Trisection: regular polygon

[biljanica]

look and check, point D changes the angle

 

[jedishrfu]

Interesting proof: my old teacher, not as old as Euclid, showed flaws in geometric intersections—arcs and lines often nearly intersect but form tiny triangles, invalidating proofs. Some angles are trisectable, but not all.

It was proven in 1837 by Wantzel that a compass and straightedge were insufficient to perform the trisection. Instead, you needed a ruler with equally spaced ruled markings to accomplish it.

https://en.wikipedia.org/wiki/Angle_trisection

There were other augmented schemes that did trisections just not the straightedge and a compass.

In fact, origami can be used to do this and other more complex problems, like lens-based ray tracing, known as optigami.

https://plus.maths.org/trisecting-angle-origami

Sadly, none of these methods can square the circle, since $\pi$, a transcendental number, can't be constructed but only approximated.

So there you have it, close but no cigar. However, now you know the secret of how to disprove anyone else's possible proof, and that is real knowledge.