Vers le site en français

Math as I like it  ... and as I tell it! 🙂

Philippe Colliard            Who I am

Little by little...

English-speaking readers requested an English-language mirror site for lesmathscommejelesaime.fr

mathasilikeit.com will be that mirror site… once I’ve finished translating
(with the invaluable help of AI) all the episodes and stories already published in French.

But that’s going to take some time, so rather than wait for the work to be completed
I thought it would be better to publish each text as soon as it’s translated.

So here are the first ones!

For the texts to come, a little more patience, please? 😊

  
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 away—very far away, farther than far—look 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 is—and what a point is—we 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 “parents” 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 “go straight”?

In our physical universe, apart from photons,
there aren't many objects that always go straight
(and even photons can deviate)!
. . .

  
Why can’t 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!

– 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!

– Thank you... and you're right, I should have waited! I always want to rush things!
. . .

  
I've heard your sighs and murmurs:

– you're... um, tiring us out with your geometry, your points, your points, your points! We want real math, math with numbers everywhere!

Okay, fine, let's tackle numbers. All numbers, from integers to complex numbers. And the numerical structures that go with them.

Obviously, it's going to take a little time and a few episodes. But who's in a hurry?

We're going to hunt down numbers together, bringing them out into the light little by little,
even though all they want is to be left alone, each in their own point.

– In their what ? You mean "in their place » ?

Uh, yes, yes, of course! In their place! So we're going to hunt them down. Note that I didn't say "create them";
they've existed for eternity, a bit like—if you remember my first episode—the points that have been there for eternity,
waiting for a point object to come and visit them one day. Well, if points wait?

– Oh no! Don't start with your points again!
. . .

  
Yes, another story!

(Have you noticed that the story logos have a “gold” background
and that these stories are linked to the episode they illustrate
by adding a letter – a, b… – to the episode number?)

I had already included a link to this story in my article on “Les harpes de Thales”,
(Images des mathématiques-CNRS)
obviously regarding the notation of whole numbers… but I felt like it belonged here even more,
forever linked to “Math as I like it”

Of course, it’s only meaningful as a supplement to Episode 5!

For the (very brief) story, Hi-Ati is the first story I ever “sold,” back in... 1980
(and no, it didn’t make me a millionaire!)
. . .