valeur de Uk

Uk-1

Angle

Radian

cosinus

sinus

N. COSME   15 mars 2011
Le tableur comme les objets graphiques ne sont pas optimisés, cela reste un fichier de travail

* n représente le nombre d'élèves assis en cercle --> objet curseur modifiable
* k représente le nombre de bonbons distribués --> objet curseur modifiable, faire l'animation sur k pour n fixé
* A et B sont les points --> dependant de k donc trace activée
  - B : les bonbons avec une coefficient s paramétrable pour mettre sous forme de spirale
  - A : les bonbons mis en cercle sans coefficient
* L2 : points des n élèves, venant du tableur (suite complexe assez simple simple...). Je ne sais pas comment enlever les noms des points créés à partir du tableur, car je n'ai pas accès aux propriétés adéquates
* c est un cerle pour placer les points B sur la spirale --> dependant de k donc trace activée
* le point D et le segment d permettent de tracer les segments délimitant les élèves ayant recu un bonbon...

Enoncé Problème 5: (source IREM Lyon) - Distribution de bonbons ( libérale avancée)
n enfants sont placés en cercle. On distribue des bonbons en tournant toujours dans le même sens sur le cercle, de la façon suivante :
On donne un bonbon à un enfant, on passe le suivant, on donne un bonbon au troisième, on passe les deux suivants, on donne un bonbon au sixième enfant, et ainsi de suite ... ( Quand on a donné le kème bonbon, on passe k enfants).
Pour quelles valeurs de n les enfants auront-ils tous au moins un bonbon ?

Enoncé

Informations sur les objets

n = 16 (slider from 1 to 100, step 1)
i = (0, 1)
A3 = 2
A2 = 1
A4: 2.0 * A3 - A2
A5: 2.0 * A4 - A3
A6: 2.0 * A5 - A4
A7: 2.0 * A6 - A5
A8: 2.0 * A7 - A6
A9: 2.0 * A8 - A7
A10: 2.0 * A9 - A8
A11: 2.0 * A10 - A9
B11: A11 * (A11 + 1.0) / 2.0
C11: B11 - 1.0
F1: n
D11: 360.0 / $F$1 * C11
E11: D11 * 3.141592653589793 / 180.0
B10: A10 * (A10 + 1.0) / 2.0
C10: B10 - 1.0
D10: 360.0 / $F$1 * C10
E10: D10 * 3.141592653589793 / 180.0
A12: 2.0 * A11 - A10
A13: 2.0 * A12 - A11
A14: 2.0 * A13 - A12
A15: 2.0 * A14 - A13
A16: 2.0 * A15 - A14
A17: 2.0 * A16 - A15
A18: 2.0 * A17 - A16
A19: 2.0 * A18 - A17
A20: 2.0 * A19 - A18
A21: 2.0 * A20 - A19
A22: 2.0 * A21 - A20
A23: 2.0 * A22 - A21
A24: 2.0 * A23 - A22
A25: 2.0 * A24 - A23
A26: 2.0 * A25 - A24
B2: A2 * (A2 + 1.0) / 2.0
B3: A3 * (A3 + 1.0) / 2.0
B4: A4 * (A4 + 1.0) / 2.0
B5: A5 * (A5 + 1.0) / 2.0
B6: A6 * (A6 + 1.0) / 2.0
B7: A7 * (A7 + 1.0) / 2.0
B8: A8 * (A8 + 1.0) / 2.0
B9: A9 * (A9 + 1.0) / 2.0
C2: B2 - 1.0
C3: B3 - 1.0
C4: B4 - 1.0
C5: B5 - 1.0
C6: B6 - 1.0
C7: B7 - 1.0
C8: B8 - 1.0
C9: B9 - 1.0
D2: 360.0 / $F$1 * C2
D3: 360.0 / $F$1 * C3
D4: 360.0 / $F$1 * C4
D5: 360.0 / $F$1 * C5
D6: 360.0 / $F$1 * C6
D7: 360.0 / $F$1 * C7
D8: 360.0 / $F$1 * C8
D9: 360.0 / $F$1 * C9
E2: D2 * 3.141592653589793 / 180.0
E3: D3 * 3.141592653589793 / 180.0
E4: D4 * 3.141592653589793 / 180.0
E5: D5 * 3.141592653589793 / 180.0
E6: D6 * 3.141592653589793 / 180.0
E7: D7 * 3.141592653589793 / 180.0
E8: D8 * 3.141592653589793 / 180.0
E9: D9 * 3.141592653589793 / 180.0
B12: A12 * (A12 + 1.0) / 2.0
B13: A13 * (A13 + 1.0) / 2.0
