Can a Thin Line Slope to 0? Exploring an Intriguing Question

[adjacent]

Look at the image!As the box gets thinner,the slope of the box decreases.and I think, if the thinning is constant i.e.(It gets thinner by dividing it's width each step),the rate of sloping decreases.Is this right?
If the above is correct,The thinnest line should be able to slope to 0.
Am I right?It's so confusing.

 

[D H]

There's no way to answer your question as you haven't given the relation between the slope and this thinning, or even what you mean by "thinning".

 

[mfb]

the rate of sloping decreases

How is that "rate of sloping" defined?
If you fit boxes into that slit, and halve the height of the boxes in each step, the angular difference between two steps will become smaller.
If that slit has no height itself, the limit of zero height will have an angle of zero, indeed.

 

[adjacent]

There's no way to answer your question as you haven't given the relation between the slope and this thinning, or even what you mean by "thinning".

What relation?I mean thinning as the width of the box decreasing.

How is that "rate of sloping" defined?
If you fit boxes into that slit, and halve the height of the boxes in each step, the angular difference between two steps will become smaller.
If that slit has no height itself, the limit of zero height will have an angle of zero, indeed.

Sorry it's rate of decreasing angle.
But if even if we keep on dividing the width by two,you can't make the width zero.So the angle cannot reach zero.My question is can we divide it infinitely and is the "rate of decreasing angle" decreasing?

 

[D H]

You have some relation in mind between width, angle, and step number. Until you tell us what those relations are there is no way to answer your questions. We can't read your mind!

 

[mfb]

You have some relation in mind between width, angle, and step number. Until you tell us what those relations are there is no way to answer your questions. We can't read your mind!

See the slit in the image. I think the box is supposed to fit into that.

Sorry it's rate of decreasing angle.
But if even if we keep on dividing the width by two,you can't make the width zero.So the angle cannot reach zero.My question is can we divide it infinitely and is the "rate of decreasing angle" decreasing?

See the middle part of my previous answer.

 

[D H]

See the slit in the image. I think the box is supposed to fit into that.

You did a better job of reading adjacent's mind than did I. Even with what you said, that graphic still doesn't communicate one thing to me.

 

[Integral]

Here is a analysis of a slab with thickness h, in a slot length L, and depth h and τ is the angle between the slab and the slot.

Hope my drawing is readable, just a pencil sketch.

If we keep the L, the length of the slot much bigger then then depth of the slot and thickness of the slab we get a linear relationship:

τ= h/Q + d/Q

If we hold d constant, then the angle changes linearly with slope 1/Q and intercept d/Q. That means that if h=0 τ=d/q again this is with the assumption that L >> h and d

 

[adjacent]

Now you have read my mind integral!Thank you.You are so intelligent

 

[Integral]

Thanks, but I think persistent is a better description. Note that the drawing was the key. I recorded the known quantities then examined the relationships until the key angles became clear. In general a good drawing is key to a solution.