Take a look at the contents of the film, or
jump to the film's guide.
How can this film be used ?
The film can be enjoyed by anyone, provided the
chapters are wellchosen.
There are 9 chapters, each 13 minutes long. Chapters 34, 56 and 78
are double chapters, but apart from that, they are more or less
independent of each other.
One can of course sit down in front of a TV
screen, or a computer, and watch the whole 117 minutes in one go!
Well, maybe there will be sequences that go too fast for you,
or others that may be too elementary. This will depend on your
interest, your prior knowledge on the subject, or simply on your mood
of the moment !... However, one can also settle for some wellchosen
chapters, and we have prepared some tips to help you get the best out
of the film. For more information, go over to the detailed
explanations pages, where you can find also short clips from
the film..
In broad terms, the level of mathematics in the
chapters increases gradually:
Chapter
1, dimension two, is
very elementary. Secondary school students should be able to appreciate
it, but we think that, even if you know already what meridians and
parallels are, you will enjoy the spectacle of the Earth rolling like a
ball ! (Look here).
Chapter
2, dimension three,
is still elementary, but requires a bit of imagination, and
it has some philosophical elements... There are even some
exercises to check that you have understood. For explanations,
additional information and references, one can consult this page
Chaptres
3 and 4 get us into the fourth dimension.
This is of course more difficult, and maybe it will make your head spin
! In order to understand everything, don't hesitate to push the pause
button on your remote, to watch these chapters several times, and to
consult this page
where
you will find references to additional information. But even if you do
not feel like making the effort to understand it all, you can always
sit back and enjoy the pictures !
Chaptres
5 and 6, complex
numbers,
contain an introduction to, well... complex numbers. In France, complex
numbers are taught in the final year of secondary school. We don't see
this as a replacement for a classic course, but we think that these
chapters could accompany such a course in a pleasant way. If you
learned about complex numbers a long time ago, and you forgot most of
it..., this could refresh your memory. If you know nothing about
complex numbers, you should push the pause button as often as
you like, and try to understand using the references that we propose. These
chapters are the most "schoollike" of the film. To thank you for your
efforts, chapter 6 ends with an amazing deep zoom scene.
Chaptres
7 and 8 give you an introduction to the
Hopf fibration,
which is not taught in secondary school, and not even in the first
years at university. This is certainly not beginner's stuff ! On the
other hand, it is quite pretty and deserves to be understood.
Everything is explained in the film, but of course, things may go a bit
fast. Here also, the references
that we provide can be useful in case you have trouble understanding...
Good luck, and enjoy the show !
Finally, chapter
9 is a special one. It shows the proof of a theorem of
geometry.
This proof uses nothing above the level of secondary school, and we
could very well have put this chapter right after chapter 1. Without
proofs for theorems mathematics would not exist, and we wanted to make
this very clear at the end of a film that is essentially about
mathematical objects. (Look here).
Here are some possible choices :
Lower secondary school (ages 1215) : 1 or 12 or 129
Higher secondary school (ages 1618) : 12(34)9
Higher secondary school with science major : 56
University sciences student (lower cycle): 2345 ou 56(789)
University science student( higher cycle) : 78(9)
General public : 1234(9)
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