- 1 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
$ # #
- 2 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
→
% &$
' ( ) * (''' (''(
→ !
! "# $ % &' (
% +
, - % ⊂
∈.
(() &$ (()∈&$
# (()∈&$ (()∈+ / 0(*∈+ &$1 ∉∉∉∉ 2
3# 0 &$
5 7
4 0, 75 ? 0, 25 ? 16 ? ?
4 4
a= × b= − c= d = e=
(
2 1−)(
2 1+)
45 ! "
6 3
4 0, 75 4 3
× = × = ∈4 / 6 5 1 5 4
0, 25 1
4 4 4 4
− = − =− = − ∉ / 6 16 4= ∈ /
6 7 1.75
4= ∉ 6
(
2 1−)(
2 1+ =) ( )
2 2− = − = ∈12 2 1 13# !
→) $ % &' $
$ % '
7 a
b 8 #
9 :
, - ⊂ ⊂
3 2
1 2
n n
n= =
3# 9 0 1
a=3 15
b= −16 c=2 d =0.012 e=π 2 3
f π
= π g= 2
- 3 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php a= ∈3
b= −16∈ / 2
c= =1 c∈ 0.012 12
d= =1000 d∈ / e= ∉π f π 2 3 π
= π = 3
2 ×π 3
=2 f ∈ g= 2∉
→* ! + ,, $ ,,
7 a10n 8
9 # &
, 10n 10 10 ... 10
n fois
= × × × # 103 = × × =10 10 10 1000 100 =1
3# ')); 16225 10002 / 0 * (< 16 0314 1002 /3 5 ( 6 10)= / 1 1 1 0.01 = 100 = 100 =10
# $
- ⊂ ⊂ID⊂
3 0 10
10 10
n n
n= =
% " & ' (
5 $ ! = >
) * " $ +- # 1
3 /
!
10
0,33...33
chiffres
1/ 3 a10n
) ,
! " '
5 $
( % + !
) % +
) ;
# ?
*
@
A 8 2= 3
3# 0 #4 3 7
? ? 4 ? ? ? 3
7 4 4
a b c d π e π f
= = − = = = π = 4
- 4 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
5 ! " & !
10n a 3
a= ∉7 ID /
7 250 1750
4 1000
b ID
×
= − = − ∈ / 40 4 10
c= = ∈ID / d = ∉π ID / e= π 4π
1 25
4 0.25 100 ID
= = = ∈ /
3 f = ∉ID
→) $ % '
$-' .
Définition.
& # #, 2, 3...
π
- # 44
B .
. $ + +
$ +
9 ?
# π+2 π π−
(
+2)
2× 2# $ / 0 1 !
2 1# '@(@(@( 2 5
B 9 *
. % #
# $ &,
⊂ ⊂ID⊂ ⊂
) $ % ' $-' /0 ,1 2
$
3 $-' 4 45 6 $ $-' 7 66
8 9 : ; , $-' 7
* : < (
+ ,, / $ (1 / $ 1
2 ; , (( + = > 2
? = > ,(
1 $
5 C # D #
+ #
5
5 a
x=b c
y= d #
a c ad bc
x y b d bd
+ = + = + 8ad bc+ ∈ bd∈ * 1 '2
#E?
- 5 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php 5
5 10n x= a
10m
y= b # #
10 10
10 10 10
m n
n m n m
a b a b
x y+ = + = ++ 8a10m +b10n∈ 10n m+ ('
#E?
+ 3 π π +3
5 $ C
*
→5 π +3 3 a
π + = b 8 #
→F 3
a 3 a b
b b
π = − ⇔ =π − π #
→ π
!? ! B π +3 . π +3
- 6 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
*
%
2 $ &$⊂+ ⊂& ⊂:⊂&,
* ; , $
( , ∈ ∉
)
! 0
→
&$ + & : &, G60;
* H6*)
<
6*)
; 64 3
π 362,1 11 I60<
J61 10 3 15+ K6 3
7
−
&67 5 π π L67
5 π π + +
M60'*****
96
(
5 7−)(
5 7+)
F6cos(60 )°
$60 *N 64,003 10× 5
3 Q 3π
π
= −
−
- 7 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
& ? ! 4
4
G O ? ! 1 H 2
# 0 324 0 &$4
5
5 ∈&$ % a
b
→G B . B .
3 & '
P) 1 2 1 )2
P* * !
P; ; !
PQ Q !
3# ! 0
* <* / ; (); / @ )(/ * (N
5 0 * <* / ; (); / @
)( )(/ * (N
5 1∈&$2 % # )
(
3# ) * ; @ (( (* (@ (Q )* ?
! " R 3 ! (''
5 ∈&$ % ! ! ." & 1 2 .
3 $ 4 *
3# (Q) *''
5 (Q)6)N * *''6)) * ;)
- 8 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
2 5
- 300
a=192 3 0 4
5
S 2 2 2
6 4
300 2 3 5 5
192 2 3 2
a= = × × =
×
S % 24×54 =2 54 4 =104
2 2 4 6
4 4 4
5 5 5 5
2 10 10
a= = × =
- 6 b= 192 300× 4
5
% 192 300 2× = 6× × × ×3 22 3 52 =28× ×32 52 ab= a× b
8 2 2 2 2 2
2 3 5 2 3 5
b= × × = × ×
x2 =x # b= × × =2 3 5 30
- F *N *''#(Q)
5
$ " 192 300 2× = 6× × × ×3 22 3 52 =28× ×32 52 2 7 2
36
192 300 2 3× = × × ×2 5 *N
*''#(Q)
- 9 -
D. PINEL, Site Mathemitec : http://mathemitec.free.fr/index.php
&$ + & : &, G60 ;
*
∉ ∉ ∉ ∈ ∈ H6*)
<
∈ ∈ ∈ ∈ ∈ 6*)
;
∉ ∉ ∈ ∈ ∈ 64
3
π ∉ ∉ ∉ ∉ ∈
362,1 11
∉ ∉ ∉ ∈ ∈
I60< ∉ ∈ ∈ ∈ ∈
J61 10
3 15+ ∈ ∈ ∈ ∈ ∈
K6 3 7
− ∉ ∉ ∉ ∈ ∈
&67 5 π π
∉ ∉ ∈ ∈ ∈ L67
5 π π + +
∉ ∉ ∉ ∉ ∈
M60'***** ∉ ∉ ∈ ∈ ∈
96
(
5 7−)(
5 7+)
∉ ∈ ∈ ∈ ∈F6cos(60 )° ∉ ∉ ∈ ∈ ∈
$60 *N ∉ ∈ ∈ ∈ ∈
64,003 10× 5 ∈ ∈ ∈ ∈ ∈
3 Q 3π
π
= −
−
∉ ∈ ∈ ∈ ∈
3 4
32 8 B= 4 =
32 64 5 10 C= = ∈
1 10 5 10 15 3 15 15 15 15 1 G= + = + = = ∈
7 7 14 5 5 10
I π ID
= π = = ∈
M60'***** 6 333335
10 ID
− ∈
(
5 7)(
5 7) ( )
5 2 72 5 49 44L= − + = − = − = − ∈
( )
1cos 60
M = ° = ∈2 ID 36 6 N= − = − ∈
4.003 105 400300
P= × = ∈
( )
3 3 1
3 3
Q π π
π π
− −
= = = − ∈
− − −
