111020 analytic geometry
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111020 analytic geometry

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Mr M. Zacharias presentation

Mr M. Zacharias presentation

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    111020 analytic geometry 111020 analytic geometry Presentation Transcript

    • Understanding versus Procedure Analytic Geometry Martin Zacharias
    • Understanding? Comprehension?
    • Everyday life in school
      • Given are to lines and
        • a) Which situation do they have? Find the points of intersection.
        • b) Describe the plane E, which includes the lines g and h.
        • c) Find a line, which has no points of intersection with g and h. Give the reason for your choice.
        • d) Find the points of intersection to the basic-planes (xy-plane, xz-plane and yz-plane) and draw the lines g and h.
        • Draw the point of intersection of both lines.
        • e) Find the angle between g and h.
        • f) Find the angle between the basic-planes.
    • Everyday life in school?
      • The exercise isn’t to bad. You have to argue, you have do draw.
      • But the finding of terms and equations and the calculation with equations is dominant.
      • Geometry and basis ideas don’t exist.
    • Vertical lines
    • Distance
    • Circle (0|0) with radius 4
    • Descartes Dictionary
      • We need activities for the pupils.
    • Concept by Objects
      • From doing to thinking in three steps
      • to comprehend the real model (situation)
      • to represent und describe it in a drawing
      • to represent and describe it in the analytic model
    • Crossing section on a cube
    • Diagonals
    • 2D of real objects
    • Forms of a roof
    • Read out the point
    • S is the summit of a pyramid
    • half of a cube
    • Cross-sections by liquids
    • Cross-section of a regular Hexagon
    • Werkzeug -CD F:VortragKiel_100922CD_AnaGeostart.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
    • Lines in the space
    • Lagebeziehung von Geraden im Raum
    • 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
    • Ebene - experimentell
    • Objektstudie
    • What happens, when … ?
      • … B goes towards F with the angle beta?