B14: A14 * (A14 + 1.0) / 2.0
B15: A15 * (A15 + 1.0) / 2.0
B16: A16 * (A16 + 1.0) / 2.0
B17: A17 * (A17 + 1.0) / 2.0
B18: A18 * (A18 + 1.0) / 2.0
B19: A19 * (A19 + 1.0) / 2.0
B20: A20 * (A20 + 1.0) / 2.0
B21: A21 * (A21 + 1.0) / 2.0
B22: A22 * (A22 + 1.0) / 2.0
B23: A23 * (A23 + 1.0) / 2.0
B24: A24 * (A24 + 1.0) / 2.0
C12: B12 - 1.0
C13: B13 - 1.0
C14: B14 - 1.0
C15: B15 - 1.0
C16: B16 - 1.0
C17: B17 - 1.0
C18: B18 - 1.0
C19: B19 - 1.0
C20: B20 - 1.0
C21: B21 - 1.0
C22: B22 - 1.0
C23: B23 - 1.0
C24: B24 - 1.0
D12: 360.0 / $F$1 * C12
D13: 360.0 / $F$1 * C13
D14: 360.0 / $F$1 * C14
D15: 360.0 / $F$1 * C15
D16: 360.0 / $F$1 * C16
D17: 360.0 / $F$1 * C17
D18: 360.0 / $F$1 * C18
D19: 360.0 / $F$1 * C19
D20: 360.0 / $F$1 * C20
D21: 360.0 / $F$1 * C21
D22: 360.0 / $F$1 * C22
D23: 360.0 / $F$1 * C23
D24: 360.0 / $F$1 * C24
E12: D12 * 3.141592653589793 / 180.0
E13: D13 * 3.141592653589793 / 180.0
E14: D14 * 3.141592653589793 / 180.0
E15: D15 * 3.141592653589793 / 180.0
E16: D16 * 3.141592653589793 / 180.0
E17: D17 * 3.141592653589793 / 180.0
E18: D18 * 3.141592653589793 / 180.0
E19: D19 * 3.141592653589793 / 180.0
E20: D20 * 3.141592653589793 / 180.0
E21: D21 * 3.141592653589793 / 180.0
E22: D22 * 3.141592653589793 / 180.0
E23: D23 * 3.141592653589793 / 180.0
E24: D24 * 3.141592653589793 / 180.0
B25: A25 * (A25 + 1.0) / 2.0
C25: B25 - 1.0
D25: 360.0 / $F$1 * C25
E25: D25 * 3.141592653589793 / 180.0
F2: exp(i * 2.0 * 3.141592653589793 * (A2 - 1.0) / $F$1)
F3: exp(i * 2.0 * 3.141592653589793 * (A3 - 1.0) / $F$1)
F4: exp(i * 2.0 * 3.141592653589793 * (A4 - 1.0) / $F$1)
F5: exp(i * 2.0 * 3.141592653589793 * (A5 - 1.0) / $F$1)
F6: exp(i * 2.0 * 3.141592653589793 * (A6 - 1.0) / $F$1)
F7: exp(i * 2.0 * 3.141592653589793 * (A7 - 1.0) / $F$1)
F8: exp(i * 2.0 * 3.141592653589793 * (A8 - 1.0) / $F$1)
F9: exp(i * 2.0 * 3.141592653589793 * (A9 - 1.0) / $F$1)
F10: exp(i * 2.0 * 3.141592653589793 * (A10 - 1.0) / $F$1)
F11: exp(i * 2.0 * 3.141592653589793 * (A11 - 1.0) / $F$1)
F12: exp(i * 2.0 * 3.141592653589793 * (A12 - 1.0) / $F$1)
F13: exp(i * 2.0 * 3.141592653589793 * (A13 - 1.0) / $F$1)
F14: exp(i * 2.0 * 3.141592653589793 * (A14 - 1.0) / $F$1)
F15: exp(i * 2.0 * 3.141592653589793 * (A15 - 1.0) / $F$1)
F16: exp(i * 2.0 * 3.141592653589793 * (A16 - 1.0) / $F$1)
F17: exp(i * 2.0 * 3.141592653589793 * (A17 - 1.0) / $F$1)
F18: exp(i * 2.0 * 3.141592653589793 * (A18 - 1.0) / $F$1)
F19: exp(i * 2.0 * 3.141592653589793 * (A19 - 1.0) / $F$1)
F20: exp(i * 2.0 * 3.141592653589793 * (A20 - 1.0) / $F$1)
F21: exp(i * 2.0 * 3.141592653589793 * (A21 - 1.0) / $F$1)
F22: exp(i * 2.0 * 3.141592653589793 * (A22 - 1.0) / $F$1)
F23: exp(i * 2.0 * 3.141592653589793 * (A23 - 1.0) / $F$1)
F24: exp(i * 2.0 * 3.141592653589793 * (A24 - 1.0) / $F$1)
F25: exp(i * 2.0 * 3.141592653589793 * (A25 - 1.0) / $F$1)
G2: exp(i * E2)
A27: 2.0 * A26 - A25
A28: 2.0 * A27 - A26
A29: 2.0 * A28 - A27
A30: 2.0 * A29 - A28
A31: 2.0 * A30 - A29
A32: 2.0 * A31 - A30
A33: 2.0 * A32 - A31
A34: 2.0 * A33 - A32
A35: 2.0 * A34 - A33
A36: 2.0 * A35 - A34
A37: 2.0 * A36 - A35
A38: 2.0 * A37 - A36
B26: A26 * (A26 + 1.0) / 2.0
