# 2D - Plane

A plane, in relation to mathematics, is a flat two-dimensional surface. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with the walls of a room, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry.

Many fundamental tasks in mathematics, geometry, trigonometry, graph theory and graphing are performed in a two-dimensional space, or in other words, in the plane.

## 2D - Plane Equations

• cos theta = (Deltax)/|Deltar|
• Delta x = |Deltar|* cos theta
• Delta y = |Deltar|* sin theta
• Deltax_t = Deltax_1 + Deltax_2
• Deltay_t = Deltay_1 + Deltay_2
• sin theta = (Deltay)/|Deltar|
• theta = cos^-1(hatA * hatB)
• vecA * vecB
• vecA + vecB
• vecA - vecB
• |r| = sqrt(Deltax^2 + Deltay^2)
• |vecA + vecB|
• A = wh/2
• Adjacent Side - Pythagorean Theorem
• Angle From Law of Sines
• Area of Regular Polygon [apothem, number of sides]
• Area of Regular Polygon [perimeter, number of sides]
• Area of Semicircle
• Area of semicircle with diameter
• Circe - Area within Triangle
• Circle - Angle of an Arc (depth)
• Circle - arc length
• Circle - area
• Circle - Area around Triangle
• Circle - Area f(Circumference)
• Circle - Area f(diameter)
• Circle - area of an arc sector
• Circle - area of an arc segment
• Circle - area of an arc segment (h)
• Circle - area of annulus
• Circle - area of arc
• Circle - area of sector
• Circle - Chord Length from Angle and Radius
• Circle - Chord Length from Arc Length and Radius
• Circle - circumference
• Circle - Diameter f(area)
• Circle - General Equation from center and point
• Circle - radius around triangle
• Circle - Radius from Area
• Circle - Radius from chord length and arc height
• Circle - radius in triangle
• Circle with the Same Area as an Ellipse
• Circle with the Same Perimeter as an Ellipse
• Circle- Circumference f(Area)
• Decagon Area
• Distance between two points
• Dodecagon Area
• Ellipse - area
• Ellipse - circumference (apx 3)
• Ellipse - circumference (apx1)
• Ellipse - circumference (apx2)
• Ellipse - circumference (apx3)
• Ellipse - eccentricity
• Ellipse - Linear Eccentricity
• Elliptical Volume
• Equilateral Triangle Area
• Equilateral Triangle Volume
• Hendecagon Area
• Heptagon Area
• Hexagon Side Length
• Hypotenuse - Pythagorean Theorem
• Interpolation
• Line - Slope Intercept
• mid-point between two points
• Nonagon Area
• Parabola
• Parabola - arc length
• Parabola - area