Things often have a shape

What is space? Well, it can be Euclidean, but it may also be non-Euclidean, and have curvature!

Trigonometry

https://en.wikipedia.org/wiki/Geometry

New Horizons in Geometry (Dolciani Mathematical Expositions) 1st Edition

See part of the book here: http://www.mamikon.com/VisualCalc.pdf

http://world.mathigon.org/

Euclidean geometry

The elements. Has some subtle flaws in mathematical rigour. Fifth postulate, in particular, was controversial.

cool colorful version (also here)

Solids: http://dmccooey.com/polyhedra/VersiRegular.html

https://mathigon.org/polypad

Geometrical constructions

Angle bisector

See game Euclidea

Non-Euclidean geometry

Elliptic geometry

Hyperbolic geometry

Riemannian geomtry

Differential geometry

See pages 88 and forth in GEB.

one can let the meanings of "point" and "line", and so on be determined by the set of theorems (or propositions) in which they occur. These are called undefined terms, and they only get meaning through these theorems.

Projective geometry

Complex geometry

http://www.engare.design/

http://www.geometrygames.org/

Algorithm to convert a polygon into another one by cutting/folding: https://dmsm.github.io/scissors-congruence/

4D toys

How to make the Minecraft world look spherical

Ritt-Wu's decomposition algorithm used in some modern proofs in geometry