C26: B26 - 1.0
D26: 360.0 / $F$1 * C26
E26: D26 * 3.141592653589793 / 180.0
F26: exp(i * 2.0 * 3.141592653589793 * (A26 - 1.0) / $F$1)
B27: A27 * (A27 + 1.0) / 2.0
C27: B27 - 1.0
D27: 360.0 / $F$1 * C27
E27: D27 * 3.141592653589793 / 180.0
F27: exp(i * 2.0 * 3.141592653589793 * (A27 - 1.0) / $F$1)
B28: A28 * (A28 + 1.0) / 2.0
C28: B28 - 1.0
D28: 360.0 / $F$1 * C28
E28: D28 * 3.141592653589793 / 180.0
F28: exp(i * 2.0 * 3.141592653589793 * (A28 - 1.0) / $F$1)
B29: A29 * (A29 + 1.0) / 2.0
C29: B29 - 1.0
D29: 360.0 / $F$1 * C29
E29: D29 * 3.141592653589793 / 180.0
F29: exp(i * 2.0 * 3.141592653589793 * (A29 - 1.0) / $F$1)
B30: A30 * (A30 + 1.0) / 2.0
C30: B30 - 1.0
D30: 360.0 / $F$1 * C30
E30: D30 * 3.141592653589793 / 180.0
F30: exp(i * 2.0 * 3.141592653589793 * (A30 - 1.0) / $F$1)
B31: A31 * (A31 + 1.0) / 2.0
C31: B31 - 1.0
D31: 360.0 / $F$1 * C31
E31: D31 * 3.141592653589793 / 180.0
F31: exp(i * 2.0 * 3.141592653589793 * (A31 - 1.0) / $F$1)
B32: A32 * (A32 + 1.0) / 2.0
C32: B32 - 1.0
D32: 360.0 / $F$1 * C32
E32: D32 * 3.141592653589793 / 180.0
F32: exp(i * 2.0 * 3.141592653589793 * (A32 - 1.0) / $F$1)
B33: A33 * (A33 + 1.0) / 2.0
C33: B33 - 1.0
D33: 360.0 / $F$1 * C33
E33: D33 * 3.141592653589793 / 180.0
F33: exp(i * 2.0 * 3.141592653589793 * (A33 - 1.0) / $F$1)
B34: A34 * (A34 + 1.0) / 2.0
C34: B34 - 1.0
D34: 360.0 / $F$1 * C34
E34: D34 * 3.141592653589793 / 180.0
F34: exp(i * 2.0 * 3.141592653589793 * (A34 - 1.0) / $F$1)
B35: A35 * (A35 + 1.0) / 2.0
C35: B35 - 1.0
D35: 360.0 / $F$1 * C35
E35: D35 * 3.141592653589793 / 180.0
F35: exp(i * 2.0 * 3.141592653589793 * (A35 - 1.0) / $F$1)
B36: A36 * (A36 + 1.0) / 2.0
C36: B36 - 1.0
D36: 360.0 / $F$1 * C36
E36: D36 * 3.141592653589793 / 180.0
F36: exp(i * 2.0 * 3.141592653589793 * (A36 - 1.0) / $F$1)
B37: A37 * (A37 + 1.0) / 2.0
C37: B37 - 1.0
D37: 360.0 / $F$1 * C37
E37: D37 * 3.141592653589793 / 180.0
F37: exp(i * 2.0 * 3.141592653589793 * (A37 - 1.0) / $F$1)
B38: A38 * (A38 + 1.0) / 2.0
C38: B38 - 1.0
D38: 360.0 / $F$1 * C38
E38: D38 * 3.141592653589793 / 180.0
F38: exp(i * 2.0 * 3.141592653589793 * (A38 - 1.0) / $F$1)
A39 = 38
B39: A39 * (A39 + 1.0) / 2.0
C39: B39 - 1.0
D39: 360.0 / $F$1 * C39
E39: D39 * 3.141592653589793 / 180.0
F39: exp(i * 2.0 * 3.141592653589793 * (A39 - 1.0) / $F$1)
A40: 2.0 * A39 - A38
A41: 2.0 * A40 - A39
A42: 2.0 * A41 - A40
A43: 2.0 * A42 - A41
A44: 2.0 * A43 - A42
A45: 2.0 * A44 - A43
A46: 2.0 * A45 - A44
A47: 2.0 * A46 - A45
A48: 2.0 * A47 - A46
A49: 2.0 * A48 - A47
A50: 2.0 * A49 - A48
A51: 2.0 * A50 - A49
A52: 2.0 * A51 - A50
A53: 2.0 * A52 - A51
A54: 2.0 * A53 - A52
A55: 2.0 * A54 - A53
A56: 2.0 * A55 - A54
A57: 2.0 * A56 - A55
A58: 2.0 * A57 - A56
A59: 2.0 * A58 - A57
A60: 2.0 * A59 - A58
A61: 2.0 * A60 - A59
A62: 2.0 * A61 - A60
A63: 2.0 * A62 - A61
A64: 2.0 * A63 - A62
A65: 2.0 * A64 - A63
A66: 2.0 * A65 - A64
A67: 2.0 * A66 - A65
A68: 2.0 * A67 - A66
A69: 2.0 * A68 - A67
A70: 2.0 * A69 - A68
B40: A40 * (A40 + 1.0) / 2.0
C40: B40 - 1.0
D40: 360.0 / $F$1 * C40
E40: D40 * 3.141592653589793 / 180.0
F40: exp(i * 2.0 * 3.141592653589793 * (A40 - 1.0) / $F$1)
