In addition to using multiples of the 45 degree angle, the Mangbetu also applied the four basic geometric transformations to their designs. Reflection acts like a mirror, flipping the image across a line. Translation slides the image to a new location. Scaling changes the size of the image. And rotation changes the angle of the image.
In mathematics, we can create an image like this by reflection. In this case it is not a perfect reflection. The images do not mirror each other exactly. But it is close enough to see that the artist is making use of the reflection idea. In the case of this double pot, we would say that the image is reflected around the Y axis. What would it look like if it had been reflected around the X axis?
Translation simply slides a shape over by a given amount. Here we see the handle of an ivory spoon. We can model this pattern as the translation of 7 copies of a sort of hat shape.
Dilation let us make images larger or smaller. Here we see a spoon handle that has a repeated pattern of loops, a small copy at bottom and a larger copy at top. We can think of the bottom as a copy of the top, dilated by less than 100%. What would this look like if the bottom was dilated by more than 100%?
Here we see a sort of “crook” shape, like a backwards question mark. It has been copied four times, and each time the copy has been rotated by 90 degrees. That makes each crook the same distance apart. If you had 5 copies, and you wanted each of the 5 to be the same distance apart, how many degrees would you want to rotate each copy?