Changes

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====Planned topics====
 
====Planned topics====
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''Primary school''
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* [[Activities/TurtleArt/Tutorials/Numerals|Numerals]]
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* [[Activities/TurtleArt/Tutorials/Kindergarten_Calculus|Kindergarten Calculus]] ([[Activities/TurtleArt/Tutorials/Tangents|tangents]], [[Activities/TurtleArt/Tutorials/Maxima|maxima]] and [[Activities/TurtleArt/Tutorials/Minima|minima]], [[Activities/TurtleArt/Tutorials/Areas|areas]]...)
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* [[Activities/TurtleArt/Tutorials/Complex_Numbers|Complex Numbers]]
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* [[Activities/TurtleArt/Tutorials/Adding_Apples_and_Oranges|Adding apples and oranges]]
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* [[Activities/TurtleArt/Tutorials/Groups_of_Symmetries|Groups of symmetries]]
 
* [[Activities/TurtleArt/Tutorials/Figurate_Numbers|Figurate numbers]]
 
* [[Activities/TurtleArt/Tutorials/Figurate_Numbers|Figurate numbers]]
 
* [[Activities/TurtleArt/Tutorials/Spirograph|Spirograph]]
 
* [[Activities/TurtleArt/Tutorials/Spirograph|Spirograph]]
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* [[Activities/TurtleArt/Tutorials/Elementary_Arithmetic|Elementary arithmetic]] with whole numbers (but no numerals)
 
* [[Activities/TurtleArt/Tutorials/Elementary_Arithmetic|Elementary arithmetic]] with whole numbers (but no numerals)
 
* [[Activities/TurtleArt/Tutorials/Shortcuts_to_the_Times_Table|Shortcuts to the times table]]
 
* [[Activities/TurtleArt/Tutorials/Shortcuts_to_the_Times_Table|Shortcuts to the times table]]
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* [[Activities/TurtleArt/Tutorials/Fractions|Fractions]] with cake, pie, and pizza slices
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* [[Activities/TurtleArt/Tutorials/Algorithms_of_Arithmetic|Algorithms of arithmetic]]
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* [[Activities/TurtleArt/Tutorials/Learning_Math_by_Teaching_the_Computer|Learning math by teaching the computer]]
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* [[Activities/TurtleArt/Tutorials/Knots|Knots]] and [[Activities/TurtleArt/Tutorials/Braids|braids]] (and knitting, crocheting, macramé, tatting...)
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* [[Activities/TurtleArt/Tutorials/Galilean_Gravity|Galilean gravity]]
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* [[Activities/TurtleArt/Tutorials/Galilean_Relativity|Galilean relativity]]
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* [[Activities/TurtleArt/Tutorials/Measuring_Slopes_of_tangents|Measuring slopes of tangents]]
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* [[Activities/TurtleArt/Tutorials/Approximate_Integrals|Approximate integrals]]
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* [[Activities/TurtleArt/Tutorials/Python_Blocks|Python blocks]]
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* [[Activities/TurtleArt/Tutorials/Transition_to_Python|Transition to Python]]
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* [[Activities/TurtleArt/Tutorials/Turtle_Art_Add-Ons|Create your own Turtle Art add-ons]] in Python
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* [[Activities/TurtleArt/Tutorials/Turtle_Graphics_in_Smalltalk|Turtle Graphics in Smalltalk]]
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* [[Activities/TurtleArt/Tutorials/Transition_to_Smalltalk|Transition to Smalltalk]]
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* [[Activities/TurtleArt/Tutorials/Transition_to_Logo|Transition to Logo]]
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* [[Activities/TurtleArt/Tutorials/Frieze_Groups|Frieze groups]]
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* [[Activities/TurtleArt/Tutorials/Moiré_Patterns|Moiré patterns]] and interference
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* [[Activities/TurtleArt/Tutorials/Tilings|Tilings]]
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* [[Activities/TurtleArt/Tutorials/Topology|Topology]] (Rubber-sheet geometry)
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* [[Activities/TurtleArt/Tutorials/Juggling|Juggling]]
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* The [[Activities/TurtleArt/Tutorials/Square_Circle|square circle]] and other [[Activities/TurtleArt/Tutorials/Metrics|metrics]]
 