B41: A41 * (A41 + 1.0) / 2.0
C41: B41 - 1.0
D41: 360.0 / $F$1 * C41
E41: D41 * 3.141592653589793 / 180.0
F41: exp(i * 2.0 * 3.141592653589793 * (A41 - 1.0) / $F$1)
B42: A42 * (A42 + 1.0) / 2.0
C42: B42 - 1.0
D42: 360.0 / $F$1 * C42
E42: D42 * 3.141592653589793 / 180.0
F42: exp(i * 2.0 * 3.141592653589793 * (A42 - 1.0) / $F$1)
B43: A43 * (A43 + 1.0) / 2.0
C43: B43 - 1.0
D43: 360.0 / $F$1 * C43
E43: D43 * 3.141592653589793 / 180.0
F43: exp(i * 2.0 * 3.141592653589793 * (A43 - 1.0) / $F$1)
B44: A44 * (A44 + 1.0) / 2.0
C44: B44 - 1.0
D44: 360.0 / $F$1 * C44
E44: D44 * 3.141592653589793 / 180.0
F44: exp(i * 2.0 * 3.141592653589793 * (A44 - 1.0) / $F$1)
B45: A45 * (A45 + 1.0) / 2.0
C45: B45 - 1.0
D45: 360.0 / $F$1 * C45
E45: D45 * 3.141592653589793 / 180.0
F45: exp(i * 2.0 * 3.141592653589793 * (A45 - 1.0) / $F$1)
B46: A46 * (A46 + 1.0) / 2.0
C46: B46 - 1.0
D46: 360.0 / $F$1 * C46
E46: D46 * 3.141592653589793 / 180.0
F46: exp(i * 2.0 * 3.141592653589793 * (A46 - 1.0) / $F$1)
B47: A47 * (A47 + 1.0) / 2.0
C47: B47 - 1.0
D47: 360.0 / $F$1 * C47
E47: D47 * 3.141592653589793 / 180.0
F47: exp(i * 2.0 * 3.141592653589793 * (A47 - 1.0) / $F$1)
B48: A48 * (A48 + 1.0) / 2.0
C48: B48 - 1.0
D48: 360.0 / $F$1 * C48
E48: D48 * 3.141592653589793 / 180.0
F48: exp(i * 2.0 * 3.141592653589793 * (A48 - 1.0) / $F$1)
B49: A49 * (A49 + 1.0) / 2.0
C49: B49 - 1.0
D49: 360.0 / $F$1 * C49
E49: D49 * 3.141592653589793 / 180.0
F49: exp(i * 2.0 * 3.141592653589793 * (A49 - 1.0) / $F$1)
B50: A50 * (A50 + 1.0) / 2.0
C50: B50 - 1.0
D50: 360.0 / $F$1 * C50
E50: D50 * 3.141592653589793 / 180.0
F50: exp(i * 2.0 * 3.141592653589793 * (A50 - 1.0) / $F$1)
B51: A51 * (A51 + 1.0) / 2.0
C51: B51 - 1.0
D51: 360.0 / $F$1 * C51
E51: D51 * 3.141592653589793 / 180.0
F51: exp(i * 2.0 * 3.141592653589793 * (A51 - 1.0) / $F$1)
B52: A52 * (A52 + 1.0) / 2.0
C52: B52 - 1.0
D52: 360.0 / $F$1 * C52
E52: D52 * 3.141592653589793 / 180.0
F52: exp(i * 2.0 * 3.141592653589793 * (A52 - 1.0) / $F$1)
B53: A53 * (A53 + 1.0) / 2.0
C53: B53 - 1.0
D53: 360.0 / $F$1 * C53
E53: D53 * 3.141592653589793 / 180.0
F53: exp(i * 2.0 * 3.141592653589793 * (A53 - 1.0) / $F$1)
B54: A54 * (A54 + 1.0) / 2.0
C54: B54 - 1.0
D54: 360.0 / $F$1 * C54
E54: D54 * 3.141592653589793 / 180.0
F54: exp(i * 2.0 * 3.141592653589793 * (A54 - 1.0) / $F$1)
B55: A55 * (A55 + 1.0) / 2.0
C55: B55 - 1.0
D55: 360.0 / $F$1 * C55
E55: D55 * 3.141592653589793 / 180.0
F55: exp(i * 2.0 * 3.141592653589793 * (A55 - 1.0) / $F$1)
B56: A56 * (A56 + 1.0) / 2.0
C56: B56 - 1.0
D56: 360.0 / $F$1 * C56
E56: D56 * 3.141592653589793 / 180.0
F56: exp(i * 2.0 * 3.141592653589793 * (A56 - 1.0) / $F$1)
B57: A57 * (A57 + 1.0) / 2.0
C57: B57 - 1.0
D57: 360.0 / $F$1 * C57
E57: D57 * 3.141592653589793 / 180.0
F57: exp(i * 2.0 * 3.141592653589793 * (A57 - 1.0) / $F$1)
B58: A58 * (A58 + 1.0) / 2.0
C58: B58 - 1.0
D58: 360.0 / $F$1 * C58
E58: D58 * 3.141592653589793 / 180.0
F58: exp(i * 2.0 * 3.141592653589793 * (A58 - 1.0) / $F$1)
B59: A59 * (A59 + 1.0) / 2.0
C59: B59 - 1.0
D59: 360.0 / $F$1 * C59
E59: D59 * 3.141592653589793 / 180.0
F59: exp(i * 2.0 * 3.141592653589793 * (A59 - 1.0) / $F$1)
