Math as I like it
... and as I tell it! đ
Philippe Colliard
Who I am
mail me at: philippe@colliard.fr
Click on the covers :
My books (in French) are available at FNAC
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(Re)building math starting from as low as possible, progressing as far as I could...
After "donc, d'aprĂšs..." (" so, according to... ") I thought I was immuneâ I have to say that I had really dug deep!
Well, no, the fever has returned. But a more reasonable fever: here I don't "do" math, I tell it...
Or more modestly, I tell math as I feel it, math to just read, to... savor?
Currently, seventeen episodes are quietly progressing along the
path of this math,
illustrated with a few far-fetched stories and
accompanied by comments from a whole little world of virtual readers.
Other readers (real ones, these) follow this site, in France... and elsewhere.
Some wanted a book version,
and there it is (on the left): It includes episodes 0 to 14âand five completely fictional stories.
There will beâI hopeâother episodes, other far-fetched stories... other compilations.
Little by little...
at a rate of one or two episodes translations per week,
the website mathasilikeit.com (English version of lesmathscommejelesaime.fr)
should be completed by the end of March 2026.
But I have partially given in to those who wanted it âright nowâ:
since I couldn't deliver the entire French site,
it wasn't too difficult to publish the elements that had already been translated.
So here they are!
For the others, a little more patience? đ
It was only an introduction to geometry, but 10 years later, I still have wonderful memories of it.
13-year-old students I had only known for a month, during which we had worked on numbers.
A month isn't long, but it's enough to start learning to work together,
to make it natural for these students to have nothing in front of them
during the thirty minutes set aside for class as such, except for a pad and a pen on their desks.
It was also natural for them to talk to each other and to me, with one absolute rule:
never interrupt anyone (and, I'm not going to lie, give me some priority).
A class of 30 students, all active, but to avoid a Tolstoy-esque proliferation of first names,
I will very arbitrarily assign the dialogues in this reconstruction to five of them...
and keep only the most significant of the many contributions,
whether for the progression or the atmosphere.
. . .
Without points, there is no geometry... But what is a point?
You've looked at the stars, of course. You know, those bright points in a completely black void.
Except that they aren't actually points
(and the completely black void isn't really empty or really black... but that's another story): :
firstly because all you have to do is hop aboard any spaceship and take a closer look at a star
to realize that it's far too big to be a point.
And also because a point is a place, and a place doesn't shine.
But it's true that stars, seen from far awayâvery far away, farther than farâlook like points...
well, if points shone!
. . .
The point, always the point. Yes, I have a monomaniacal side!
But this time, it's at the heart of the first chapter of a story I wrote for my daughter
when she was in seventh grade, about twenty years ago.
Please be kind!
. . .
My very first story about the point, back in 1993! It's silly, but I love it.
(Then I promise I'll move on to something else! But the point deserved three articles, right?).
. . .
Okay, clearly, writing on a curve... takes more than one line!
Now that we know what a point object isâand what a point isâwe can move on
to the next question:
what is a curve?
(Nooo, it's not a stroke, any more than a point is a stain!)
. . .
Why did I dwell so much on the point object, the point, the curve?
Because they are the basic elements of geometry, of course...
but especially because they are the âparentsâ of the line.
And without the line, Euclidean geometry wouldn't get very far!
What's that? The line is easy, it's a curve that goes straight?
Sigh: first of all, a curve is a place, it doesn't go anywhere...
and secondly, what does it mean for an object to âgo straightâ?
In our physical universe, apart from photons,
there aren't many objects that always go straight
(and even photons can deviate)!
. . .
Why canât you bypass the plane?
Because it is one of the three basic elements of Euclidean geometry
(and, 22 centuries later, Hilbert's geometry): the point, the line, and the plane!
What I wrote about the line is just as true for the plane: without it, Euclidean geometry would not get very far!
(Without the point either, of course, but if after all the previous episodes you're not convinced of that, I give up!)
But the plane is essential for another reason as well... I'll come back to that soon.
Well, shall we start at the beginning?
To invent the plane, we're going to need lines (that was episode 3)... and surfaces.
I haven't told you anything about surfaces yet, and I don't really want to devote an entire episode to them,
so would you mind if we just settle for a paragraph 0 in this episode? Here we go!
â Hey, why are you asking for our opinion if you're not even waiting for our answer? Well, yes, okay, we're fine with that!
â Thank you... and you're right, I should have waited! I always want to rush things!
. . .
