I have never seen a rectangular or triangular shaped mole. Is there any reason for why moles are roughly circular in shape?
Note: I am not stating that moles are in general circular in shape because there are no statistical studies to conclusively state so. This answer is mostly about default circular shape of cell colonies.
Moles (melanocytic naevi) are not strictly circular but generally have have a rough circular shape. Moles can have irregular shapes too and you can easily check that by a simple google image search.
The exact causes and mechanisms of mole formation are not known but the somewhat circular shape can be explained by a simple spatiotemporal model of growth.
Moles are formed because of pigmented cells called melanocytes (which contain the dark pigment melanin). A mole would grow when a very small population of these pigmented cells divide and expand. In a 2D surface, cells would continue to divide and expand along both the axis at an equal rate, if there are no specific constraints. Since the expansion is same along both the axes, you get a roughly circular shape. For similar reasons, bacterial colonies (on petri plates) are also more or less circular. Note that there are stochastic factors that would contribute to irregularity.
Triangles and rectangles are very specific geometries. There need to be some constraints that would limit the cell growth to adopt these geometries. So the default shape would be mostly circular.
Naevi do not have to be circular in shape. In fact, they come in a wide variety of shapes and colors.
There are various types of naevi:
- Congenital naevi are present from birth and occur in about one in 100 people. They may be more likely to develop into melanoma (cancer) than nevi appearing after birth (WebMD).
- Acquired naevi develop later in life (Dermatology Net NZ);
- Dysplastic naevi are typically larger than average and more irregular in shape. They tend to have uneven color with dark brown centers and lighter, uneven edges. These nevi are more likely to become melanomas (malignant skin cancer) (WebMD).
- Dysplastic naevi may turn into melanomas (NIH), but melanomas are outside the scope of this question.
Now let's turn to your question - not all naevi are circular. Below I have illustrated just a mere tiny handful of the wide gamut of shapes found among different types of naevi. In fact, naevi come in a wide variety of shapes and colors (source: Dermatology Net NZ):
In fact, naevi occur in more extreme forms too:
source: No Hands but Ours