Geometry Invented or Discovered?

Question

Back it up.

Lol back it up means provide evidence or at least good reason to believe

Answer 1

Nice question. The answer is most likely both. Without any prior experience, one would not be able to formulate the axioms of geometry. But, since mathematics is a formal science, not a natural science, once these axioms are in place, whether a position is valid or not is determined only by these axioms, with no external recourse. Hence, this supports the point of view that it is "invented". Since various geometries exist outside of Euclid's, meaning they prescribe to different axioms, (E.g. Reimenian) invented seems appropriate, but to take this stance, means that any perception or explanation of phenomena is by its nature, "invented". Michael M's terse statement below says it best.

Answer 2

I would say invented, but it depends on how you define geometry.
If you define geometry as the actual relationships in nature, then the answer is "discovered." Personally, I define math (or in this case, geometry) as a language/system created to describe quantifiable relationships that exist in nature. While the relationships themselves have always existed and were therefore discovered, math as a language was invented. Numbers themselves and formulas have not always existed, only the things that they describe.

Answer 3

Mathematics is discovered. Consciousness would not exist without thought, and thought would not exist without a symbolic code. It is those symbols that each human converts into language to communicate with others. Mathematical concepts are part of that symbolic code. Humans were adding and subtracting before numbers were invented. In my view, mathematics were created because the human operation is rudimentary and fallible, and we get reliable results by formalizing operations. In that aspect, we discovered mathematics. That said, mathematics is now much more than adding and subtracting. For centuries, we have been elaborating and developing operations. In that aspect, we are inventing mathematics.

Answer 4

Geometry has always existed, so it obviously was not invented. Chances are there are still some areas of geometry yet to be understood or discovered yet.

Answer 5

It was discovered. I don't know what you mean by "back it up". That sounds like some kind of demand rather than a request. Geometry always existed. There have been many mathematicians who have discovered geometrical relationships such as righ triangles and circles.

Answer 6

We invented a system of rules for looking at what we have discovered. It is a way we have discovered works on some level to explain the world.

Answer 7

When Was Geometry Invented