Topology : Dual Graph (对偶图) & Urban Planning

Just modify only 4 roads, the above complicated city road congestion improved : by Topology Dual Graphs.

【区别:代数拓扑 (Algebraic Topology)  微分拓扑 (Differential Topology )  微分几何 ( Differential Geometry ) 代数几何 (Algebraic Geometry ) 交换代数  (Commutative Algebra ) 微分流形 (Differential Manifold )

​【区别:代数拓扑 (Algebraic Topology)  微分拓扑 (Differential Topology )  微分几何 ( Differential Geometry ) 代数几何 (Algebraic Grometry ) 交换代数  (Commutative Algebra ) 微分流形 (Differential Manifold ) ?】月如歌:并不能理解什么叫做楼主所说的配对。我简要谈下我对于上述所列名词的理解。… (分享自知乎网)

Sheaves do not belong to algebraic geometry:

Who cares about topology? (inscribed rectangle problem)

Excellent video for the curious minds! Who cares about Topology such as Torus (aka donut) or Mobius Strip ? They can be used to prove difficult math such as the unsolved problem “Inscribed square/rectangle inside any closed loop”.

To understand the Topology on Loops, please view the lecture  here : Homotopy (同伦) and the Fundamental Group (群) of surface.