A remarkable fact in mathematics is the accordance between algebra and geometry: since the time
of Descartes it is possible to express geometric phenomena in terms of numbers. And after doing
calculations with these numbers we can draw geometric conclusions from them. However soon it
appeared that for instance a circle and a line outside that circle have 'imaginary' meeting
points: points that have imaginary coordinates but can not be found in the figure. Karl von
Staudt found a brilliant way to visualize imaginary geometric points lines and planes and
Felix Klein simplified and extended his method. In this book imaginary elements appear as
Klein-movements in our real space. Apart from its mathematical importance these movements may
be seen as an alternative for the remarkable occurrences of complex numbers in physics viz.
quantum physics. Lou de Boer (*1947) studied mathematics and music in Amsterdam. From 1971 to
1986 he was a math teacher at a gymnasium in the same city and from 1986 till 1993 he was an
ICT-consultant at the Dutch Telecom-company. After that he took mathematics up again studied
gave lectures and wrote articles and books. In 1977 after having been a convinced materialist
reductionist for seven years he met anthroposophy. Since then he tries to work in accordance
with spiritual science
