@misc{RichterGebert, author = {Richter-Gebert, J{\"u}rgen}, title = {Mechanical Theorem Proving in Projective Geometry.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1013}, number = {SC-93-05}, abstract = {We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an implementation of this power and present a series of examples treated by the prover, including {\it Pappos' and Desargues' Theorems,} the {\it Sixteen Point Theorem, Saam's Theorem, }the {\it Bundle Condition,} the uniqueness of a harmonic Point and {\it Pascal's Theorem.}}, language = {en} } @misc{RichterGebertZiegler, author = {Richter-Gebert, J{\"u}rgen and Ziegler, G{\"u}nter M.}, title = {Zonotopal Tilings and the Bohne-Dress Theorem.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1212}, number = {SC-93-25}, abstract = {We prove a natural bijection between the polytopal tilings of a zonotope \$Z\$ by zonotopes, and the one-element-liftings of the oriented matroid \${\cal M}(Z)\$ associated with \$Z\$. This yields a simple proof and a strengthening of the Bohne-Dress Theorem on zonotopal tilings.}, language = {en} }