Why is this paper stack not flat? So we have lots of paper for photocopy.  They come in a bundle. What I have noticed is that There are sine curves or maybe cosine when I saw them from the side. That's Look like:

Is there any explanation for these curves?
 A: This is an artifact of the so-called conversion process, by which a continuous ribbon of paper hundreds or thousands of feet long and four feet wide on a huge roll is slit to width and then sheared to length and the cut sheets then stacked and wrapped into packages for shipment.
Since the initial spooling process by which the master roll is made occurs when the paper is still hot from the drying process and occurs under significant tension, the paper takes a set on the roll and the sheets cut from it exhibit "curl" after being cut.
That curl becomes cyclic when the master roll is left to rest on a concrete floor and deforms slightly under its own weight as it cools. The net effect is small for sheets that originate in the outermost layers of the roll (which is typically 4 feet in diameter at full size) and becomes progressively of shorter period by the time you get towards the end of the roll (which is wrapped onto a core that is only ~4 inches in diameter).
If the package contains a mix of sheets cut from a variety of rolls, then some of the sheets will have cyclic curl and others will be relatively flat in comparison.
Inkjet printers re-humidify the paper, which greatly magnifies the curl- in fact, paper sheets which start out almost perfectly flat will curl like crazy because the water-based ink is applied to only one side of the sheet, which then tends to roll itself up into a tube when the residual curl coincides with the wetter side of the sheet. In injket printing circles, this is known as the "diploma effect".
A: Let's assume that they were originally perfectly stacked. If you apply some nonuniform external force to the whole stack, some sheets might slightly slide around (which is true in this case, as visible in the photo; note sides of the stack). This can be viewed as a deformation of the whole stack. Due to being stacked, upper sheets will press down on the lower layers, thus creating  friction, which ultimately prevents the whole stack to reverse the deformation completely.
To compensate these inner stresses, paper can either compress or decompress in its own plane or bend in the third dimension. Apparently paper prefers to bend more than to stretch or compress.
(By the way, sine and cosine is basically the same, just shifted by $\pi /2$ )
A: I notice one tendency. Biggest sheets distortion is in the bottom pages. If you go upwards, you'll see that distortions will become smaller and smaller and paper will be getting more straight and almost plane-like at the top. This seems a little-bit counter-intuitive, because bottom sheets experiences highest load from paper mass above, still they warped most ! This suggests one possible explanation  -  heat flow from some source below paper tower through paper stack dissipating vertically upon reaching top sheets. This explains why  bottom sheets are mostly warped - they get highest heat amount. It can be seen in picture that there are some wires in left side of paper tower and some device too (probably copier or printer). I don't know if it is functioning or not, but if it is - printers certainly produce a lot of heat, because they need to physically heat a dye particles. This adds to the same idea.