* [[Activities/TurtleArt/Tutorials/Abacus|Abacus]], [[Activities/TurtleArt/Tutorials/Abacus/Chisanpeop|Chisanpeop]] (abacus on fingers), and [[Activities/TurtleArt/Tutorials/Visual_Numerals|visual numerals]]
 
* [[Activities/TurtleArt/Tutorials/Abacus|Abacus]], [[Activities/TurtleArt/Tutorials/Abacus/Chisanpeop|Chisanpeop]] (abacus on fingers), and [[Activities/TurtleArt/Tutorials/Visual_Numerals|visual numerals]]
* [[Activities/TurtleArt/Tutorials/Fractions|Fractions]] with cake, pie, and pizza slices
   
* [[Activities/TurtleArt/Tutorials/Infinite_Sequences|Infinite sequences]] and [[Activities/TurtleArt/Tutorials/Infinite_Series|series]]
 
* [[Activities/TurtleArt/Tutorials/Infinite_Sequences|Infinite sequences]] and [[Activities/TurtleArt/Tutorials/Infinite_Series|series]]
* [[Activities/TurtleArt/Tutorials/Groups_of_Symmetries|Groups of symmetries]]
   
* [[Activities/TurtleArt/Tutorials/Permutations|Permutations]] and [[Activities/TurtleArt/Tutorials/Permutation_Groups|permutation groups]]
 
* [[Activities/TurtleArt/Tutorials/Permutations|Permutations]] and [[Activities/TurtleArt/Tutorials/Permutation_Groups|permutation groups]]
 
* The ring of [[Activities/TurtleArt/Tutorials/Clock_Time|clock time]]
 
* The ring of [[Activities/TurtleArt/Tutorials/Clock_Time|clock time]]
* The fields of [[Activities/TurtleArt/Tutorials/Rational_Numbers|rationals]] and [[Activities/TurtleArt/Tutorials/Real_Numbers|reals]]
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* [[Activities/TurtleArt/Tutorials/Knots|Knots]] and [[Activities/TurtleArt/Tutorials/Braids|braids]] (and knitting, crocheting, macramé, tatting...)
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* [[Activities/TurtleArt/Tutorials/Kindergarten_Calculus|Kindergarten Calculus]] ([[Activities/TurtleArt/Tutorials/Tangents|tangents]], [[Activities/TurtleArt/Tutorials/Maxima|maxima]] and [[Activities/TurtleArt/Tutorials/Minima|minima]], [[Activities/TurtleArt/Tutorials/Areas|areas]]...)
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* [[Activities/TurtleArt/Tutorials/Adding_Apples_and_Oranges|Adding apples and oranges]]
   
* [[Activities/TurtleArt/Tutorials/Vectors|Vectors]]
 
* [[Activities/TurtleArt/Tutorials/Vectors|Vectors]]
 
* [[Activities/TurtleArt/Tutorials/Venn_Diagrams|Venn diagrams]]
 
* [[Activities/TurtleArt/Tutorials/Venn_Diagrams|Venn diagrams]]
 
* [[Activities/TurtleArt/Tutorials/Euclid|Euclid]], Book I: triangles, parallelograms, squares
 
* [[Activities/TurtleArt/Tutorials/Euclid|Euclid]], Book I: triangles, parallelograms, squares
 
* [[Activities/TurtleArt/Tutorials/Spherical_Geometry|Spherical geometry]] (Riemann)
 
