Multiplicative distance

In algebraic geometry, [math]\displaystyle{ \mu }[/math] is said to be a multiplicative distance function over a field if it satisfies

• [math]\displaystyle{ \mu(AB)\gt 1.\, }[/math]
• AB is congruent to A'B' iff [math]\displaystyle{ \mu(AB)=\mu(A'B').\, }[/math]
• AB < A'B' iff [math]\displaystyle{ \mu(AB)\lt \mu(A'B').\, }[/math]
• [math]\displaystyle{ \mu(AB+CD)=\mu(AB)\mu(CD).\, }[/math]

See also

• Algebraic geometry
• Hyperbolic geometry
• Poincaré disc model
• Hilbert's arithmetic of ends