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From almost everywhere, a straight line is linear defined as $C(t)=P_0+tV_0$. And I am wonder what does a straight line but is not linear by the means of the parameter $t$. For example $C(t)=P_0+tV_0+t^2V_0+t^3V_0$.

So would it means a straight line is not really needed to be linear? Would that be the case that the definition for a straight line is: For any two points $p=C(a),q=C(b)$,

(1):$C'(a)\times C'(b)=0$

(2):$C'(a)\bullet C'(b)>0$

  • 1
    A function of the form $f(x)=a_0+a_1x +a_2 x^2$ is already called "parabola". Why should we call it "nonlinear straight line of order 2"?2012-08-30
  • 5
    This is close to incomprehensible. Can you work a little more to explain what your question is?2012-08-30

2 Answers 2