S . D . ▁San rem ese ▁Cal cio ▁man agers ▁Category : Associ ation ▁football ▁def enders <0x0A> </s> ▁In ▁geometry , ▁De hn ▁introduced ▁two ▁examples ▁of ▁plan es , ▁a ▁semi - E uclidean ▁geometry ▁and ▁a ▁non - Leg end rian ▁geometry , ▁that ▁have ▁infinitely ▁many ▁lines ▁parallel ▁to ▁a ▁given ▁one ▁that ▁pass ▁through ▁a ▁given ▁point , ▁but ▁where ▁the ▁sum ▁of ▁the ▁angles ▁of ▁a ▁triangle ▁is ▁at ▁least ▁ π . ▁ ▁A ▁similar ▁phenomen on ▁occurs ▁in ▁hyper bol ic ▁geometry , ▁except ▁that ▁the ▁sum ▁of ▁the ▁angles ▁of ▁a ▁triangle ▁is ▁less ▁than ▁ π . ▁▁ ▁De hn ' s ▁examples ▁use ▁a ▁non - Arch im ede an ▁field , ▁so ▁that ▁the ▁Arch im ede an ▁ax iom ▁is ▁viol ated . ▁ ▁They ▁were ▁introduced ▁by ▁ ▁and ▁discussed ▁by ▁. ▁ ▁De hn ' s ▁non - arch im ede an ▁field ▁ Ω ( t ) ▁ ▁To ▁construct ▁his ▁geomet ries , ▁De hn ▁used ▁a ▁non - Arch im ede an ▁ordered ▁P yth ag ore an ▁field ▁ Ω ( t ), ▁a ▁P yth ag ore an ▁closure ▁of ▁the ▁field ▁of ▁rational ▁functions ▁R ( t ), ▁ ▁consisting ▁of ▁the ▁smallest ▁field ▁of ▁real - valu ed ▁functions ▁on ▁the ▁real ▁line ▁containing ▁the ▁real ▁constants , ▁the ▁identity ▁function ▁t ▁( t aking ▁any ▁real ▁number ▁to ▁itself ) ▁and ▁closed ▁under ▁the ▁operation ▁ ω ▁→ ▁.