B60: A60 * (A60 + 1.0) / 2.0
C60: B60 - 1.0
D60: 360.0 / $F$1 * C60
E60: D60 * 3.141592653589793 / 180.0
F60: exp(i * 2.0 * 3.141592653589793 * (A60 - 1.0) / $F$1)
B61: A61 * (A61 + 1.0) / 2.0
C61: B61 - 1.0
D61: 360.0 / $F$1 * C61
E61: D61 * 3.141592653589793 / 180.0
F61: exp(i * 2.0 * 3.141592653589793 * (A61 - 1.0) / $F$1)
B62: A62 * (A62 + 1.0) / 2.0
C62: B62 - 1.0
D62: 360.0 / $F$1 * C62
E62: D62 * 3.141592653589793 / 180.0
F62: exp(i * 2.0 * 3.141592653589793 * (A62 - 1.0) / $F$1)
B63: A63 * (A63 + 1.0) / 2.0
C63: B63 - 1.0
D63: 360.0 / $F$1 * C63
E63: D63 * 3.141592653589793 / 180.0
F63: exp(i * 2.0 * 3.141592653589793 * (A63 - 1.0) / $F$1)
B64: A64 * (A64 + 1.0) / 2.0
C64: B64 - 1.0
D64: 360.0 / $F$1 * C64
E64: D64 * 3.141592653589793 / 180.0
F64: exp(i * 2.0 * 3.141592653589793 * (A64 - 1.0) / $F$1)
B65: A65 * (A65 + 1.0) / 2.0
C65: B65 - 1.0
D65: 360.0 / $F$1 * C65
E65: D65 * 3.141592653589793 / 180.0
F65: exp(i * 2.0 * 3.141592653589793 * (A65 - 1.0) / $F$1)
B66: A66 * (A66 + 1.0) / 2.0
C66: B66 - 1.0
D66: 360.0 / $F$1 * C66
E66: D66 * 3.141592653589793 / 180.0
F66: exp(i * 2.0 * 3.141592653589793 * (A66 - 1.0) / $F$1)
B67: A67 * (A67 + 1.0) / 2.0
C67: B67 - 1.0
D67: 360.0 / $F$1 * C67
E67: D67 * 3.141592653589793 / 180.0
F67: exp(i * 2.0 * 3.141592653589793 * (A67 - 1.0) / $F$1)
B68: A68 * (A68 + 1.0) / 2.0
C68: B68 - 1.0
D68: 360.0 / $F$1 * C68
E68: D68 * 3.141592653589793 / 180.0
F68: exp(i * 2.0 * 3.141592653589793 * (A68 - 1.0) / $F$1)
B69: A69 * (A69 + 1.0) / 2.0
C69: B69 - 1.0
D69: 360.0 / $F$1 * C69
E69: D69 * 3.141592653589793 / 180.0
F69: exp(i * 2.0 * 3.141592653589793 * (A69 - 1.0) / $F$1)
B70: A70 * (A70 + 1.0) / 2.0
C70: B70 - 1.0
D70: 360.0 / $F$1 * C70
E70: D70 * 3.141592653589793 / 180.0
F70: exp(i * 2.0 * 3.141592653589793 * (A70 - 1.0) / $F$1)
A71: 2.0 * A70 - A69
A72: 2.0 * A71 - A70
A73: 2.0 * A72 - A71
A74: 2.0 * A73 - A72
A75: 2.0 * A74 - A73
A76: 2.0 * A75 - A74
A77: 2.0 * A76 - A75
A78: 2.0 * A77 - A76
B71: A71 * (A71 + 1.0) / 2.0
C71: B71 - 1.0
D71: 360.0 / $F$1 * C71
E71: D71 * 3.141592653589793 / 180.0
F71: exp(i * 2.0 * 3.141592653589793 * (A71 - 1.0) / $F$1)
B72: A72 * (A72 + 1.0) / 2.0
C72: B72 - 1.0
D72: 360.0 / $F$1 * C72
E72: D72 * 3.141592653589793 / 180.0
F72: exp(i * 2.0 * 3.141592653589793 * (A72 - 1.0) / $F$1)
B73: A73 * (A73 + 1.0) / 2.0
C73: B73 - 1.0
D73: 360.0 / $F$1 * C73
E73: D73 * 3.141592653589793 / 180.0
F73: exp(i * 2.0 * 3.141592653589793 * (A73 - 1.0) / $F$1)
B74: A74 * (A74 + 1.0) / 2.0
C74: B74 - 1.0
D74: 360.0 / $F$1 * C74
E74: D74 * 3.141592653589793 / 180.0
F74: exp(i * 2.0 * 3.141592653589793 * (A74 - 1.0) / $F$1)
B75: A75 * (A75 + 1.0) / 2.0
C75: B75 - 1.0
D75: 360.0 / $F$1 * C75
E75: D75 * 3.141592653589793 / 180.0
F75: exp(i * 2.0 * 3.141592653589793 * (A75 - 1.0) / $F$1)
B76: A76 * (A76 + 1.0) / 2.0
C76: B76 - 1.0
D76: 360.0 / $F$1 * C76
E76: D76 * 3.141592653589793 / 180.0
F76: exp(i * 2.0 * 3.141592653589793 * (A76 - 1.0) / $F$1)
B77: A77 * (A77 + 1.0) / 2.0
C77: B77 - 1.0
D77: 360.0 / $F$1 * C77
E77: D77 * 3.141592653589793 / 180.0
F77: exp(i * 2.0 * 3.141592653589793 * (A77 - 1.0) / $F$1)
