GeoGebra Principia (EN)

Rafael Losada Liste, 3 лип. 2023

[color=#008486]This GeoGebra book contains the content of the conference given at the International GeoGebra Congress* held in Córdoba (Spain) from November 9 to 12, 2023. This content is also available, in the original format used in the conference, at the address: [url]https://geogebra.es/principia/[/url] (Original) Spanish version of this GeoGebra book: [url]https://www.geogebra.org/m/vbvavfjz[/url] Portuguese version of this GeoGebra book: [url]https://www.geogebra.org/m/k7fgbjwc[/url] Note: The English translation has been done semi-automatically. Please excuse any errors that may have occurred. Rafael Losada GeoGebra Institute of Cantabria[/color] *Organized by the Spanish Federation of Societies of Mathematics Teachers (FESPM), speakers from Argentina, Brazil, Ecuador, Spain, France, Portugal and Uruguay participated in it, as well as the international GeoGebra team led by its creator, Markus Hohenwarter. Its objective was to show, through conferences, workshops and communications, that Geogebra can promote a methodological change in teaching. The congress had the support of the Organization of Ibero-American States (OEI) as well as the University of Córdoba (Spain) and other associations such as the Ibero-American Federation of Mathematics Education Societies (FISEM) and the Andalusian Society of Mathematical Education Thales. All the information has been available at [url]https://www.congresogeogebra.org[/url]

Зміст

  1. Introduction
    1. Abstract and Introduction
    2. GeoGebra: Geometry and Algebra
  2. Distances
    1. Static Offset
    2. Dynamic Offset with Activated Trace
    3. Implicit Curves from Definitions in CAS
  3. Equidistances
    1. Two or Three Points
    2. A Point and a Line
    3. A Point and a Circle
    4. A Point and a Conic
    5. Two Lines
    6. Line-Circle and Two Circles
    7. Voronoi Diagram and Similar Maps
    8. Two Curves
  4. Constant Distances
    1. Point-Point
    2. Ratio Point-Line
    3. Linear Combination
    4. Logarithmic Linear Combination
    5. Sum to Three or Four Points
  5. Algebraic Eqs. and Inequalities
    1. Algebraic Equation
    2. Constraints on Inequation Representation
    3. Equal Sums of Distances to Two Pairs of Points
    4. Families of Curves
  6. Angles
    1. Angles
  7. Taxicab Distance
    1. Minkowski Distances
    2. Taxicab Geometry
    3. Basic T-Constructions
    4. T-Angles
    5. T-Equidistances
    6. T-Conics
    7. T-Constant Linear Combination
    8. T-Constant Logarithmic Linear Combination
    9. T-Sphere
    10. T-Ellipsoid
  8. Fields
    1. Preliminary Constructions
    2. Points on a Line
    3. Perpendicular Bisectors from a Point
    4. Parabolas from a Line
    5. Conics from a Circle
  9. Lists of Polylines
    1. The Static Closed Polyline
    2. Armillary Sphere
    3. The Self-Generated Static Polyline
  10. Elastic Geometry
    1. Scripts and Vectors
    2. Linkages
    3. Animated Slider Scripts
    4. Fluid
    5. Amorphous
    6. Funicular Polygon
  11. Newton's Principia
    1. Vector Sum
    2. Circular Confinement Between Repelling Points
    3. Square Confinement Between Repelling Points
    4. Spherical Confinement Between Repelling Points
    5. Minimal Path
    6. Orbit
    7. Chaos
    8. Bubbles (using JavaScript)
  12. Tensegrities
    1. Tensegrity
    2. Calculation of Tensions
    3. Tensegrity of a Triangular Prism (simplex)
    4. Icosahedral Tensegrity by Tensioning Cables
    5. Icosahedral Tensegrity by Extending Bars
  13. Conclusions
    1. Conclusions and Acknowledgments
  14. References
    1. References
    2. Bibliography

1.

Introduction

  • 1. Abstract and Introduction
  • 2. GeoGebra: Geometry and Algebra

1.1.

–

1.2.

–

2.

Distances

  • 1. Static Offset
  • 2. Dynamic Offset with Activated Trace
  • 3. Implicit Curves from Definitions in CAS

2.1.

–

2.2.

–

2.3.

–

3.

Equidistances

  • 1. Two or Three Points
  • 2. A Point and a Line
  • 3. A Point and a Circle
  • 4. A Point and a Conic
  • 5. Two Lines
  • 6. Line-Circle and Two Circles
  • 7. Voronoi Diagram and Similar Maps
  • 8. Two Curves

3.1.

–

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

4.

Constant Distances

  • 1. Point-Point
  • 2. Ratio Point-Line
  • 3. Linear Combination
  • 4. Logarithmic Linear Combination
  • 5. Sum to Three or Four Points

4.1.

–

4.2.

–

4.3.

–

4.4.

–

4.5.

–

5.

Algebraic Eqs. and Inequalities

  • 1. Algebraic Equation
  • 2. Constraints on Inequation Representation
  • 3. Equal Sums of Distances to Two Pairs of Points
  • 4. Families of Curves

5.1.

–

5.2.

–

5.3.

–

5.4.

–

6.

Angles

  • 1. Angles

6.1.

–

7.

Taxicab Distance

  • 1. Minkowski Distances
  • 2. Taxicab Geometry
  • 3. Basic T-Constructions
  • 4. T-Angles
  • 5. T-Equidistances
  • 6. T-Conics
  • 7. T-Constant Linear Combination
  • 8. T-Constant Logarithmic Linear Combination
  • 9. T-Sphere
  • 10. T-Ellipsoid

7.1.

–

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

–

7.8.

–

7.9.

–

7.10.

–

8.

Fields

  • 1. Preliminary Constructions
  • 2. Points on a Line
  • 3. Perpendicular Bisectors from a Point
  • 4. Parabolas from a Line
  • 5. Conics from a Circle

8.1.

–

8.2.

–

8.3.

–

8.4.

–

8.5.

–

9.

Lists of Polylines

  • 1. The Static Closed Polyline
  • 2. Armillary Sphere
  • 3. The Self-Generated Static Polyline

9.1.

–

9.2.

–

9.3.

–

10.

Elastic Geometry

  • 1. Scripts and Vectors
  • 2. Linkages
  • 3. Animated Slider Scripts
  • 4. Fluid
  • 5. Amorphous
  • 6. Funicular Polygon

10.1.

–

10.2.

–

10.3.

–

10.4.

–

10.5.

–

10.6.

–

11.

Newton's Principia

  • 1. Vector Sum
  • 2. Circular Confinement Between Repelling Points
  • 3. Square Confinement Between Repelling Points
  • 4. Spherical Confinement Between Repelling Points
  • 5. Minimal Path
  • 6. Orbit
  • 7. Chaos
  • 8. Bubbles (using JavaScript)

11.1.

–

11.2.

–

11.3.

–

11.4.

–

11.5.

–

11.6.

–

11.7.

–

11.8.

–

12.

Tensegrities

  • 1. Tensegrity
  • 2. Calculation of Tensions
  • 3. Tensegrity of a Triangular Prism (simplex)
  • 4. Icosahedral Tensegrity by Tensioning Cables
  • 5. Icosahedral Tensegrity by Extending Bars

12.1.

–

12.2.

–

12.3.

–

12.4.

–

12.5.

–

13.

Conclusions

  • 1. Conclusions and Acknowledgments

13.1.

–

14.

References

  • 1. References
  • 2. Bibliography

14.1.

–

14.2.

–

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