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English: Supplemental material for the High School Geometry Wikibook, providing teachers with additional activities, puzzles, and games to allow for additional problem solving opportunities. Date 7 December 2009
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Print/export Download as PDF; ... Euclidean plane geometry (11 C, 96 P) R. Reflection groups (1 C, ... Book of Lemmas; British flag theorem;
Print/export Download as PDF; Printable version; In other projects Wikidata item; ... Euclidean plane geometry (11 C, 96 P) G. Planar graphs (1 C, 88 P) T.
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A plane segment or planar region (or simply "plane", in lay use) is a planar surface region; it is analogous to a line segment. A bivector is an oriented plane segment, analogous to directed line segments. [a] A face is a plane segment bounding a solid object. [1] A slab is a region bounded by two parallel planes.
The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. [1]
Removing five axioms mentioning "plane" in an essential way, namely I.4–8, and modifying III.4 and IV.1 to omit mention of planes, yields an axiomatization of Euclidean plane geometry. Hilbert's axioms, unlike Tarski's axioms , do not constitute a first-order theory because the axioms V.1–2 cannot be expressed in first-order logic .