I don’t remember all my geometric rules I guess, but can an arc, intersecting a line, ever truly be a right angle? At no possible length of segment along that arc can you draw a line that’s perpendicular to the first.
Wake up babe new shape just dropped
Submitted 3 weeks ago by Gork@sopuli.xyz to science_memes@mander.xyz
https://sopuli.xyz/pictrs/image/557defa5-96e9-4263-97b8-1db19d831456.webp
Comments
credo@lemmy.world 3 weeks ago
filcuk@lemmy.zip 3 weeks ago
An infinitely small segment of the arc can be.
Geometrically there isn’t a problem. If you draw a line from that point to the center of the arc, it will make it clearer.credo@lemmy.world 3 weeks ago
I guess if we define it as a calculus problem, I can see the point…
I didn’t mean to pun but there it is and I’m leaving it. Any way, there is no infinitely small section that’s perpendicular. Only the tangent at a single (infinitely small) point along a smooth curve, as we approach for either direction. Maybe that’s still called perpendicular.
pooberbee@lemmy.ml 3 weeks ago
A right angle exists between the radius of the circle and the line tangent to the circle at the point that the radial line intersects it. So we can say the radius forms a right angle with the circle at that point because the slope of the curve is equal to that of the tangent line at that point.
traches@sh.itjust.works 3 weeks ago
but they aren’t parallel
neukenindekeuken@sh.itjust.works 3 weeks ago
And the right angles are supposed to be inside, not 2 out 2 in
wolframhydroxide@sh.itjust.works 2 weeks ago
I think that, in order to have this be a projection of a square, the space between the interior right angles of the space from which it was projected would have to be not just curved, but also twisted, like a Möbius strip, such that a person “walking” the square and starting from the rightmost angle down and to the left would start walking as if they were on your screen (their head coming out away from the screen), but then they would need to have their perspective twist so that they are now walking on the “underside” of the figure (their head now pointing into your phone). This would allow them to perceive the two “external” turns as “internal” turns, as well.
redsand@lemmy.dbzer0.com 3 weeks ago
They could be in some n-dimensional spaces
cRazi_man@europe.pub 3 weeks ago
“That’s …like…just your perspective, man”
agamemnonymous@sh.itjust.works 3 weeks ago
You could just use polar coordinates
TheFogan@programming.dev 3 weeks ago
Going off webster… it looks like this really is only stretching the lines to fit one adjective
deikoepfiges_dreirad@lemmy.zip 3 weeks ago
Those are not 4 right angles, but 2 right angles and 2 angles of 270 degrees
psx_crab@lemmy.zip 3 weeks ago
So 2 right angle and two wrong angle. Got it.
PlutoniumAcid@lemmy.world 3 weeks ago
Two wrongs don’t make a right, but three lefts will.
BuboScandiacus@mander.xyz 3 weeks ago
A squary is a polygon
logicbomb@lemmy.world 3 weeks ago
Yeah, that pretty much sums it up. Wikipedia calls a square a “regular quadrilateral,” which seems like a decent enough definition.
Today I learned that when you make up your own inadequate definition, then it’s easy to match the definition with something inadequate.
Angry_Autist@lemmy.world 3 weeks ago
It wasn’t funny when Diogenes did it and it isn’t funny now but it keeps getting reposted anyway and we have to pretend it is
miss_demeanour@lemmy.dbzer0.com 3 weeks ago
I understand Diogenes was usually the life of the party, so they just pretended it was funny.
Angry_Autist@lemmy.world 3 weeks ago
Philosophers of that era spend a lot of time drunk.
I mean who the fuck dies from laughing to death at a donkey eating figs?
NONE_dc@lemmy.world 3 weeks ago
Fuck off, Diogenes!
quediuspayu@lemmy.dbzer0.com 3 weeks ago
The square is a parallelogram, this is not a parallelogram.
Zerush@lemmy.ml 3 weeks ago
Explain it to a ball
TheLeadenSea@sh.itjust.works 3 weeks ago
This is why you specify that they are straight, parallel lines.
AnarchoEngineer@lemmy.dbzer0.com 3 weeks ago
Perhaps this is just a projection of a square from a non-Euclidean space in which the lines are in fact straight and parallel.
I think the 2D surface of a cone (or double cone) would be an appropriate space, allowing you to construct this shape such that angles and distances around geodesics are conserved in both the space itself and the projected view.
This shape in that space would have four sides of equal length connected by four right angles AND the lines would be geodesics (straight lines) that are parallel.
captain_aggravated@sh.itjust.works 3 weeks ago
I suppose you could get a shape like this if you tried to draw a square by true headings and bearings near the North pole of a circle. “Turn heading 090, travel 10 miles. Turn heading 180, travel 10 miles.” and so forth. Start at a spot close to the pole and this will be your ground track.
potoo22@programming.dev 3 weeks ago
They could be if we’re talking about non-euclidian geometry.
Angry_Autist@lemmy.world 3 weeks ago
there is no definition that someone can’t fuck up, that’s the point of this exercise, not to find a perfect definition
But as usual 70% of you miss it
Zorque@lemmy.world 3 weeks ago
The point of this exercise is to say “ha-ha gotcha, I’m so clever neener neener” while everyone else rolls their eyes.
Fredthefishlord@lemmy.blahaj.zone 3 weeks ago
The way science advances is in part making definitions harder and harder to screw up