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Understanding versus Procedure Analytic Geometry    Martin Zacharias
Understanding?  Comprehension?
Everyday life in school ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Everyday life in school?
[object Object],[object Object],[object Object]
111020 analytic geometry
Vertical lines
Distance
Circle (0|0) with radius 4
Descartes Dictionary
[object Object]
Concept by Objects ,[object Object],[object Object],[object Object],[object Object]
Crossing section on a cube
Diagonals
111020 analytic geometry
2D of real objects
Forms of a roof
Read out the point
S is the summit of a pyramid
half of a cube
111020 analytic geometry
111020 analytic geometry
Cross-sections by liquids
Cross-section of a regular Hexagon
Werkzeug -CD F:ortragiel_100922D_AnaGeotart.htm
Schrägbilddarstellungen
Corner of a cube C=(8|3|6), F=(2|9|6), G=(4|5|10), H=(0|1|8)
Vector
Vectors in objects
Vectors in objects
Regular Hexagon in a cube
Regular Hexagon in an Oktaeder
Rectangle in a cube Center of the cube – center of the rectangle.
Cross-section
Diagonals in the space
Mittendreieck
111020 analytic geometry
111020 analytic geometry
Lines in the space
Lagebeziehung von Geraden im Raum
111020 analytic geometry
Area in a roof  (Walmdach) Describe the blue area with lines.
Line segments in a Pyramid
„ Haus des Nikolaus“
Cube with a cut off corner
Cut off cube (Kuboktaeder)
Position of lines
Point of intersection? No, it doesn’t exist a point of intersection.
Lagebeziehung mit GTR
Lagebeziehung und GTR
Ebenen im Raum
experiment - search
111020 analytic geometry
Ebene - experimentell
Objektstudie
111020 analytic geometry
What happens, when …  ? ,[object Object]
111020 analytic geometry

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111020 analytic geometry