Definition/Meaning  Word/Phrase 
geometry of affine transformations 
affine geometry

Egyptian polymath (born in Iraq) whose research in geometry and optics was influential into the 17th century; established experiments as the norm of proof in physics (died in 1040) 
AlHasan ibn alHaytham
,
alHaytham
,
Alhacen
,
Alhazen
,
Ibn alHaytham

(geometry) the angle formed by the xaxis and a given line (measured counterclockwise from the positive half of the xaxis) 
angle of inclination
,
inclination

Greek mathematician and physicist noted for his work in hydrostatics and mechanics and geometry (287212 BC) 
Archimedes

pioneer of nonEuclidean geometry (18261866) 
Bernhard Riemann
,
Georg Friedrich Bernhard Riemann
,
Riemann

geometry, device for drawing circles or arcs in 
compass
,
pair of compasses

(geometry) a curve generated by the intersection of a plane and a circular cone 
conic
,
conic section

geometry of properties that remain invariant under projection 
descriptive geometry
,
projective geometry

(geometry) a straight line connecting any two vertices of a polygon that are not adjacent 
diagonal

(geometry) the interchangeability of the roles of points and planes in the theorems of projective geometry 
duality

(geometry) a ratio describing the shape of a conic section; the ratio of the distance between the foci to the length of the major axis 
eccentricity

geometry based on Euclid's axioms: e.g., only one line can be drawn through a point parallel to another line 
elementary geometry
,
Euclidean geometry
,
parabolic geometry

nonEuclidean geometry that regards space is like a sphere and a line is a great circle 
elliptic geometry
,
Riemannian geometry

(geometry) a plane rectangle with four equal sides and four right angles; a foursided regular polygon 
foursquare
,
square

(mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry 
fractal

geometry of fractals 
fractal geometry

mathematician specializing in geometry 
geometer
,
geometrician

someone who teaches geometry 
geometry teacher

nonEuclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane 
hyperbolic geometry

Russian mathematician who independently discovered nonEuclidean geometry (17921856) 
Lobachevsky
,
Nikolai Ivanovich Lobachevsky
