Utkast
MalinC's GeoGebra-book
All worksheets from http://www.malinc.se/math/ divided into chapters according to the menu at the site.
Innehåll
Linear Algebra
- Curve of Pursuit
- Translations along vector
- Definition of vector addition
- Construct the vector OP, using u and t
- Equation of a line through point along vector
- Equation of a line through two points
- Equation of a line, through two points
- Linear transformations
- Reaching a point in the Cartesian plane
- Rotating cube
- Vector subtraction and bound vectors
- Transformed graph
- w defined by the basis vectors u and v.
- Triangles
Trigonometry
- Addition formula for cosine
- Addition formula for sine
- Area law
- Aristarchus' distance to the sun
- Aryabhata's half chord
- Chords in ancient Greece
- Combined transformations
- Cosine rule for acute triangle
- Dilated trigonometric functions
- Epitrochoid
- Eratosthenes' radius of the earth
- Graphs of tangent and cotangent
- Hypotrochoid
- Inverse functions
- Inverse trigonometric functions
- Law of cosine using obtuse triangle
- Ptolemy and epicycles
- Sine and cosine
- Stellar parallax
- Sun, earth and moon
- Tangent and cotangent
- The Sine theorem, ambiguous case
- Translated trigonometric functions
- Triangle definition of sine and cosine
- Triangle in unit circle
- Trigonometric functions using degrees
- Trigonometric functions using radians
- Trigonometric identities in unit circle
- Tycho Brahe's mural quadrant
- Sextant
Statistics
Calculus
- Archimedes Pi
- Area function as antiderivative
- Derivative as a function
- Derivative at point
- Derivative at point, absolut value of function
- Derivative of a polynomial
- Derivative of exponential function
- Derivative of logarithmic function
- Derivative of sine and cosine
- Integral demonstration
- Limit of sin(x)/x
- s-t-diagram and v-t-diagram
- Step functions
Functions
- Non-Cartesian cars
- Cartesian cars
- Annuity loan
- Slope
- Linear points
- Linear points rotated
- Linear and exponential growth
- Translation using vector notation
- Translate function using tool
- Completing the square
- Vertex form
- Parabola
- Explanation of parabola
- Focus of the parabola
- Other conics
- Polynomials
- Quadratic and line
- Cubic and quadratic
- Composite functions
- Domain and range
- Swap axes to show inverse function
- Inverse functions
Geometry
- Quadrilaterals
- Triangles
- Pattern of Quadrilaterals
- Pattern of circles
- Transformations
- Translation
- Reflection
- Rotation
- Dynamic tessellation made of points placed on triangles
- Symmetries - reflection and rotation
- Shapes reflected in circles
- Circle mirror
- Make copies
- Copy from triangle along line
- Fractions as parts of squares
- Fractions as parts of circles.
- Positive fractions on the number line
- Negative fractions on the number line
- Multiply unit fractions
- Multiply fractions
- Area of triangle
- Area of a parallelogram
- Area of trapezium
- Summary of polygon areas
- Area of a circle
- Angle sum of a triangle
- Alternate angles at parallel lines
- Corresponding angles at parallel lines
- Vertical angles
- Exterior angle of a triangle
- Summary - Angles
- Two angles in triangle
- Sun, earth and moon
- Corollary of proportionality theorem
- Triangle proportionality theorem
- Angle bisector theorem
- Similar Triangles, exercise 1
- Triangles, exercise 2
- Apollonius Circles
- Square inscribed in triangle
- Midpoint & distance
- Strandbeest
- Points in triangle
- Trisect segment
- Angles along rays.
- Angle sum of a triangle
GeoGebra Tutorial
- Interactive GeoGebra logo
- Pentagram
- Dragging test
- Demo of construction protocol
- Ruler and compass construction
- Animated Pythagoras' Theorem Jigsaw Puzzle
- Pythagoras' Theorem showing numerical values
- Rotations, reflections, translations
- Animated Tessellated Pythagoras' Theorem Jigsaw Puzzle
- Aristotle's Wheel Paradox
- Measuring angles
- Sun, earth and moon
- Cats on ladder
- Cat on Ladder
- Möbius Transformations of Doyle Circles
- Complex mappings of a circle
- Complex mappings of a line
- Mobius transformations
- Points and vectors
- Polar coordinates
- Clock
- Pool Table
- A general cubic function
- Input box and composite functions
- Riemann sums
- Polar coordinates demo
- Implicit heart and smiley
- Lissajou curve
- Anaglyphic 3D Lissajou
- Ellipse or hyperbola
- Parabola made using spreadsheet
- Symmetries made using lists
- Infinitely many stars
- Button demonstration - move point
- Button demonstration
Fractals
Non-Euclidean Geometry