Themodynamics is the study of how changes in temperature and pressure (or similar parameters) affect the properies of systems. These "systems" are different topological structures.

Thermodynamics treat of three methods of transporting heat:

• conduction, transporting between different topological systems.
• convection, transporting with the same topological system.
• radiation, transporting within a system or between systems.

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HOMOLOGY OF EULER'S POLYGONAL RULE (TOPOLOGICAL CHARACTERISTIC) AND GIBB'S PHASE RULE

• EULER'S POLYGONAL RULE: V + F - E = 2, where V denotes number of polygonal vertices, F denotes number of polygonal faces, E denotes number of polygonal edges;
• GIBB'S PHASE RULE: D + P - C = 2, where D denotes number of degrees of freedom of thermodynamic system, P denotes number of phases of thermodynamic system, C denotes number of components of thermodynamic system;
• HOMOLOGY of Euler to Gibbs: V : D :: F : P :: E : C, that is, V D, F P , E C, and EULER'S RULE GIBB'S RULE.

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ASSIGNMENT: POINCARÉ generalized this rule to allow for "holes" and such. Is this homologous to any thermodynamic aspect?