Maths online Gallery
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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


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