Post on 26-Jun-2015
description
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Understanding versus Procedure
Analytic Geometry
Martin Zacharias
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Understanding? Comprehension?
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Everyday life in schoolGiven are to lines and
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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. …
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Everyday life in school?
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• 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.
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Vertical lines
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Distance
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Circle (0|0) with radius 4
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Descartes Dictionary
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•We need activities for the pupils.
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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
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Crossing section on a cube
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Diagonals
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2D of real objects
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Forms of a roof
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Read out the point
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S is the summit of a pyramid
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half of a cube
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Cross-sections by liquids
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Cross-section of a regular Hexagon
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Werkzeug -CDF:\Vortrag\Kiel_100922\CD_AnaGeo\start.htm
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Schrägbilddarstellungen
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Corner of a cube
C=(8|3|6), F=(2|9|6), G=(4|5|10), H=(0|1|8)
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Vector
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Vectors in objects
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Vectors in objects
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Regular Hexagon in a cube
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Regular Hexagon in an Oktaeder
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Rectangle in a cubeCenter of the cube – center of the rectangle.
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Cross-section
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Diagonals in the space
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Mittendreieck
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Lines in the space
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Lagebeziehung von Geraden im Raum
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Area in a roof (Walmdach)
Describe the blue area with lines.
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Line segments in a Pyramid
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„Haus des Nikolaus“
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Cube with a cut off corner
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Cut off cube (Kuboktaeder)
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Position of lines
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Point of intersection?
No, it doesn’t exist a point of intersection.
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Lagebeziehung mit GTR
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Lagebeziehung und GTR
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Ebenen im Raum
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experiment - search
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Ebene - experimentell
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Objektstudie
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What happens, when … ?
…B goes towards F with the angle beta?
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