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→Duality : logical and topological: spacing
For example, consider the axiom or initial equation that is shown below:
For example, consider the axiom or initial equation that is shown below:
{| align="center" border="0" cellpadding="10" cellspacing="0"
{| align="center" cellpadding="10"
| [[Image:Logical_Graph_Figure_3_Visible_Frame.jpg|500px]] || (3)
| [[Image:Logical_Graph_Figure_3_Visible_Frame.jpg|500px]] || (3)
|}
|}
This can be written inline as “ <math>(~(~)~)~=</math> ” or set off in a text display:
This can be written inline as “ <math>(~(~)~)~=</math> ” or set off in a text display:
{| align="center" cellpadding="10"
| width="33%" | <math>(~(~)~)</math>
| width="34%" | <math>=\!</math>
| width="33%" |
|}
When we turn to representing the corresponding expressions in computer memory, where they can be manipulated with utmost facility, we begin by transforming the planar graphs into their [[duality (mathematics)|topological dual]]s. The planar regions of the original graph correspond to nodes (or points) of the [[dual graph]], and the boundaries between planar regions in the original graph correspond to edges (or lines) between the nodes of the [[dual graph]].
When we turn to representing the corresponding expressions in computer memory, where they can be manipulated with utmost facility, we begin by transforming the planar graphs into their [[duality (mathematics)|topological dual]]s. The planar regions of the original graph correspond to nodes (or points) of the [[dual graph]], and the boundaries between planar regions in the original graph correspond to edges (or lines) between the nodes of the [[dual graph]].