How do you see these points moving ?
Ben Sparks @SparksMaths started a great talk last week for #latemaths with this simple animation. People see different things. What do *you* see ?
Ben Sparks @SparksMaths started a great talk last week for #latemaths with this simple animation. People see different things. What do *you* see ?
Some see the endpoints of a twirling baton as @shskaercher mentioned it.
And Mark even pictured the trace of this baton whose envelope is an astroid.
Similarily you might see the points turning in circles (or maybe you have a bad WiFi like @TeaKayB )
You might have noticed like @k1monfared or @Karl4MarioMugan or @OlivierReims that the points move like this, forming a + sign.
But you might also see something else like @MarcdeFalco. Here's a hint.
Now it should be clear...
Now, can you explain why the twirling baton has a fixed length ?
Now @aknauft saw it in 3D, which would absolutely give the same thing.
Here points (cos(t), sin(t), 0) and (0, cos(t), sin(t)) which projected onto the xOz plane shows (cos(t),0) and (0, sin(t)).
Here points (cos(t), sin(t), 0) and (0, cos(t), sin(t)) which projected onto the xOz plane shows (cos(t),0) and (0, sin(t)).
Now if you do the same thing on two other lines perpendicular lines y=+/- x, it's hard not to see a rotating square (especially now that it's drawn 😄) where all the vertices are actually moving along a straight line.
Remove the circle and the lines to get a cool illusion. Hard to spot that the points move along straight lines now.