B78: A78 * (A78 + 1.0) / 2.0
C78: B78 - 1.0
D78: 360.0 / $F$1 * C78
E78: D78 * 3.141592653589793 / 180.0
F78: exp(i * 2.0 * 3.141592653589793 * (A78 - 1.0) / $F$1)
A79: 2.0 * A78 - A77
A80: 2.0 * A79 - A78
A81: 2.0 * A80 - A79
A82: 2.0 * A81 - A80
A83: 2.0 * A82 - A81
A84: 2.0 * A83 - A82
A85: 2.0 * A84 - A83
A86: 2.0 * A85 - A84
A87: 2.0 * A86 - A85
A88: 2.0 * A87 - A86
A89: 2.0 * A88 - A87
A90: 2.0 * A89 - A88
A91: 2.0 * A90 - A89
A92: 2.0 * A91 - A90
A93: 2.0 * A92 - A91
A94: 2.0 * A93 - A92
A95: 2.0 * A94 - A93
A96: 2.0 * A95 - A94
A97: 2.0 * A96 - A95
A98: 2.0 * A97 - A96
A99: 2.0 * A98 - A97
A100: 2.0 * A99 - A98
B79: A79 * (A79 + 1.0) / 2.0
C79: B79 - 1.0
D79: 360.0 / $F$1 * C79
E79: D79 * 3.141592653589793 / 180.0
F79: exp(i * 2.0 * 3.141592653589793 * (A79 - 1.0) / $F$1)
B80: A80 * (A80 + 1.0) / 2.0
C80: B80 - 1.0
D80: 360.0 / $F$1 * C80
E80: D80 * 3.141592653589793 / 180.0
F80: exp(i * 2.0 * 3.141592653589793 * (A80 - 1.0) / $F$1)
B81: A81 * (A81 + 1.0) / 2.0
C81: B81 - 1.0
D81: 360.0 / $F$1 * C81
E81: D81 * 3.141592653589793 / 180.0
F81: exp(i * 2.0 * 3.141592653589793 * (A81 - 1.0) / $F$1)
B82: A82 * (A82 + 1.0) / 2.0
C82: B82 - 1.0
D82: 360.0 / $F$1 * C82
E82: D82 * 3.141592653589793 / 180.0
F82: exp(i * 2.0 * 3.141592653589793 * (A82 - 1.0) / $F$1)
B83: A83 * (A83 + 1.0) / 2.0
C83: B83 - 1.0
D83: 360.0 / $F$1 * C83
E83: D83 * 3.141592653589793 / 180.0
F83: exp(i * 2.0 * 3.141592653589793 * (A83 - 1.0) / $F$1)
B84: A84 * (A84 + 1.0) / 2.0
C84: B84 - 1.0
D84: 360.0 / $F$1 * C84
E84: D84 * 3.141592653589793 / 180.0
F84: exp(i * 2.0 * 3.141592653589793 * (A84 - 1.0) / $F$1)
B85: A85 * (A85 + 1.0) / 2.0
C85: B85 - 1.0
D85: 360.0 / $F$1 * C85
E85: D85 * 3.141592653589793 / 180.0
F85: exp(i * 2.0 * 3.141592653589793 * (A85 - 1.0) / $F$1)
B86: A86 * (A86 + 1.0) / 2.0
C86: B86 - 1.0
D86: 360.0 / $F$1 * C86
E86: D86 * 3.141592653589793 / 180.0
F86: exp(i * 2.0 * 3.141592653589793 * (A86 - 1.0) / $F$1)
B87: A87 * (A87 + 1.0) / 2.0
C87: B87 - 1.0
D87: 360.0 / $F$1 * C87
E87: D87 * 3.141592653589793 / 180.0
F87: exp(i * 2.0 * 3.141592653589793 * (A87 - 1.0) / $F$1)
B88: A88 * (A88 + 1.0) / 2.0
C88: B88 - 1.0
D88: 360.0 / $F$1 * C88
E88: D88 * 3.141592653589793 / 180.0
F88: exp(i * 2.0 * 3.141592653589793 * (A88 - 1.0) / $F$1)
B89: A89 * (A89 + 1.0) / 2.0
C89: B89 - 1.0
D89: 360.0 / $F$1 * C89
E89: D89 * 3.141592653589793 / 180.0
F89: exp(i * 2.0 * 3.141592653589793 * (A89 - 1.0) / $F$1)
B90: A90 * (A90 + 1.0) / 2.0
C90: B90 - 1.0
D90: 360.0 / $F$1 * C90
E90: D90 * 3.141592653589793 / 180.0
F90: exp(i * 2.0 * 3.141592653589793 * (A90 - 1.0) / $F$1)
B91: A91 * (A91 + 1.0) / 2.0
C91: B91 - 1.0
D91: 360.0 / $F$1 * C91
E91: D91 * 3.141592653589793 / 180.0
F91: exp(i * 2.0 * 3.141592653589793 * (A91 - 1.0) / $F$1)
B92: A92 * (A92 + 1.0) / 2.0
C92: B92 - 1.0
D92: 360.0 / $F$1 * C92
E92: D92 * 3.141592653589793 / 180.0
F92: exp(i * 2.0 * 3.141592653589793 * (A92 - 1.0) / $F$1)
B93: A93 * (A93 + 1.0) / 2.0
C93: B93 - 1.0
D93: 360.0 / $F$1 * C93
E93: D93 * 3.141592653589793 / 180.0
F93: exp(i * 2.0 * 3.141592653589793 * (A93 - 1.0) / $F$1)
