3133-Math 2500.sagews

Math 2500

Niles Johnson, University of Georgia

var('x,y')
f(x,y) = x^2 - y^2
plot3d(f(x,y),(x,-1,1),(y,-1,1))

var('t')

def tangent_line(P,v=vector((1,0))):
    return P + t*v

P = vector((1,1,0))
v = vector((1,3,0))/sqrt(10)
tangent_line(P,v)

(1/10*sqrt(10)*t + 1, 3/10*sqrt(10)*t + 1, 0)

var('s,t')
r = tangent_line(P,v)
def curve(t):
    return r(t=t) + vector((0,0,f(*r(t=t))))
graph = parametric_plot(r + vector((0,0,s)), (t,-3,1), (s,-1,1), color='yellow', opacity=.7)+ \
    plot3d(f(x,y),(x,-1,1),(y,-1,1)) + \
    parametric_plot(r, (t,-3,1), thickness=3, color='darkgreen') + \
    parametric_plot(curve(t),(t,-2.2,.3), thickness = 3, color='violet')
    
graph.show(spin=True)

graph.rotate((0,0,1),.05*pi).show(viewer='tachyon')