the point isn't to prove that the triangle is a triangle it's to prove that the system of mathematics you made up actually works
Until you prove that you can't prove that the system you made up works.
Nobody is practically concerned with the "incompleteness" aspect of Gödel's theorems. The unprovable statements are so pathological/contrived that it doesn't appear to suggest any practical statement might be unprovable. Consistency is obviously more important. Sufficiently weak systems may also not be limited by the incompleteness theorems, i.e. they can be proved both complete and consistent.
You just reminded me of having to prove that math signs work and do what they do from basic axioms to integers and rational numbers using logical proofs... Damn that was interesting but SO tedious...
Well, at that level I think it's more to show you know how to prove it. You're working under the assumption the axioms of the system you've been told work.
that won't work for yoda, though. for him, there is no triangle. there's just doangle or donotangle.
How have I not heard this before 😆
I nearly failed geometry because I didn't understand what my instructor wanted from me.
Yes but what if one side is so slightly curved that it's invisible to the naked eye? Then your total angles would be 179.99 degrees and it's not a triangle.
Non-Euclidian horrors beyond comprehension
Commonly known as reality
But isn't a curve just many angles next to one another?
Yes, but infinitely many.
From a calculus perspective, you may be able to define it as infinitely many angles infinitely close to one another, but I don't think that'd be a particularly good definition.
Even philosophy 101 can give you a ton of reasons why looking at it just isn't enough
Especially Philosophy 101
How Can Triangles Be Real If Our Eyes Aren't Real?
"If we can't prove these two triangles are similar while not being congruent, the world is doomed."
"Oh my god. We need a 10th grader with at least a B-average, stat!"
LoL, actual.
I loved geometry. It made algebra make sense. Plus I had a really awesome geometry teacher. He looked like Shel Silverstein and was super pumped every day to teach math.
I loved geometry. It's the class where I first got experience programming. I just sat in class programming stuff on my calculator not really paying attention. I did fine in the class luckily.
Totally unrelated, but I (30 yo) recently realized I'm almost certainly ADHD. There definitely weren't any identifiable signs before that people should have noticed...
In one of my last CS classes, we did proofs and would use "by observation" for this kind of thing.
Equilateral triangle. All three sides are equal length and it has three interior angles that add up to exactly 180 degrees.
Are you telling me that "you can see this is a triangle" ??! You can see ?? How dear you say that!
