For example, all of the following points are on the xy plane: The xy plane can be described as the set of all points (x, y, z) where z = 0. In 3D space (also called xyz space), the xy plane contains the x-axis and y-axis: Equiangular Spiral, Spira Mirabilis (Logarithmic Spiral).x and y intercepts: The points where a graph crosses the x-axis or y-axis.x, y coordinate system: A system with a horizontal (x) axis and vertical (y) axis.Velocity: Rate of change of displacement.Trilinear Coordinates: a way to represent a point in the plane using a triangle as the coordinate system.Transformations: shifts, dilations and other “movement” along the x or y axis.Tautochrone Problem / Brachistochrone: Classic problems about swinging pendulums.See also: Vertical Tangents and Horizontal Tangents. Tangent line: a line that touches a graph at only one point and is practically parallel.Spherical coordinates: Coordinate system on a sphere.Sketching Graphs on the Cartesian Plane.Secant line: A secant line connects two ore more points on a curve An external secant is the “outside” part of the secant line.Riemann Sums: Estimating the area under a curve with rectangles.Quadrant: one of the four regions of the Cartesian plane / x-y axis.Slope: the ratio of a change in x (δx) to a change in y (δy).Rate of change: a measure (a rate) of how things are changing.Polar coordinates: “Circular” coordinates on a plane.Pedal Coordinates: Tangential coordinates.Parallel Cross Sections: repeated cross sections for a solid, parallel to each other.Parabola: a u-shaped curve The graph of a quadratic function.Level Curve: Analogous to contour lines on a map.Length of a Line Segment: Measuring “how far” along an x or y axis.Intersection of lines: The place where two or more graphs cross each other.Hyperbola: Two symmetrical curves that have special properties.Epicycles of Ptolemy: A ancient model of the universe.Displacement Function: gives us how far a particle has moved from a starting point at an given time.Delta x / Delta y: Distance traveled along the x- or y-axis.Distance Formula / Function: measures the distance between two points in a set (e.g.Coterminal Angles: Angles that have the same terminal side.
Center function: gives the trilinear coordinates of a triangle’s center.Bipolar Coordinate System: An unusual system used in GIS and electrical field theory.Centroid: The average of all points in an object (e.g.Area under the curve: Calculating the area between a graph and the x-axis.Area of a Bounded Region: are of a shape contained within a set of functions.Arc Length Formula: An “arc” is a curve segment The arc length formula tells you how long this segment is.It’s more common to take a course in Calculus and Analytic Geometry, which blends the principles of basic analytic geometry with concepts like functions, limits, continuity, derivatives, antiderivatives, and definite integrals. Calculus and Analytic GeometryĬalculus and analytic geometry have become so intertwined, it’s rare nowadays to find a course in pure “Analytic Geometry”. For example, the linear function f(x) = x 2 – 2 (an equation) can also be represented by a graph:Įuclidean Geometry is based solely on geometric axioms without formulas or co-ordinates Analytic geometry is the “marriage” of algebra and geometry with axes and co-ordinates. Analytic geometry creates a connection between graphs and equations.
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