For this discussion to begin, you all must know what is a "frustrum of a cone".. It almost looks like a cone whose apex has been cut out.. and now, it looks like a 'cylinder'whose one base end is small and the other is big..

It all happened when i unknowingly hit a steel glass (the one used for drinking, which is in the shape of cone's frustrum), which then went on rolling on the floor.... But wait.. i noticed something keen.. the rolling glass didnt go straight, but it rolls in an arc like fashion... And i realized, that this motion, if made to complete, it forms a circle..!! the arc motion is extrapolated to form a circle... CIRCLE !! It again makes me go mad and think deep..

This happened some 4 years before, after noticing which, i formulated a physical theory and worked out some mathematical equations and values, which i tested with a limited number of observations, and proved correct myself.. but unfortunately, my papers have missed... and i didnt care it for long time because i've been forced to join medicine by my parents, despite my aim to become a theoretical physicist... Now i feel that however small a discovery, it should be brought out, to be tested, and be published.. And i feel bad for missing those papers.. Anyway, i could reconstruct it, but takes a while.. and hope i wil do it.. as for now, i would explain how that phenomenon happens.... the mathematical part, which i had to reconstruct, and hence wont deal with it..

In a cone's frustrum, it has two bases, both in a circular shape, but one circular base is smaller than the other.. (better you imagine its picture)

And here in this case, these two circular bases are attached as a part of cone's frustrum and hence these two circular bases should roll(on the floor) simultaneously, rather than independently...

Consider two SEPARATE circular wheels, one larger and the other smaller. The larger wheel, in one complete rotation, covers a larger distance (on the road). but the smaller wheel, in one complete rotation, covers only a smaller distance. Inorder to reach the distance covered by one rotation of larger wheel, the smaller wheel has to perform multiple rotations (the number of rotations required depend upon the size variation between the two wheels).

But in an object with the shape of cone's frustrum, these two circular bases(one big, the other small), are continuous and attached with each other, and hence cannot perform different number of rotations, as in the previous wheel experiment.. Hence, when this object is rolled on a flat surface, its two circular bases have to face a 'MUST' obey condition:

1) They both should perform same number of rotations and should move simultaneously.

By this condition, it results that 'larger base' of the frustrum would cover a larger distance and the 'smaller base' would cover a smaller distance..............., but how an 'object (frustrum)' could cover two different distances simulataneously.

The answer lies in CIRCLE.. This object rolls on a circular path. But Why should this object choose a circular path??

In this circular path, there are two concentric circles (inner & outer)...!! The 'smaller base' would cast a smaller circle(inner circle- smaller distance), and the 'larger base' at the other end, would cast a larger circle(outer circle- larger distance). these two happen simultaneoulsy, and the whole object also moves along a circular path.. By doing so, the conditions are fulfilled.

* both the 'bases' perform equal number of rotations

* larger base covers a larger distance, and smaller base covers a smaller distance

You can't fulfill these conditions in any other motion, but only in a circular path..!!

Based on the difference in size of its two bases, the object may cast a smaller or larger circular path..

If the difference is too high, the object would cast a smaller circular path.. if the difference is small, it would cast a larger circle.. and if the difference is too small and insignificant, then you would get a very very large circle, which on short course, appears to be a straight line..

As the difference approaches zero, the trace approaches to become a straight line... And if there is no difference, then it would cast a straight line..!!

You could see a cylinder roll along a straight path, it is because the two bases are equal sized(difference=0)... But if there is difference in size between the bases, it should go along a circular path, however small the difference may be...

Mathematical formulations of the theory needs to be reconstructed.... hope would post them in near future.....

*******************your suggestions and comments are welcome******************