A Unified Theory of Proportion
A Unified Theory of Proportion
A universal convex set in Euclidean space
A Variant of Jung΄s Theorem
A weighted geometric inequality and its applications.
About a determinant of rectangular matrix and its geometric interpretation.
Absolute Geometrie nach Johann Bolyai [Book]
Achèvement de la démonstration géométrique élémentaire donnée par Steiner pour ce théorème : «le cercle possède la plus grande parmi toutes les figures planes isopérimètres»
Affine and projective generalization of Wallace lines.
Algebraic proofs for geometric statements.
Algorithmische Transformation von Papierstrukturen - Ein Beitrag zur Verallgemeinerung des Konstruktionsbegriffes
Alternative Proof of Sine's Theorem on the Size of a Regular Polygon in Rn with the l...-Metric.
Altitude, Orthocenter of a Triangle and Triangulation
We introduce the altitudes of a triangle (the cevians perpendicular to the opposite sides). Using the generalized Ceva’s Theorem, we prove the existence and uniqueness of the orthocenter of a triangle [7]. Finally, we formalize in Mizar [1] some formulas [2] to calculate distance using triangulation.
An Algorithm for Lifting Points in a Tropical Variety
An Analogue of the Pythagorean Theorem with Regualr n-Gons instead of Squares.
An axiom system for full -dimensional Euclidean geometry
We present an axiom system for class of full Euclidean spaces (i.e. of projective closures of Euclidean spaces) and prove the representation theorem for our system, using connections between Euclidean spaces and elliptic planes.
An Axiomatics for Hyperbolic Projective-Metric Planes in Terms of Lines and Orthogonality
Hyperbolic projective-metric planes, first axiomatized by R. Lingenberg [7], are shown to be axiomatizable in terms of lines and orthogonality.
An eigenvalue problem with mixed boundary conditions and trace theorems.
An elementary proof of Blundon's inequality.
An elementary proof of the Theorem of Beckmann and Quarles.