Paths on a surface 
Product (app)
[cylinder - studying the surface]
Instructions
In the figure we have represented two cylinders. The first has two paths on its surface and the second illustrates the product path of these two paths.
Next to the first cylinder there are two bars with which we can control the points \(\mbox{rot }x\) and \(\mbox{rot }z\) to rotate the surfaces, allowing us to observe the paths from different perspectives.
In the middle there are two grids with the latitude and longitude of the points defining the paths over the cylinders. The one on the top corresponds to the first cylinder and the one at the bottom corresponds to the second. By activating the option Change scale, located on the horizontal bar between the two grids, a point appears on the first grid which we can move horizontally allowing us to zoom in or out over the grid.
We can also manipulate the two initial paths. For this click and grag the points signaled on the first grid, to control the latitude and longitude of the points on the first cylinder. The product path will then be automatically adapted to the manipulated paths.
