8 ms·
Is that like saying sin(x)=x?
by ThrowawayTestr 4y ago
Is that like saying sin(x)=x?
- joe__f 4y agoYou mean, for small x, sin(x) ~= x? I've been thinking for a while and I can't see a way that it's like that
- ThrowawayTestr 4y agoLike if you zoom in on a circle close enough it looks like a straight line.
- topaz0 4y agoThis is basically it, yes, along with cos(x) = 1. If the axis of rotation is much further than the distance that you move through upon rotation, the angle of rotation is very close to zero, so the approximations are very good. In the limit that the axis of rotation is infinitely far away, it is exact.
- hoseja 4y agoCoincidentally, a recent relevant XKCD: https://xkcd.com/2761/ https://xkcd.com/2761/
- afiori 4y agoIt is more like saying 1/∞ = 0. "Translations are rotations around infinity" is what you get if you compactify the real plane with projective geometry, 1/∞ = 0 is what you get when you close the complex field with an holomorphic-friendly point at infinity.
- gowld 4y agosort of... A line is a circle (more precisely, a cline ("circle-or-line") with infinite radius and center on the "horizon" (In 1D, the horizon is the 2 points at +/infinity. In 2-D, the horizon an infinite circular boundary around the plane. In 3-D, it's an infinite circular sphere). The center's position determines the slope/angle of the line. For a translational "rotation" in 3D, the axis of rotation is the line that is tangent to the infinite "celestial" sphere and perpendicular to the line of translational motion.