Definitions of Mutuality:[br][br]Please read the description below, copied from [url=https://csdt.org/culture/adinkra/geometry.html]https://csdt.org/culture/adinkra/geometry.html[/url] .[br][br][br]Is There an African Geometry That Is Not Part of Europe’s?[br][br]One of the fascinating questions we can ask in ethnomathematics: are there some math ideas outside of those created in Europe?[br][br]Consider the adinkra symbol Boa Me Na Me Mmoa Wo, which translates to "Help me and let me help you". [br][br]The upper triangle is missing a square, but has an extra circle. The lower triangle is missing a circle, but has an extra square. Each has what the other needs to complete themselves. As a social symbol, the meaning is clear: mutual aid. But how do we express that relation in math? [br][br]At first the word “symmetry” comes to mind, but reflection symmetry would require that each side is a mirror image; exactly the same. Here they are complements of each other, not reflections.[br][br][br]Let's call this new math property “mutuality”. Perhaps if colonialism never happened, Africans would have created a collection of proofs and theorems based on mutuality, just as Europe did for symmetry. We could start with a definition: two figures are said to be “mutuals” if their parts can be exchanged to create two completed wholes. There are still some details to work out (how do we define “parts”? or “completed”?). But assuming those challenges can be solved, it might open up new ways of thinking.[br][br]Can mutuals be in sets of 3 rather than pairs? In higher numbers? Could they be fractional or statistical (“figure A is an 82% mutual to figure B”)? What are the real-world applications? For example, when medical researchers study molecules, they often describe it as a “lock and key model”. We may know what a particular virus looks like, but not the shape of the molecule that can attach to its surface. Perhaps developing new forms of math based on “mutuals” could create new opportunities for medical research.