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Geometry1a) Non-Euclidean geometries This
allows us to break the rules of conventional
geometry for example, angles in a triangle no
longer add up to 180 degrees. In some geometries
triangles add up to more than 180 degrees, in
others less than 180 degrees.1b) The shape of
the universe non-Euclidean Geometry is at the
heart of Einsteins theories on General
Relativity and essential to understanding the
shape and behavior of the universe.2)
Hexaflexagons These are origami style shapes
that through folding can reveal extra faces.3)
Minimal surfaces and soap bubbles Soap bubbles
assume the minimum possible surface area to
contain a given volume.