Schola Europaea European School Brussels II

INTRODUCTION
In the wake of the PISA study and high
unemployment rates, the public is calling for
a reform of our education system; politicians
want urgent improvements in this area. All over
Europe the different ministries for education
are eagerly tinkering with new curricula.
This article also addresses teachers of
maths and computer science as well as the
relevant personnel in the Ministries.
T h e t e n d e n c y t o n e g l e c t t r a i n i n g
in conventional geometry in favour of more
modern methods in algebra and statistics is
obvious, but might be short sighted as I will
point out in this article. It will show the close
structural relationship between Euclidean
BASIC ELEMENTS
The point and the straight line are the
simplest geometrical ‘objects’ (notice the
linguistic relationship to computer science).
In school they are always associated
with the action of drawing and a specific
notation. The classical programming
languages possess so-called ‘simple data
ALGORITHMS
In the 80s and 90s the teaching of computer
science was usually done by mathematics
and physics teachers who emphasized
algorithms. That a clever choice of the
data structure can be substantial to the
solution of a problem was neglected in
most cases. Naturally algorithms play an
important role in computer science and
there is a close relationship with geometry.
The following description of a construction
also illustrates the relationship between
geometry and computer science—which
is not to be mistaken for clicking buttons
in the applications of a well-known software
producer. This should also please the ‘real’
computer scientist who is inventing new
applications and developing new concepts.
In many discussions over the training of
our students both with colleagues and with
computer scientists working in the industry
I saw that in most of their minds geometry
and computer science seemed to be
separate subjects. In a comparison I would
like to show the profound connection of
the concepts of Euclidean geometry and
computer science, which I began to fully
realize in the course of my teaching activity.
types’ (integers, floating-point numbers,
characters and strings etc.) as the simplest
objects. There are simple instructions
operating on them associated with the
action of the computer being coded in the
syntax of a specific programming language.
geometry and different programming
languages 1 :
(1) AB with AB = 7 cm
(2) {C1, C2}={Major Arcover AB, angle γ = 70°}∩{line
parallele to AB, distance hc = 4,5 cm}
Geometry has its own notation like every
programming language. The syntax
used here is very common in German
secondary schools and essentially
the same as that used in set theory.
1 The author uses a notation for geometric constructions which is very common in Germany: Large characters in italics like A denote
points of the plane, two characters like AB a line between the given points. Sets of points are denoted by {properties of the set},
the symbol ∩ means an intersection of sets. k (X; r = z) means: Draw a circle around X with radius z.
PANORAMA 109