* [[Activities/TurtleArt/Tutorials/Spherical_Geometry|Spherical geometry]] (Riemann)
* [[Activities/TurtleArt/Tutorials/Pseudospherical_Geometry|Pseudospherical geometry]] (Lobachevsky)
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* [[Activities/TurtleArt/Tutorials/Projective_Geometry|Projective geometry]]
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* [[Activities/TurtleArt/Tutorials/Geometric_Optics|Geometric optics]]
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* [[Activities/TurtleArt/Tutorials/Moiré_Patterns|Moiré patterns]] and interference
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* [[Activities/TurtleArt/Tutorials/Tilings|Tilings]]
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* [[Activities/TurtleArt/Tutorials/Topology|Topology]] (Rubber-sheet geometry)
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* [[Activities/TurtleArt/Tutorials/Juggling|Juggling]]
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* The [[Activities/TurtleArt/Tutorials/Square_Circle|square circle]] and other [[Activities/TurtleArt/Tutorials/Metrics|metrics]]
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* [[Activities/TurtleArt/Tutorials/Periodic_Functions|Periodic]] and [[Activities/TurtleArt/Tutorials/Almost-Periodic_Functions|Almost-periodic functions]] (Lissajous figures)
   
* [[Activities/TurtleArt/Tutorials/Maps|Maps]]
 
* [[Activities/TurtleArt/Tutorials/Maps|Maps]]
* [[Activities/TurtleArt/Tutorials/Complex_Numbers|Complex Numbers]]
   
* [[Activities/TurtleArt/Tutorials/Iterated_Functions|Iterated functions]] (attractors, chaos)
 
* [[Activities/TurtleArt/Tutorials/Iterated_Functions|Iterated functions]] (attractors, chaos)
 
* [[Activities/TurtleArt/Tutorials/Fractals|Fractals]]
 
* [[Activities/TurtleArt/Tutorials/Fractals|Fractals]]
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* [[Activities/TurtleArt/Tutorials/Combinatorics|Combinatorics]]
 
* [[Activities/TurtleArt/Tutorials/Combinatorics|Combinatorics]]
 
* [[Activities/TurtleArt/Tutorials/Models_of_Simple_Molecules|Models of simple molecules]]
 
* [[Activities/TurtleArt/Tutorials/Models_of_Simple_Molecules|Models of simple molecules]]
* [[Activities/TurtleArt/Tutorials/Sensors and Actuators|Moving between Turtle Art and the physical world]]
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''Primary school''
  −
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* [[Activities/TurtleArt/Tutorials/Algorithms_of_Arithmetic|Algorithms of arithmetic]]
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* [[Activities/TurtleArt/Tutorials/Numerals|Numerals]]
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* [[Activities/TurtleArt/Tutorials/Learning_Math_by_Teaching_the_Computer|Learning math by teaching the computer]]
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* [[Activities/TurtleArt/Tutorials/Galilean_Gravity|Galilean gravity]]
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* [[Activities/TurtleArt/Tutorials/Galilean_Relativity|Galilean relativity]]
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* [[Activities/TurtleArt/Tutorials/Measuring_Slopes_of_tangents|Measuring slopes of tangents]]
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* [[Activities/TurtleArt/Tutorials/Approximate_Integrals|Approximate integrals]]
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* [[Activities/TurtleArt/Tutorials/Python_Blocks|Python blocks]]
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* [[Activities/TurtleArt/Tutorials/Transition_to_Python|Transition to Python]]
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* [[Activities/TurtleArt/Tutorials/Turtle_Art_Add-Ons|Create your own Turtle Art add-ons]] in Python
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* [[Activities/TurtleArt/Tutorials/Turtle_Graphics_in_Smalltalk|Turtle Graphics in Smalltalk]]
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* [[Activities/TurtleArt/Tutorials/Transition_to_Smalltalk|Transition to Smalltalk]]
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* [[Activities/TurtleArt/Tutorials/Transition_to_Logo|Transition to Logo]]
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* [[Activities/TurtleArt/Tutorials/Frieze_Groups|Frieze groups]]
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* [[Activities/TurtleArt/Tutorials/3D_Tilings|3D tilings]] and crystallographic groups
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* [[Activities/TurtleArt/Tutorials/Coordinate_Geometry|Coordinate geometry]], Cartesian and Polar
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* [[Activities/TurtleArt/Tutorials/Conditional_Probabilities|Conditional probabilities]]
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* [[Activities/TurtleArt/Tutorials/Elementary_Statistics|Elementary statistics]]
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* Models of [[Activities/TurtleArt/Tutorials/Molecular_Structures|Molecular Structures]]; nomenclature
      
''Higher''
 
''Higher''
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At this level it is not necessary to use Turtle Art_to_introduce ideas. Nevertheless the ability to display a topic in Turtle Art demonstrates that it is of only a moderate level of complexity.
 
