first exhibit places a mirror and some tridimensional models, representing
"a half" of a milanese
building, at the visitor's disposal. If you put one of these models
to the mirror, you can rebuild the whole building. The image in
the mirror and the beginning piece make a building identical to
the original... or "almost" identical; quite often symmetry is seeming
only, as there are one or more elements that break it and that are
evident if you compare the images from life, that are reproduced
in one of the exhibition posters, with those in the mirror. The
same mirror can be used to look for symmetry in plane figures, such
as in some rose windows of the Duomo or in some Roman mosaics of
the Ortaglia Domus in Brescia: a slot allows the rose windows image to
slide under the mirror and to look for a position where the half
image, together with the reflected one, rebuild the whole rose window...
or even to admire those figures that reproduce themselves in different
It is possible to make a similar test with two perpendicular mirrors:
this time the tridimensional models represent "a quarter" of some
buildings, and once again, the whole building, almost identical
to the original, could be built by putting those models among mirrors.
And in the same way, if you put "a quarter" of a rose window among
mirrors, the whole rose window could be built occasionally (sometimes
not: it is the visitors' duty to understand when it's happening
or it isn't).
the third exhibit proposes a test looking for another kind of symmetry,
which is not realized by means of mirrors: in a specially provided
box, let's rotate two copies of
the same figure, one upon the other one, to verify when the figure
goes back to one's starting point, even before the tour is over.
The rose windows of the Duomo together with the Roman mosaics of
the Ortaglia Domus in Brescia give the best idea for exploring
this possibility again. A "gallery of virtual images" increases
the number of available images and allows them to be admired in
groups according to their kind of symmetry.
Trying to use
three mirrors and a eighth after
having employed a ...half monument (and one mirror only) and then a quarter
(and two mirrors) to rebuild the whole monument is a natural consequence.
It is not easy to find examples of monuments that can be built in this way,
because the top and the bottom side should be specular (for instance each door
should have a corresponding one on the ceiling): and yet we have found something.
the course of this part you come across a room whose four walls
are mirrors; if you insert a drawing in the provided slot you can
observe the result: an extensible floor... "to infinity". In
Milan there are many floorings with this symmetry draft and they
can be rebuilt in this way, starting from the Duomo floor. It is
also possible to find these decorations, that recur at regular intervals
with a four mirrors scheme, on the walls of some buildings (for
instance some places at the Castello Sforzesco, but even on private
However not all decorations are done in this way, of course: some
of them need a box of mirrors of different shapes, while some others
cannot be rebuilt with mirrors; some posters present many examples
and the visitor is invited to recognize "the outsider", that is
to say, which is the drawing that you cannot rebuild by means of
mirrors. Some interactive animations allow different possibilities
to be explored and let the visitor build a mosaic, by means of a
mirror room, and then try to recognize the kind of symmetry.
visitor is invited to go into a large-sized mirror room, to admire
the red and white triangle flooring you come across in corso Vittorio Emanuele:
the visitor will have to choose the right floor tile, among three
types at his/her disposal, to rebuild the flooring reproduced in
Friezes, that is to say,
drawings that recur at regular intervals in one direction only,
are another kind of decorations we often come face to face. Seven
posters suggest a collection of examples: they are presented "in
groups" according to possible schemes of symmetry (and they are
seven, just seven). One of these schemes is just the symmetry scheme
of our footprints (for instance
on the sand) when we are walking at regular steps; the others too
can be illustrated by a sequence of footprints, but it will
be necessary to jump to one's feet joined or to hop or move in other
Some animations allow the visitor to observe different types of
friezes and, furthermore, to recognize types and try to make them
by himself/herself using the seven different schemes.