Mathematical Imagery by Jos Leys

Topology movies

Topics in topology

Galleries :

The Klein bottle
Construction of a Klein bottle by joining the edges of a rectangle.
Added on 2016-02-16
Two Moebius strips make a Klein bottle
Added on 2016-02-16
The figure 8 Klein bottle
The less-known form of the Klein bottle...
Added on 2016-02-16
Multiple Klein bottles
Linked Klein bottles. Note that the number of "bottles" needs to be uneven in order to have a non-orientable surface.
Added on 2016-02-16
From an octagon to a genus 2 surface
An octagon can be bent into a genus two surface (a surface with two holes) by joining the sides with the same colour..
Added on 2016-02-16
From a 16-gon to a genus 4 surface
A polygon with 16 sides can be formed into a genus 4 surface, a surface with 4 holes.
Added on 2016-02-16
From a 40-gon to a genus 10 surface.
A polygon with 40 edges can be bent into a genus 10 surface (a surface with 10 holes).
Added on 2016-02-16
The real projective plane and the Moebius strip
The real projective plane minus a disc is a Moebius strip.
Added on 2016-02-18
The cross-cap.
The construction of the cross-cap.
Added on 2016-02-17
The Boy surface
The construction of a Boy surface.
Added on 2016-02-17
Moebius strip and cross-cap
Visual proof that a Moebius strip is homeomorphic to a cross-cap with a disc removed.
Added on 2016-03-01
The Klein Quartic II
The transition from a hyperbolic 14-gon to a genus 3 surface, while preserving the tiling by 24 heptagons.
Added on 2016-02-16
Connected sum of two real projective planes
Visual proof that the connected sum of two real projective planes is a Klein bottle.
Added on 2016-02-18
Connected sums of real projective plane and torus or Klein bottle.
Visual proof that the connected sum of a real projective plane and a torus , and the connected sum of a real projective plane and a Klein bottle are homeomorphic.
Added on 2016-02-20
Dodecahedral tesselation of the hypersphere
A dissection of the 120 cell in twelve rings of 10 dodecahedra. Two sets of six rings form 2 solid interlocked tori. The film starts by showing the 600 cell, the dual of the 120 cell.
Added on 2016-02-21
The Klein Quartic I
How this hyperbolic tiling can be folded into a genus 3 surface.
Added on 2016-02-16

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