t en s

dist_{Tortue}

dist_{Coureur}

Achille et la tortue

Le curseur v_T commande la vitesse de la tortue

d_T est la courbe qui décrit la distance parcourue par la tortue en m: y =v_T*t + 1000

d_C est la courbe qui décrit la distance parcourue par le coureur en m: y =10*v_T*t 

I est le point commun à d_T et d_C: ses coordonnées dépendent de v_T

Les représentations sont faites à l'échelle 1/20 ème pour faciliter la lecture sur l'écran

Pour les positions

v_T = 1.4 (slider from 0.5 to 5, step 0.1)
d_T(x) = ((0.05 * v_T) * x) + 50
d_C(x) = ((0.5 * v_T) * x)
I = Intersect(d_C, d_T)
A2 = 0
A3: A2 + 1
A4: A3 + 1
A5: A4 + 1
A6: A5 + 1
A7: A6 + 1
A8: A7 + 1
A9: A8 + 1
A10: A9 + 1
A11: A10 + 1
A12: A11 + 1
A13: A12 + 1
A14: A13 + 1
A15: A14 + 1
A16: A15 + 1
A17: A16 + 1
A18: A17 + 1
A19: A18 + 1
A20: A19 + 1
A21: A20 + 1
A22: A21 + 1
A23: A22 + 1
A24: A23 + 1
A25: A24 + 1
B2: d_T(A2)
B3: d_T(A3)
B4: d_T(A4)
B5: d_T(A5)
B6: d_T(A6)
B7: d_T(A7)
B8: d_T(A8)
B9: d_T(A9)
B10: d_T(A10)
B11: d_T(A11)
B12: d_T(A12)
B13: d_T(A13)
B14: d_T(A14)
B15: d_T(A15)
B16: d_T(A16)
B17: d_T(A17)
B18: d_T(A18)
B19: d_T(A19)
B20: d_T(A20)
B21: d_T(A21)
B22: d_T(A22)
B23: d_T(A23)
B24: d_T(A24)
B25: d_T(A25)
C2: d_C(A2)
C3: d_C(A3)
C4: d_C(A4)
C5: d_C(A5)
C6: d_C(A6)
C7: d_C(A7)
C8: d_C(A8)
C9: d_C(A9)
C10: d_C(A10)
C11: d_C(A11)
C12: d_C(A12)
C13: d_C(A13)
C14: d_C(A14)
C15: d_C(A15)
C16: d_C(A16)
C17: d_C(A17)
C18: d_C(A18)
C19: d_C(A19)
C20: d_C(A20)
C21: d_C(A21)
C22: d_C(A22)
C23: d_C(A23)
C24: d_C(A24)
C25: d_C(A25)
A26: A25 + 1
A27: A26 + 1
A28: A27 + 1
A29: A28 + 1
A30: A29 + 1
A31: A30 + 1
A32: A31 + 1
A33: A32 + 1
A34: A33 + 1
A35: A34 + 1
A36: A35 + 1
A37: A36 + 1
A38: A37 + 1
A39: A38 + 1
A40: A39 + 1
A41: A40 + 1
A42: A41 + 1
A43: A42 + 1
A44: A43 + 1
A45: A44 + 1
A46: A45 + 1
A47: A46 + 1
A48: A47 + 1
A49: A48 + 1
A50: A49 + 1
A51: A50 + 1
A52: A51 + 1
A53: A52 + 1
A54: A53 + 1
A55: A54 + 1
A56: A55 + 1
A57: A56 + 1
A58: A57 + 1
A59: A58 + 1
A60: A59 + 1
A61: A60 + 1
A62: A61 + 1
A63: A62 + 1
A64: A63 + 1
A65: A64 + 1
A66: A65 + 1
A67: A66 + 1
A68: A67 + 1
A69: A68 + 1
B26: d_T(A26)
B27: d_T(A27)
B28: d_T(A28)
B29: d_T(A29)
B30: d_T(A30)
B31: d_T(A31)
B32: d_T(A32)
B33: d_T(A33)
B34: d_T(A34)
B35: d_T(A35)
B36: d_T(A36)
B37: d_T(A37)
B38: d_T(A38)
B39: d_T(A39)
B40: d_T(A40)
B41: d_T(A41)
B42: d_T(A42)
B43: d_T(A43)
B44: d_T(A44)
B45: d_T(A45)
B46: d_T(A46)
B47: d_T(A47)
B48: d_T(A48)
B49: d_T(A49)
B50: d_T(A50)
B51: d_T(A51)
B52: d_T(A52)
B53: d_T(A53)
B54: d_T(A54)
B55: d_T(A55)
B56: d_T(A56)