At this level it is not necessary to use Turtle Art_to_introduce ideas. Nevertheless the ability to display a topic in Turtle Art demonstrates that it is of only a moderate level of complexity.
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* [[Activities/TurtleArt/Tutorials/Trigonometry|Trigonometry]]
 
* The [[Activities/TurtleArt/Tutorials/Chomsky_Hierarchy|Chomsky_hierarchy of machines and languages]]
 
* The [[Activities/TurtleArt/Tutorials/Chomsky_Hierarchy|Chomsky_hierarchy of machines and languages]]
 
** [[Activities/TurtleArt/Tutorials/Finite_State_Machine|Finite state machine/automaton]]
 
** [[Activities/TurtleArt/Tutorials/Finite_State_Machine|Finite state machine/automaton]]
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** [[Activities/TurtleArt/Tutorials/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine|Turtle Art Turing Machine]]
 
** [[Activities/TurtleArt/Tutorials/Activities/TurtleArt/Tutorials/Turtle_Art_Turing_Machine|Turtle Art Turing Machine]]
 
* [[Activities/TurtleArt/Tutorials/Algebra|Algebra]] (Solving equations; structures (groups, rings, fields,...)
 
* [[Activities/TurtleArt/Tutorials/Algebra|Algebra]] (Solving equations; structures (groups, rings, fields,...)
* [[Activities/TurtleArt/Tutorials/Trigonometry|Trigonometry]]
   
* [[Activities/TurtleArt/Tutorials/3D_Coordinate_Geometry|3D coordinate geometry]]
 
* [[Activities/TurtleArt/Tutorials/3D_Coordinate_Geometry|3D coordinate geometry]]
 
* [[Activities/TurtleArt/Tutorials/Elementary_Differential_Equations|Elementary differential equations]]
 
* [[Activities/TurtleArt/Tutorials/Elementary_Differential_Equations|Elementary differential equations]]
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* [[Activities/TurtleArt/Tutorials/Algebraic_Structures|Algebraic structures]]
 
* [[Activities/TurtleArt/Tutorials/Algebraic_Structures|Algebraic structures]]
 
* [[Activities/TurtleArt/Tutorials/Statistical_Analysis|Statistical analysis]]
 
* [[Activities/TurtleArt/Tutorials/Statistical_Analysis|Statistical analysis]]
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* Models of [[Activities/TurtleArt/Tutorials/Molecular_Structures|Molecular Structures]]; nomenclature
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* [[Activities/TurtleArt/Tutorials/3D_Tilings|3D tilings]] and crystallographic groups
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* [[Activities/TurtleArt/Tutorials/Coordinate_Geometry|Coordinate geometry]], Cartesian and Polar
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* [[Activities/TurtleArt/Tutorials/Conditional_Probabilities|Conditional probabilities]]
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* [[Activities/TurtleArt/Tutorials/Elementary_Statistics|Elementary statistics]]
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* The fields of [[Activities/TurtleArt/Tutorials/Rational_Numbers|rationals]] and [[Activities/TurtleArt/Tutorials/Real_Numbers|reals]]
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* [[Activities/TurtleArt/Tutorials/Pseudospherical_Geometry|Pseudospherical geometry]] (Lobachevsky)
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* [[Activities/TurtleArt/Tutorials/Projective_Geometry|Projective geometry]]
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* [[Activities/TurtleArt/Tutorials/Geometric_Optics|Geometric optics]]
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* [[Activities/TurtleArt/Tutorials/Periodic_Functions|Periodic]] and [[Activities/TurtleArt/Tutorials/Almost-Periodic_Functions|Almost-periodic functions]] (Lissajous figures)
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* [[Activities/TurtleArt/Tutorials/Sensors and Actuators|Moving between Turtle Art and the physical world]]
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