Classical Geometry: Euclidean, Transformational, Inversive, and Projective

INDEX

Symbols

I Ideal point

Extended Euclidean plane

Inversive plane

Projective plane

[ABCD]

Symbol for area of quadrilateral ABCD

[XYZ] Symbol for area of ΔXYZ

≡ Symbol for congruence

C(P, r) Circle with center P and radius r

~ Symbol for similarity

l ⊥ m Lines l and m are perpendicular

l || m Lines l and m are parallel

A

Abelian group

Adjacent angles

Altitudes

Analysis figure

Angle Bisector Theorem

Angle bisectors

Characterization

Concurrent

Internal

Angle-Side Inequality

Angles

Congruent

Directed

Undirected

Vertically opposite

Antiquity, three problems of

Apollonius’ Theorem

Arbelos Theorem

Archimedean tiling

Area

Additivity property

Bounded figures

Circle

Fundamental unit

Invariance property

Parallelogram

Polygon

Postulates

Ratios

Rectangle

Square

Trapezoid

Triangle

Unit square

Area of a triangle

Base-altitude formula

Heron’s Formula

Inradius formula

Arithmetic progression

Arms of an angle

B

Basic constructions

Bijection

Brianchon’s Theorem

Butterfly Theorem

C

Cairo tiling

Cancellation laws

Cayley table

Center of inversion

Center of perspectivity

Center of reciprocation

Center of rotation

Center of similitude

Centroid

Triangle

Ceva’s Theorem

Altitudes concurrent

Applications

Extended plane

Extended version

Internal angle bisectors concurrent

Medians concurrent

Proof

To compute ratio or distance

Cevian

Cevian product

Circle

Tangent line

Circle of Apollonius

Inversion

Circle of inversion

Circle of reciprocation

Circumcenter

Circumcircle

Circumcircle of a triangle

Closest point ...