Science Memes

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Wake up babe new shape just dropped (sopuli.xyz)

submitted 5 days ago by [email protected] to c/[email protected]

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[–] [email protected] 37 points 5 days ago (2 children)

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.

[–] [email protected] 14 points 5 days ago (1 children)

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.

[–] [email protected] 5 points 5 days ago* (last edited 5 days 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 from either direction. Maybe that’s still called perpendicular.

[–] [email protected] 5 points 5 days 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.