B94: A94 * (A94 + 1.0) / 2.0
C94: B94 - 1.0
D94: 360.0 / $F$1 * C94
E94: D94 * 3.141592653589793 / 180.0
F94: exp(i * 2.0 * 3.141592653589793 * (A94 - 1.0) / $F$1)
B95: A95 * (A95 + 1.0) / 2.0
C95: B95 - 1.0
D95: 360.0 / $F$1 * C95
E95: D95 * 3.141592653589793 / 180.0
F95: exp(i * 2.0 * 3.141592653589793 * (A95 - 1.0) / $F$1)
B96: A96 * (A96 + 1.0) / 2.0
C96: B96 - 1.0
D96: 360.0 / $F$1 * C96
E96: D96 * 3.141592653589793 / 180.0
F96: exp(i * 2.0 * 3.141592653589793 * (A96 - 1.0) / $F$1)
B97: A97 * (A97 + 1.0) / 2.0
C97: B97 - 1.0
D97: 360.0 / $F$1 * C97
E97: D97 * 3.141592653589793 / 180.0
F97: exp(i * 2.0 * 3.141592653589793 * (A97 - 1.0) / $F$1)
B98: A98 * (A98 + 1.0) / 2.0
C98: B98 - 1.0
D98: 360.0 / $F$1 * C98
E98: D98 * 3.141592653589793 / 180.0
F98: exp(i * 2.0 * 3.141592653589793 * (A98 - 1.0) / $F$1)
B99: A99 * (A99 + 1.0) / 2.0
C99: B99 - 1.0
D99: 360.0 / $F$1 * C99
E99: D99 * 3.141592653589793 / 180.0
F99: exp(i * 2.0 * 3.141592653589793 * (A99 - 1.0) / $F$1)
B100: A100 * (A100 + 1.0) / 2.0
C100: B100 - 1.0
D100: 360.0 / $F$1 * C100
E100: D100 * 3.141592653589793 / 180.0
F100: exp(i * 2.0 * 3.141592653589793 * (A100 - 1.0) / $F$1)
G3: exp(i * E3)
G4: exp(i * E4)
G5: exp(i * E5)
G6: exp(i * E6)
G7: exp(i * E7)
G8: exp(i * E8)
G9: exp(i * E9)
G10: exp(i * E10)
G11: exp(i * E11)
G12: exp(i * E12)
G13: exp(i * E13)
G14: exp(i * E14)
G15: exp(i * E15)
G16: exp(i * E16)
G17: exp(i * E17)
G18: exp(i * E18)
G19: exp(i * E19)
G20: exp(i * E20)
G21: exp(i * E21)
G22: exp(i * E22)
G23: exp(i * E23)
G24: exp(i * E24)
G25: exp(i * E25)
G26: exp(i * E26)
G27: exp(i * E27)
G28: exp(i * E28)
G29: exp(i * E29)
G30: exp(i * E30)
G31: exp(i * E31)
G32: exp(i * E32)
G33: exp(i * E33)
G34: exp(i * E34)
G35: exp(i * E35)
G36: exp(i * E36)
G37: exp(i * E37)
G38: exp(i * E38)
G39: exp(i * E39)
G40: exp(i * E40)
G41: exp(i * E41)
G42: exp(i * E42)
G43: exp(i * E43)
G44: exp(i * E44)
G45: exp(i * E45)
G46: exp(i * E46)
G47: exp(i * E47)
G48: exp(i * E48)
G49: exp(i * E49)
G50: exp(i * E50)
G51: exp(i * E51)
G52: exp(i * E52)
G53: exp(i * E53)
G54: exp(i * E54)
G55: exp(i * E55)
G56: exp(i * E56)
G57: exp(i * E57)
G58: exp(i * E58)
G59: exp(i * E59)
G60: exp(i * E60)
G61: exp(i * E61)
G62: exp(i * E62)
G63: exp(i * E63)
G64: exp(i * E64)
H3: cos(E3)
H4: cos(E4)
H5: cos(E5)
H6: cos(E6)
H7: cos(E7)
H8: cos(E8)
H9: cos(E9)
H10: cos(E10)
H11: cos(E11)
H12: cos(E12)
H13: cos(E13)
H14: cos(E14)
H15: cos(E15)
H16: cos(E16)
H17: cos(E17)
H18: cos(E18)
H19: cos(E19)
H20: cos(E20)
H21: cos(E21)
H22: cos(E22)
H23: cos(E23)
H24: cos(E24)
H25: cos(E25)
H26: cos(E26)
H27: cos(E27)
H28: cos(E28)
H29: cos(E29)
H30: cos(E30)
H31: cos(E31)
H32: cos(E32)
H33: cos(E33)
H34: cos(E34)
H35: cos(E35)
H36: cos(E36)
H37: cos(E37)
H38: cos(E38)
H39: cos(E39)
H40: cos(E40)
H41: cos(E41)
H42: cos(E42)
H43: cos(E43)
H44: cos(E44)
H45: cos(E45)
H46: cos(E46)
H47: cos(E47)
H48: cos(E48)
H49: cos(E49)
H50: cos(E50)
H51: cos(E51)
H52: cos(E52)
H53: cos(E53)
H54: cos(E54)
H55: cos(E55)
H56: cos(E56)
H57: cos(E57)
H58: cos(E58)
H59: cos(E59)
H60: cos(E60)
H61: cos(E61)
H62: cos(E62)
H63: cos(E63)
