What u think?
well it’s obvious what the real answer is, so i picked the fun answer.
droppin’ science like Galileo dropped the orange.
What the fuck does non-euclidean geometry even entail? Like on a curved plane or something? It always seemed like “why do we even have this”
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I tried that a few years ago and didn’t get anything out of it. Maybe I’ll try again.
Non-Euclidean geometry rose out of the attempt to prove the converse of Euclid’s 5th postulate. The postulate said that if two lines are cut by a transversal so that the sum of the interior angles on one sider was less than 180 deg, the lines would intersect on that side. The converse of the statement leads to the idea that if the sum of the two angles is equal to 180, then the lines do not intersect anywhere. This leads to Playfair’s axiom that given a point and a line, exactly one line can be drawn through the point that is parallel to the given line. But this cannot be proven using Euclidean geometry and is too complex to be accepted as a postulate (that doesn’t need a proof)
Basically, Euclid assumed that parallel lines existed without proving that they did. By attempting to prove this by contradiction (eliminating all other possibilities), mathematitions stumbled upon hyperbolic and spherical geometries which are based on curved spaces.
The fact that Euclidean geometry (sometimes called Plane Geometry) does not fully describe reality is in front of our eyes every day. The fact that parallel train tracks seem to converge at some point in the distance does not hold with Euclids postulates. In fact, as the lines move into the distance, they aren’t even straight. They appear to be straight because we are so small compared to space we live within. They actually move closer at a faster rate when they are near to us and at a slower rate as they move into the distance, forming a hyperbola. We dismiss this as a trick of binocular visions instead of a glimpse into the possibility that we live within a curved space, not a flat one.
Euclidean geometry seems to describe things very well on a small scale. We believe that we can create two lines on the earth that are straight and parallel even though being “on the earth” (on a sphere), “straight” and “parallel” are all mutually exclusive terms in sperical geometry. We’re just too small to see it.
It is generally accepted that the ability to draw one line parallel to another is impossible to prove using Euclid’s axioms and postulates.
Goddamn geometry spam.
Jacques Cousteau could never get this low.
My brain just imploded from reading that mess
basically, two parallel lines will intersect eventually.
That’s some real conversation for your ass.
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I’m cherry bombin’ shits… BOOM!
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[quote=“Critical Jeff”]basically, two parallel lines will intersect eventually.
[/quote] well in that case I’ll stay on track and see what happens
So the car didn’t actually cut me off, it’s just that our parallel courses intersected. Ah ha!
I’m still waiting for someone to call me out. I just pulled that shit out of my ass from when I took Non-Euclidean Geom. in university 6 years ago. But, yeah. My 11th grade class didn’t like it too much when I explained it to them either.
I think you’re saying something here.