# Jon Letendre

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Jon Letendre

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• ### turkeyfoot

Knowing now you mean NOT the rolling wheel, the line of tangency you seek is the line that intersects your point and touches the end point of the cycloid being drawn.

Merlin, we are all,discussing the topic of the thread that you started. We're not much discussing cycloids. My answer to you, that there is only one line of tangency is correct given I thought you were talking about a rolling wheel, which is, again, the topic of the thread and current discussion,

A figment of my imagination. You feel compelled to talk about me. You could skip that sentence, your geometric point is made by the following sentences. But you can't keep personality out of it, because you don't seem to have the discipline. One of your many character flaws. Shall we discuss them at length? Or geometry? I'll have your answer soon, I suppose. Baal is on YOUR side, not mine, you say. I'm glad you have something important to you going. Maybe you're right, but I don't care who else does or does not see truth ,I'll just keep aiming for truth and ignore personalities. You do whatever seems good for you. You sure do like making bets.

Yes.

Yes, thank you, that is correct, Ellen. Resolving the paradox is as simple as grasping those two sentences. Amazing as it seems, Merlin does not yet grasp them.

It doesn't have one. Only the point, the one and only point, the one on the outside circumference of a rolling wheel, the one point currently in contact with the road, has a tangent line. And the tangent line is the road. A moment later, that point's neighbor is in contact with the road and now this neighboring point is the point of tangency, meaning the point where wheel touches road.

Yes, agreed.
8. ## Donald Trump

Nicely stated.

That is correct, so long as by "rim" you mean the rubber on the road. Both Merlin and I have used "rim" to mean a circle on the wheel having a radius shorter than the wheel. The rim is the round steel part that holds a rubber tire,

"Goes along for the ride" sounds to me like you almost have it. Aristotle's setup is that it does not "go along for a ride" but rather that it rolls honestly, in non-slipping contact with its imaginary road. Only by accepting that lie of Aristotle's can any apparent paradox arise.

Hit the button at middle bottom for replays. Aristotle's setup has one imagine that the black hatch marks will stay in non-slippage contact with each other, but that is not so. The inner, green "wheel" slips, skids over its imaginary road.