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- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/zz%3A_Back_Matter/20%3A_GlossaryExample and Directions Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pag...Example and Directions Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] (Optional) Caption for Image (Optional) External or Internal Link (Optional) Source for Definition "Genetic, Hereditary, DNA ...") (Eg. "Relating to genes or heredity") The infamous double helix CC-BY-SA; Delmar Larsen Glossary Entries Definition Image Sample Word 1 Sample Definition 1
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/01%3A_Completeness_and_Consistency/1.3%3A_ConsistencyDefinition: Five Point Geometry Use the following axioms and definitions of intersection and parallel as a definition of the five point geometry. There exist exactly five points. There exist exactly f...Definition: Five Point Geometry Use the following axioms and definitions of intersection and parallel as a definition of the five point geometry. There exist exactly five points. There exist exactly five lines. Any two distinct points have exactly one line on both of them. Each line is on exactly two points. Explore the five point geometry as follows. Draw five points using Geogebra. Use Axiom 3 to draw all required lines. How many lines did you construct? Compare this answer to Axiom 2.
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/05%3A_Hyperbolic_Geometry
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/02%3A_Neutral_Geometry
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/03%3A_Synthetic_Euclidean_Geometry/3.04%3A_New_PageFor each construction figure out how to do it using the classic Greek tools: a straight edge and rusty compass (okay that isn't quite classic Greek). Construct an equilateral triangle with side length...For each construction figure out how to do it using the classic Greek tools: a straight edge and rusty compass (okay that isn't quite classic Greek). Construct an equilateral triangle with side length matching a given segment. Given a line segment construct the perpendicular bisector of it. Construct a square with side length matching a given segment. Construct the midpoint of a line segment. Construct a line parallel to a given line through a given point.
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/zz%3A_Back_Matter
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/06%3A_Projective_Geometry/6.02%3A_New_PageA transformation is a perspectivity if and only if it maps the points of a line to the points of another line such that all lines from points to their images are incident in a single point. Choose thr...A transformation is a perspectivity if and only if it maps the points of a line to the points of another line such that all lines from points to their images are incident in a single point. Choose three points on one of the lines and find the points on the second line to which they are mapped by the perspectivity defined by your chosen point. Two triangles are perspective with respect to a point if and only if the lines connecting corresponding pairs of vertices are incident in a point.
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/06%3A_Projective_Geometry
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/05%3A_Hyperbolic_Geometry/5.01%3A_New_PageHyperbolic geometry results by replacing the Euclidean parallel postulate with the following. Axiom Given a line and a point not on that line there exists at least two lines through the point and para...Hyperbolic geometry results by replacing the Euclidean parallel postulate with the following. Axiom Given a line and a point not on that line there exists at least two lines through the point and parallel to the lines. There were three major variants (wordings) of the Euclidean parallel postulate. Conjecture what these look like in hyperbolic geometry.
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/01%3A_Completeness_and_Consistency/1.02%3A_New_PageUse the following axioms and definitions of intersection and parallel as a definition of the Fano geometry. Add the axiom: every point is on at least one line. To your line with three points, and one ...Use the following axioms and definitions of intersection and parallel as a definition of the Fano geometry. Add the axiom: every point is on at least one line. To your line with three points, and one point not on that line add any lines required by this new axiom. If so, do so, and be sure the axioms are satisfied. What do the answers to 5, 9, and 11 say about this attempt at constructing a geometry? What is needed to fix the difficulty noted in the previous question?
- https://math.libretexts.org/Bookshelves/Geometry/An_IBL_Introduction_to_Geometries_(Mark_Fitch)/03%3A_Synthetic_Euclidean_Geometry
