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Representations of Solids and Surfaces Within the TI N’Spire
Environment
Jean-Jacques [email protected]
IREM of Toulouse
Time 2012 July 10/14 2012
Tartu, ESTONIA
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INTRODUCTION
Representing 3D objects in 2D with two parallel perspectives
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The « cavaliere » and the « military » perspectives
« Cavaliere » perspective « Military » perspective
PC.cg3 PM.cg3
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Theses perspectives with dynamic numbers in the « Geometry » application of TI
N’Spire
Paper1 problem 1
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An example of representation Circles in base planes
Paper1 problem 1
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Another example using dynamic numbers: Dynamic coordinates for movable points
Paper 1 problem 2
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PART 1 CYLINDERS and CONES
Their representations in« cavaliere » and « military »
perspectives
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With traces and loci
Paper1 problems 3, 4
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PART 2FOLDING and UNFOLDING
In « military » perspective
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Folding and unfolding cylindersin « military » perspective
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The technique
Paper1 problems 5
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The result
Paper1 problems 5
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Folding and unfolding conesin « military » perspective
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The model
Paper2 problem 1
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PART 3The experimental process of discovery with technology
Two conjectures obtained with the model of unfolding a
cone and their proofs
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Unfolding a cone onto half a disk
Paper2 problems 2
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Formal proof
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Evaluation of a limit of a ratio (between two angles)
Paper2 problem 3
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Formal proof
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PART 4SURFACES z = f(x,y)
Two possible approaches
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With the « Graphs » application of TI N’Spire
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Paper3 problem1
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Paper3 problem 2
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With the « 3D Graphing » tool of TI N’Spire
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z = sin(x)+cos(y)
z = 0
Paper3 problem 3
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z = sin(x)+cos(y)
z = 0
Paper3 problem 4
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CONCLUSIONas a new title
Dynamic numbers for a dynamic approach of 3D analytic geometry
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z = sin(x)- k.cos(y)
Paper3 problem 5
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[email protected] YouTube channel
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I recommand you the work of:
Oysten Nordvik (Norway)About
Representations in central perspective with TI N’Spire
Go to his website