax + By + C = 0
where the sign is chosen so that the distance is nonnegative.
ANGLE ψ BETWEEN TWO LINES HAVING SLOPES m1, AND m2
Lines are parallel or coincident if and only if mx = m2.
Lines are perpendicular if and only if m2 = -1/m1.
AREA OF TRIANGLE WITH VERTICES AT (x1, y1), (x2, y2), (x3, y3)
Area
= ± ½ (x1y2 + y1x3 + y3x2 - y2x3 - y1x2 - x1y3)
= ± ½ (x1y2 + y1x3 + y3x2 - y2x3 - y1x2 - x1y3)
where the sign is chosen so that the area is nonnegative. If the area is zero the points all lie on a line.
