Cordes à nœuds

Cordes à nœuds
Henry Plane
illustrations de Julien Lyotard
"F;=5FR  ,.< *:<2,4. 576<:. ,755.6< -.; ,7:-.; C 6S=-; 8.:5.<<.6< -. /*2:.
*88*:*I<:.-.;*604.;7=-.;874@076.;8*:<2,=42.:;-.<:2;.,<.:=6*604.5*2;*=;;2
/*2<4.42.6*>.,=63.=-.5.,,*67
La classique corde à 13 nœuds.
<-T*+7:-4*84=;,F4G+:.R4*,7:-.C<:.2A.6S=-;$:.2A.6S=-;:F0=42G:.5.6<
.;8*,F;9=2-F<.:526.6<*26;226<.:>*44.;F0*=?
$7=;4.;7=>:*0.;;=:4.;>2.=?5F<2.:;.68*:4.6<;*<:*,./20=:.;=:4.;5=:;-.
>2.244.;F042;.;6.//.<;276-2;87;.,.;4760=.=:;87=:/7:5.:=6<:2*604.-76<
4.;,K<F;76<87=:5.;=:..<-.,.;;.05.6<;F0*=?,.<:2*604..;<:.,<*604.
/20=:.6*>*2<*26;2=6*604.-:72<R24@*>*2<4C=6[email protected]87=:,1*:8.6<2.:7=
<*244.=:-.82.::.;-=[email protected]D0.-.;T*;;=:.:9=.;76<:*>*244TF<*2<F0*4.5.6<
*2;*>.,5726;-.6S=-;:F0=42.:;-T*=<:.;,7:-.;76<5F:2<F*<<.6<276
La corde à 4 nœuds.
>.,6S=-;;72<;.05.6<;F0*=?76/7:5.-T*+7:-=6<:2*604.F9=24*<F:*4
874@076.C4*/72;F9=24*<F:*4.<F9=2*604./20=:.%6*604.-.N8.=<<7=37=:;
H<:.=<24.5*2;67=;*4476;<:7=>.:4C4.8:7+4G5.-.4*<:2;.,<276-.4T*604.
Pour chercher et approfondir 199
APMEP
no508
.<*:<2,4.*-F3CF<F8=+42F-*6;4*.=244.-.&206.M-F,.5+:.-.4"
-.2376
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#72<=6*604. /20=:.
x¢7887;F.Cx
687;.4.-.=?2G5.6S=-.6.<4.8:.52.:;=:y6,1.:,1.*47:;C87;.:4.
9=*<:2G5.6S=-;=:x¢.<C*4206.:4.;6S=-;.<=6.:G04.8.=<H<:.=<24.
#72<a4*5.;=:.-. 
4>2.6<R#2   
6**=9=*<:2G5.6S=-4.<2.:;-.4T*604. *8:G;*>72:<:*,F(x¢
x yO
234
= = a213 231 2
=+=a231 423 243 2
=a423
= + = + =x y a a aO 241 214 2 3
x yO
200 Pour chercher et approfondir APMEP
no508
Corde-Texte_Mise en page 1 15/03/14 11:58 Page200

