EricDesbiaux/IntegerAndCycloids

[Eric]

Hello,

just an interrogation...
there is no link with integer sequence immediatly but it will come (or not
that depends of what already exist in database)

our cartesian coordinate system is based on integers...
so the space between two point on each axis is the same...apart from scale,
it looks like an elastic...

the origin is zero 0, crossroad between the two elastic axis.
On these axis,...to multiply is the same thing than to stretch the X-axis
and Y-axis...
and to divide is the same thing than to loosen the X-axis and Y-axis.

When i read an article about Brachistochrone curves,
i was surprised to notice that each brachistochrone curve can be defined by
a rectangle, of which width and length are respectively 2R and 2PI()R...


now, we know that a brachistochrone curve is "the best way" to connect two
distinct points in shorter time.

why not to base the coordinate system on this particularity/peculiarity...

Monte Carlo method
and Buffon needles...

in my point of view,
the various way to determine the needle position,
is the same think than look a segment describes an astroid (type of cycloid
curve)

it's easy to find on the web a lots of representations for different type of
curves based on Brachystochrone....
cycloid, nephroid sliding outside deltoid, Tetracuspid, spheric cycloid,
Beetle curve, ellispe...

it's me? or it seems that all could be made of cycloids?

there is one meeting place,
it's PI()...
but who was the first? circle or cycloid?
the wheel doesn't exist in nature but the kinematics of brachystochrone
curve, and his multiple way, yes..

With buffon technic we can approach PI(),
if we dont take into account the Physic laws...(our reality is not
euclidian...but its disturbing in this exemple)
we can find the probabilities for needles (some demo on the web)


Perhaps Gauss Lemme, Gauss and Eisenstein integers, are linked to my
question...
because if we consider a grid :

 x x x x x x x x x x ...
 x x x x x x x x x x ...
 x x x x x x x x x x ...
 . . . . . . . . . .
 . . . . . . . . . .

if you select a point (x) to take a look,
which (x) are invisible and visible for you?
the wellknown answer is : 6/(PI()^2)

what the way choose by the light in this configuration? what about spin?

sorry for this text made of more wastetimequestion than integer sequence :o)

Best Regards
Eric

Thanks