H64: cos(E64)
H65: cos(E65)
H66: cos(E66)
H67: cos(E67)
H68: cos(E68)
H69: cos(E69)
H70: cos(E70)
I2: sin(E2)
I3: sin(E3)
I4: sin(E4)
I5: sin(E5)
I6: sin(E6)
I7: sin(E7)
I8: sin(E8)
I9: sin(E9)
I10: sin(E10)
I11: sin(E11)
I12: sin(E12)
I13: sin(E13)
I14: sin(E14)
I15: sin(E15)
I16: sin(E16)
I17: sin(E17)
I18: sin(E18)
I19: sin(E19)
I20: sin(E20)
I21: sin(E21)
I22: sin(E22)
I23: sin(E23)
I24: sin(E24)
I25: sin(E25)
I26: sin(E26)
I27: sin(E27)
I28: sin(E28)
I29: sin(E29)
I30: sin(E30)
I31: sin(E31)
I32: sin(E32)
I33: sin(E33)
I34: sin(E34)
I35: sin(E35)
I36: sin(E36)
I37: sin(E37)
I38: sin(E38)
I39: sin(E39)
I40: sin(E40)
I41: sin(E41)
I42: sin(E42)
I43: sin(E43)
I44: sin(E44)
I45: sin(E45)
I46: sin(E46)
I47: sin(E47)
I48: sin(E48)
I49: sin(E49)
I50: sin(E50)
I51: sin(E51)
I52: sin(E52)
I53: sin(E53)
I54: sin(E54)
I55: sin(E55)
I56: sin(E56)
I57: sin(E57)
I58: sin(E58)
I59: sin(E59)
I60: sin(E60)
I61: sin(E61)
I62: sin(E62)
I63: sin(E63)
I64: sin(E64)
I65: sin(E65)
I66: sin(E66)
I67: sin(E67)
I68: sin(E68)
I69: sin(E69)
I70: sin(E70)
L_2: {I2, I3, I4, I5, I6, I7, I8, I9, I10, I11, I12, I13, I14, I15, I16, I17, I18, I19, I20, I21, I22, I23, I24, I25, I26, I27, I28, I29, I30, I31, I32, I33, I34, I35, I36, I37, I38, I39, I40, I41, I42, I43, I44, I45, I46, I47, I48, I49, I50, I51, I52, I53, I54, I55, I56, I57, I58, I59, I60, I61, I62, I63, I64, I65, I66, I67, I68, I69, I70}
P_2: (H3, I3)
P_3: (H4, I4)
P_4: (H5, I5)
P_5: (H6, I6)
P_6: (H7, I7)
P_7: (H8, I8)
P_8: (H9, I9)
P_9: (H10, I10)
P_{10}: (H11, I11)
P_{11}: (H12, I12)
P_{12}: (H13, I13)
P_{13}: (H14, I14)
P_{14}: (H15, I15)
P_{15}: (H16, I16)
P_{16}: (H17, I17)
P_{17}: (H18, I18)
P_{18}: (H19, I19)
P_{19}: (H20, I20)
P_{20}: (H21, I21)
P_{21}: (H22, I22)
P_{22}: (H23, I23)
P_{23}: (H24, I24)
P_{24}: (H25, I25)
P_{25}: (H26, I26)
P_{26}: (H27, I27)
P_{27}: (H28, I28)
P_{28}: (H29, I29)
P_{29}: (H30, I30)
P_{30}: (H31, I31)
P_{31}: (H32, I32)
P_{32}: (H33, I33)
P_{33}: (H34, I34)
P_{34}: (H35, I35)
P_{35}: (H36, I36)
P_{36}: (H37, I37)
P_{37}: (H38, I38)
P_{38}: (H39, I39)
P_{39}: (H40, I40)
P_{40}: (H41, I41)
P_{41}: (H42, I42)
P_{42}: (H43, I43)
P_{43}: (H44, I44)
P_{44}: (H45, I45)
P_{45}: (H46, I46)
P_{46}: (H47, I47)
P_{47}: (H48, I48)
P_{48}: (H49, I49)
P_{49}: (H50, I50)
P_{50}: (H51, I51)
P_{51}: (H52, I52)
P_{52}: (H53, I53)
P_{53}: (H54, I54)
P_{54}: (H55, I55)
P_{55}: (H56, I56)
P_{56}: (H57, I57)
P_{57}: (H58, I58)
P_{58}: (H59, I59)
P_{59}: (H60, I60)
P_{60}: (H61, I61)
P_{61}: (H62, I62)
P_{62}: (H63, I63)
P_{63}: (H64, I64)
P_{64}: (H65, I65)
P_{65}: (H66, I66)
P_{66}: (H67, I67)
P_{67}: (H68, I68)
P_{68}: (H69, I69)
P_{69}: (H70, I70)
k = 1 (slider from 1 to 150, step 1)
A: (cos(2.0 * 3.141592653589793 / n * (k * (k + 1.0) / 2.0 - 1.0)), sin(2.0 * 3.141592653589793 / n * (k * (k + 1.0) / 2.0 - 1.0)))
s: 1.1 + 0.5 * k / n
B: (s * cos(2.0 * 3.141592653589793 / n * (k * (k + 1.0) / 2.0 - 1.0)), s * sin(2.0 * 3.141592653589793 / n * (k * (k + 1.0) / 2.0 - 1.0)))
c: 1.0 * 1.0 x^(2.0) + 1.0 * 1.0 y^(2.0) = s^(2.0)
C = (0, 0)
D: (300.0 * x(A), 300.0 * y(A))
b = Segment(C, D)
a = true
d = true