B57: d_T(A57)
B58: d_T(A58)
B59: d_T(A59)
B60: d_T(A60)
B61: d_T(A61)
B62: d_T(A62)
B63: d_T(A63)
B64: d_T(A64)
B65: d_T(A65)
B66: d_T(A66)
B67: d_T(A67)
B68: d_T(A68)
B69: d_T(A69)
C26: d_C(A26)
C27: d_C(A27)
C28: d_C(A28)
C29: d_C(A29)
C30: d_C(A30)
C31: d_C(A31)
C32: d_C(A32)
C33: d_C(A33)
C34: d_C(A34)
C35: d_C(A35)
C36: d_C(A36)
C37: d_C(A37)
C38: d_C(A38)
C39: d_C(A39)
C40: d_C(A40)
C41: d_C(A41)
C42: d_C(A42)
C43: d_C(A43)
C44: d_C(A44)
C45: d_C(A45)
C46: d_C(A46)
C47: d_C(A47)
C48: d_C(A48)
C49: d_C(A49)
C50: d_C(A50)
C51: d_C(A51)
C52: d_C(A52)
C53: d_C(A53)
C54: d_C(A54)
C55: d_C(A55)
C56: d_C(A56)
C57: d_C(A57)
C58: d_C(A58)
C59: d_C(A59)
C60: d_C(A60)
C61: d_C(A61)
C62: d_C(A62)
C63: d_C(A63)
C64: d_C(A64)
C65: d_C(A65)
C66: d_C(A66)
C67: d_C(A67)
C68: d_C(A68)
C69: d_C(A69)
A70: A69 + 1
A71: A70 + 1
A72: A71 + 1
A73: A72 + 1
A74: A73 + 1
A75: A74 + 1
A76: A75 + 1
A77: A76 + 1
A78: A77 + 1
A79: A78 + 1
A80: A79 + 1
A81: A80 + 1
A82: A81 + 1
A83: A82 + 1
A84: A83 + 1
A85: A84 + 1
A86: A85 + 1
A87: A86 + 1
A88: A87 + 1
A89: A88 + 1
A90: A89 + 1
A91: A90 + 1
A92: A91 + 1
A93: A92 + 1
A94: A93 + 1
A95: A94 + 1
A96: A95 + 1
A97: A96 + 1
A98: A97 + 1
A99: A98 + 1
A100: A99 + 1
A101: A100 + 1
A102: A101 + 1
A103: A102 + 1
B70: d_T(A70)
B71: d_T(A71)
B72: d_T(A72)
B73: d_T(A73)
B74: d_T(A74)
B75: d_T(A75)
B76: d_T(A76)
B77: d_T(A77)
B78: d_T(A78)
B79: d_T(A79)
B80: d_T(A80)
B81: d_T(A81)
B82: d_T(A82)
B83: d_T(A83)
B84: d_T(A84)
B85: d_T(A85)
B86: d_T(A86)
B87: d_T(A87)
B88: d_T(A88)
B89: d_T(A89)
B90: d_T(A90)
B91: d_T(A91)
B92: d_T(A92)
B93: d_T(A93)
B94: d_T(A94)
B95: d_T(A95)
B96: d_T(A96)
B97: d_T(A97)
B98: d_T(A98)
B99: d_T(A99)
B100: d_T(A100)
B101: d_T(A101)
B102: d_T(A102)
B103: d_T(A103)
C70: d_C(A70)
C71: d_C(A71)
C72: d_C(A72)
C73: d_C(A73)
C74: d_C(A74)
C75: d_C(A75)
C76: d_C(A76)
C77: d_C(A77)
C78: d_C(A78)
C79: d_C(A79)
C80: d_C(A80)
C81: d_C(A81)
C82: d_C(A82)
C83: d_C(A83)
C84: d_C(A84)
C85: d_C(A85)
C86: d_C(A86)
C87: d_C(A87)
C88: d_C(A88)
C89: d_C(A89)
C90: d_C(A90)
C91: d_C(A91)
C92: d_C(A92)
C93: d_C(A93)
C94: d_C(A94)
C95: d_C(A95)
C96: d_C(A96)
C97: d_C(A97)
C98: d_C(A98)
C99: d_C(A99)
C100: d_C(A100)
C101: d_C(A101)
C102: d_C(A102)
C103: d_C(A103)
a: x(I)
b: y(I)
texte1: "I\left(" + (LaTeX[a]) + "," + (LaTeX[b]) + "  \right) "
p = 55 (slider from 0 to 240, step 1)
T: (p, d_T(p))
C: (p, d_C(p))
J: (x(T) - 20, d_T(x(T) - 20))
A = (248.7673473793737, 88)
B = (259.0756468569826, 88)
D = (225.5687079052331, 158.4)
K: (x(C) - 19, d_C(x(C) - 19))
R: (p + 8, y(C) - 12)