Analytic geometry

one-dimensional infinite non-curved geometric object

geometric object that has magnitude (or length) and direction

system for determining the position of a point

curve obtained by intersecting a cone and a plane

study of geometry using a coordinate system

geometric model in which a point is specified by three parameters

coordinate system that specifies each point uniquely by a pair of real numbers called coordinates

thumb|A hyperbola is an open curve with two branches, the intersection of a plane (geometry)|plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.|alt=The image shows a double cone in which a geometrical plane has sliced off parts of the top and bottom half; the boundary curve of the slice on the cone is the hyperbola. A double cone consists of two cones stacked point-to-point and sharing the same axis of rotation; it may be generated by rotating a line about an axis that passes through a point of

algebraic operation that takes two equal-length sequences of numbers

two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space

mathematical operation on two vectors giving a vector as result

right|thumb|Slope: m = \frac{\Delta y}{\Delta x} = \tan(\theta)

220px|right|thumb|Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. 220px|right|thumb|Tangent plane to a sphere

circle with radius one

right|thumb|250px|The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x) right|thumb|250px|A curve intersecting an asymptote infinitely many times

eccentricity of a conic section

point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave to convex, or vice versa

differential operator describing the rotation at a point in a 3D vector field

thumb|right|This chain, whose ends hang from two points, forms a catenary. thumb|right|The silk on this spider web forms multiple elastic catenaries.

three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system

stationary point that is not a local extremum

282px|thumb|The midpoint of the segment (1, 1) to (2, 2)

formula that the area of a planar polygon whose vertices all have integer coordinates equals the number of interior integer points plus half the number of boundary integer points minus one

relative distance of a point from a circle

surface through every point of which runs a straight line which equally is on the surface

family of curves in geometry

subgroup of a real vector space

line determined by two circles

geometric inequality which sets a lower bound on the surface area of a set given its volume

theorem

theorem

matrix of inner products of a set of vectors

thumb|Stereographic projection of the hypersphere's parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles: the curves that intersect have infinite radius (= straight line). In this picture, the whole 3D space maps the surface of the hypersphere, whereas in the next picture the 3D space contained the shadow of the bulk hypersphere. thumb|Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spher

geometric figure

Concept in 3-dimensional geometry

angle between the tangent line to the curve at the given point and the x-axis

representation of a plane as a normal and distance

formula

handedness of a vector space with ordered bases

branch of finite geometry

two closely related mathematical subjects

steepest slope on a surface