Table of contents

The Gallery consists of interactive multimedia learning units on various issues that shall facilitate understanding. Technically, most units are Java applets, some are graphical supplements or other programs (JavaScript). For practice and (self) control, visit the collection of interactive tests.

A more systematic outline of the underlying mathematical background is included in the German version of maths online. (It is one of our future plans to translate this part into English language).

The Gallery is under construction since March 1998, and new learning units are added continuously. We appreciate feedback about your experience with our material.

The learning units of the Gallery

You may call the learning units directly by clicking the respective icon
  for applets,
  for graphics or sequences of graphics, and
  for other programs
A click on a hyperlink leads you to a page collecting and briefly describing all learning units of a chapter. Occasionally, remarks on additional material and further information on the web are made.


Definition of sets

Drawing plane and coordinate system

Cartesian coordinates
Coordinate system
Polar coordinates
Oblique coordinates

Variables, terms, formulae, and identities

Recognize structures 1  (use abbreviations)
Recognize structures 2  (formal properties of expressions)
Recognize structures 3  (numerical properties of expressions)


Equivalence transformations
Quadratic equations 1  (Proof of solution formula)
Quadratic equations 2  (Three solution methods)

Vectors 1

Introducing 3-vectors

Analytic geometry 1

The slope of a straight line
Spatial coordinates
Straight lines in 3-space

Functions 1

Function and graph
  Graphs of simple power functions
Recognize functions 1  (simple polynomial functions)
Recognize graphs 1  (functions of at most second order)
Polynomial of third order (cubic polynomial)
  Function plotter

Trigonometric functions

Definition of the trig functions


Triangle and Law of Sines

Functions 2

Recognize functions 2  (functions containing negative powers)
Recognize graphs 2  (functions containing negative powers)
The graphs of sin, cos and tan
  Graphs of elementary trigonometric functions
  Graphs of some exponential and logarithm functions
Recognize functions 3  (sine and cosine functions)
Recognize graphs 3  (sine and cosine functions)
  Function plotter

Limiting processes

  Numerical computation of sequences
  Numerical computation of series
  What is a fault? A tale that makes you smile

Analytic geometry 2

Planes in 3-space

Differentiation 1

On the definition of the derivative
Derivative puzzle 1
Derivative puzzle 2
Derivative puzzle 3
First and second derivative

Applications of differential calculus

How to find a function's extremum

Power series

Power series 1  (input by scroll bar)
Power series 2  (numerical input)
  Function plotter

Analytic geometry 3

Logarithmic spirals

Differentiation 2

Nowhere differentiable functions

Probability and statistics 1

The Gauss distribution


Intuitively understanding the integral

Mathematical structures and spaces

Lorentz transformation

Fourier series

Fourier series

Model-building and simulation

Game of Life

Maths by playing

Warp image

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Bundesministerium für Unterricht und kulturelle Angelegenheiten
Verband Wiener Volksbildung
Magistrat der Stadt Wien, MA13
Oesterreichische Nationalbank