# vector Tangent on sequence of curves

jean-pierre Ortolland shared this question 4 years ago

Hi

I would like the vector tangent to the first pink curve segment (pf_n at the point P to be tangent to the other curve segments as well when the point P is running (P animation) the other segment of curves .

pf_n = Sequence(Curve(t + 2n a, cosh(asinh(1)) - cosh(t), t, -a, a), n, 0, 5, 1)

f'_n = Sequence(Curve(t + 2n a, -sinh(t), t, -a, a), n, 0, 5, 1)

qf_n = Sequence(Curve(t + 2n a, cosh(asinh(1)) - cosh(t) + L / (2*cos(atan(sinh(t)))), t, -a, a), n, 0, 5, 1)

u_x = Vector((0, 0), (1, 0))

u_y = Vector((0, 0), (0, 1))

u = Vector(P, u_x *(x(P)+cos(atan(-sinh(x(P))))) + u_y(y(P)+ sin(atan(-sinh(x(P))))))

Hello jean-pierre!

I hope that helps you.

I think one problem is the different periodicity of the trigonometric functions.

So I created only a factor "c" that makes sure that the "first correct vector" will be chosen every time.

Kind regards

mire2

1

Hello jean-pierre!

I hope that helps you.

I think one problem is the different periodicity of the trigonometric functions.

So I created only a factor "c" that makes sure that the "first correct vector" will be chosen every time.

Kind regards

mire2

1

Thank you very much Mire2,

that's exactly what I wanted to do. I had spent (without success) 1 hour trying to do , what you did successfully ;-).

1

Hi

the final result:

this animation is the result of a given problem in the course

EDX.org

MITx: 18.01.3x

Calculus 1C: Coordinate Systems and Infinite Series

I love that course

`pf_n = Sequence(Curve(t + 2n a, cosh(asinh(1)) - cosh(t), t, -a, a), n, 0, 5, 1)f'_n = Sequence(Curve(t + 2n a, -sinh(t), t, -a, a), n, 0, 5, 1)qf_n = Sequence(Curve(t + 2n a, cosh(asinh(1)) - cosh(t) + L / (2*cos(atan(sinh(t)))), t, -a, a), n, 0, 5, 1)u_x = Vector((0, 0), (1, 0))u_y = Vector((0, 0), (0, 1))########################## my first version of the line below did not work correctly (worked only on the first curve segment ) # u = Vector(P, u_x *(x(P)+cos(atan(-sinh(x(P))))) + u_y(y(P)+ sin(atan(-sinh(x(P))))))# solution by Mire2# this trick was given by mire2 on the Geogebra forum website.# https://help.geogebra.org/t...) / a) / 2), ceil(x(P) / a), ceil(x(P) / a) - 1)u = Vector(P, u_x (x(P) + cos(atan(-sinh(x(P) - c a)))) + u_y (y(P) + sin(atan(-sinh(x(P) - c a)))))α = Angle(u_x, u)C=if(α>0,Point(P, u*(sin(α))*qp),Point(P, -u*(sin(α))*qp ) )D=Point(C, u*(L/2) ) E=Point(C, -u*(L/2) )u_p=PerpendicularVector( u )F=Point(E, L*u_p )G=Point(D, L*u_p )Polygon(D, E, F,G)########################## script in button StartAnimate#StartAnimation( P,true)# script in button StopAnimate#StartAnimation( P,false)`