26;247:;9=.4T*604.-.5.;=:.Q:.8:F;.6<F8*: >*:2.x:.;<*6</2?.y¢y
82>7<.*=<7=:-.4.8726<-F,:2<4.,.:,4.-.,.6<:..<-.:*@76(),76;<*6<
.8726<-F,:2<=6.,7=:+. g 7+<.6=..68:74760.*6<4*,7:-.()-=,.:,4.-T=6.
4760=.=:F0*4.*=:*@76-.,.4=2,2
g 6.-F8.6-9=.-=,.:,4..<-=8726<
.<<.;2<=*<2766T*8*;F,1*88F;.5+4.<24CB<2.66. *;,*44.8G:.-.4*2;.
*;.=4.,766*2;;*6,.-. g 8.:5.<-T7+<.62:.6=6*604.-.5.;=:.QC8*:<2:
-. ,76>.6*+4.5.6<84*,F
T.;< "7+.:>*4 9=2 -766* C  g  4. 675 -. Limaçon de Pascal *6; 4*
<.:52674702.*,<=.44.24;T*02<.6:F*42<F-T=6,*;8*:<2,=42.:-.;425*E76;-. *;,*4
.<<. ,7=:+. ,76,17J-. -. ,.:,4. ;. :F>F4.:* 8*: 4* ;=2<. F0*4.5.6< 87-*2:. .<
F82,@,47J-.-=,.:,4..4*5F:2<*2<-.;T@*::H<.:Q
La corde à 5 nœuds.
>.,;.05.6<;-76,6S=-;F9=2-2;<*6<;;276:F=62<4.;-.=?.?<:H5.;.<
 .6 <.6-*6< 4. <7=< 24 >2.6< <7=37=:; =6 47;*60. 874@076. F9=24*<G:. 5*2; 8*;
<7=37=:;F9=2*604.-.8F:25G<:.,76;<*6<5*2;-T*2:.>*:2*+4.Q
*2; <7=37=:; 87=: 4. 0F75G<:. 4.; -2*076*4.; 5F-2*<:2,.; 4T=6. -. 4T*=<:. .<
+2;;.,<:2,.; -.; *604.; 7887;F; $7=< ,.4* +2.6 =<24. 87=: 7+<.62: 4. 5242.= -T=6
;.05.6<7=4*572<2F-T=6*604..<-.;-:72<.;7:<17076*4.;Q
4 6T@ * 8*; 9=. 4=2 87=: ;T.6 H<:. ;.:>2 < 8=2; 24 @ * -.=? ,7=84.; -. -:72<.;
8*:*44G4.;
#=:,.-.:62.:8726<24;.5+4.9=.4.;9=*<:.57:,.*=?-.,7:-./=:.6<*;;.A<K<
:.584*,F;8*:9=*<:.+*0=.<<.;-76<4.;8726<;-T*:<2,=4*<276/7:5*2.6<4.47;*60.
8:F,F-.6<./=<4T7=<249=2/20=:*2<-*6;4*+.;*,.-.<7=<-.;;26*<.=:5*2;9=26T*
8*;4*2;;F-.675
66.;*2<9=*6-,.OR8*:*44F470:*55.C8*:*44G4.;RP.;<*88*:=
x yO
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Cordes à nœuds 201
APMEP
no508
Corde-Texte_Mise en page 1 15/03/14 11:58 Page201

La corde à 6 nœuds.
>.,;.05.6<;F0*=?5H5.;276:F=62<4.;.?<:H5.;4*>*:2F<F-.;<@8.;-.
/20=:.;*=05.6<.6.<<.5.6<
*6; ,. -.:62.: <@8. =6. /20=:. *<<2:. 67<:. *<<.6<276 .44. 8:74760. =6.
7+;.:>*<276-F3C/*2<.
====*>.,.<*4206F;-T=6.8*:<.<.<F0*4.5.6<
=6.:G04./*,242<.4T78F:*<276
202 Pour chercher et approfondir APMEP
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6,76;<*<.=6.;@5F<:2.-.4*/20=:.8*::*887:<C4*5F-2*<:2,.()!=.8.=<76
@42:.R
$:2*604.2;7,G4.;2  .< 
$:2*604.2;7,G4. 
*6;4.<:2*604.R
T*604..6*87=:5.;=:. -76,.;<4.,K<F-=-F,*076.:F0=42.:26;,:2<
-*6;4.,.:,4.-.,.6<:..<-.:*@76= r
!=284=;.;<4.;<:2*604.;2;7,G4.;.<;76<;.5+4*+4.;R .<
=-
68:.6*6<(),755.=62<F-.4760=.=:24>2.6<R 7= r
-=
r -
T.;<4*/*5.=;.:.4*<276-F/262;;*6<4.OR675+:.-T7:RP-76, 
#2 .;<4.,K<F-T=6-F,*076.:F0=42.:,.4=2,2.;<26;,:28<2+4.-*6;=6,.:,4.-.
:*@76 
<4*OR,7:-.C6S=-;RP8.:5.<<*2<4*,76;<:=,<276T.6:.;<76;8*;4C
$:*E76;4.,.:,4.-.,.6<:. .< 8*;;*6< 8*:.<$:*,.:-.;,.:,4.;*>.,-.;
,7:-.;87=::*@76,.6.;76<8*;4.;0F75G<:.;9=2;T@:./=;.:76<
.,.:,4.:.,7=8..6R4.<:2*604..;<2;7,G4..<
Figure 9
= θ COD
= θ DCO
θ = =DBC CDB 2
θ == DBCCDB2
θθθθ
π=++=++= COBOBCBCO225.
π
5
=
BC
OB
AC
BC
="
ρ
ρ 11
1
=+ ρ
15
2
+ 15
2
= = π BAE 2BOC 2 5.
Cordes à nœuds 203
APMEP
no508
Corde-Texte_Mise en page 1 15/03/14 11:58 Page203