I would like to know if it is possible to construct a "spiral-esque" object from a piece of thin cardboard, like the type of stuff a cereal box is made from.
If it is possible, how would one do it? The reason I ask about cardboard, is that it could not be stretched, and I would like to know if a helicoid, auger, or similar such thing can be physically constructed without stretching or deforming the material.
I know that there are formulas for the helicoids that have to do with x, y , and z, but I don't know how that can be transferred to the "real world" and actually construct something physical. I would like to know how to construct something physical.
I don't know the proper names of any of this, so I will try to explain this the best I can. Consider a vertical auger or spiral that has a 6" diameter tube through the center, and the outside of the auger had a 24" diameter. If anyone would care to respond to this, they can decide the angle ( or any other of the dimensions ).
It seems to me that the inside edge of the auger' s "flight" - the actual material forming the spiral - could be represented by a triangle wrapped around the center tube, with the hypotenuse tracing the inside edge of the flight, the height of the triangle having to do with the angle, and the "opposite" end of the triangle being the circumference of the "tube" . Same thing about the outside edge of the flight and the "cylinder" of the outside of the auger .
It also seems to me that this should produce a circular pattern with the inside circumference being the hypotenuse of the triangle wrapped around the inside tube and the outside circumference being the hypotenuse of the triangle wrapped around the cylinder formed by the outside of the auger.
I have tried to construct something of this nature, but have never been able to accomplish it, and I can't see why not.
Could someone help me out... Like so many things, it seems so simple, but it apparently is not.... thanks
If it is possible, how would one do it? The reason I ask about cardboard, is that it could not be stretched, and I would like to know if a helicoid, auger, or similar such thing can be physically constructed without stretching or deforming the material.
I know that there are formulas for the helicoids that have to do with x, y , and z, but I don't know how that can be transferred to the "real world" and actually construct something physical. I would like to know how to construct something physical.
I don't know the proper names of any of this, so I will try to explain this the best I can. Consider a vertical auger or spiral that has a 6" diameter tube through the center, and the outside of the auger had a 24" diameter. If anyone would care to respond to this, they can decide the angle ( or any other of the dimensions ).
It seems to me that the inside edge of the auger' s "flight" - the actual material forming the spiral - could be represented by a triangle wrapped around the center tube, with the hypotenuse tracing the inside edge of the flight, the height of the triangle having to do with the angle, and the "opposite" end of the triangle being the circumference of the "tube" . Same thing about the outside edge of the flight and the "cylinder" of the outside of the auger .
It also seems to me that this should produce a circular pattern with the inside circumference being the hypotenuse of the triangle wrapped around the inside tube and the outside circumference being the hypotenuse of the triangle wrapped around the cylinder formed by the outside of the auger.
I have tried to construct something of this nature, but have never been able to accomplish it, and I can't see why not.
Could someone help me out... Like so many things, it seems so simple, but it apparently is not.... thanks