Goys, I just solved the trisection of the angle.
The angle between a and b hast to be divided into 3 equal sections.
>1)black lines
>2)blue lines; drawing a line and making three equally long sections
>3)red line; connecting the intersections
>4)green lines; creating 2 parallel lines to the red one
>5)yellow lines; connecting the intersections to the origin.
Call me God.
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What is the flaw?
how do you ensure it's a perfect parallelogram?
well for starters it doesn't work
here's another one I cooked up in geometer's sketchpad
9:00
youtube.com
What is she doing wrong then?
she trisected the segment, not the angle
But if you construct the trhird black line with a compass like i did in my picture, then the trisection of the line segment is equal to the trisection of the angle.
you know, like this
god this is so radically different from what you thought she was doing that I'm almost certain you're an idiot
Gods don't watch Numberphile.
that statement is trivially false
I have corrected the diagram
it's still false
Obviously you have to connect the blue line to the black line.
Just like in the video i posted.
here is a much more extreme example illustrating why your construction doesn't work
Ok. So it is a fact, that the line segments FH, HI, and IJ do all have the equal length?
If so, then i finally come closer to the actual problem. So, the trisection of a line segment is easily possible, but with an angle its impossible.
Thats interesting. Because it looks like it would work.
Thanks a lot! Fuck am I stupid.
you can divide any line segment into any number of congruent sub-segments using only a compass and straightedge
you can also bisect an angle using a compass and straightedge
You can trisect (or more generally n-sect) an angle using a compass and straightedge, but if the n you choose isn't expressible as [math]2^k[/math] it will take an infinite number of bisections. For example, 1/3 = 1/4 + 1/16 + 1/64 + 1/256... = [math]\sum _{k=1}^{\infty}2^{-2k}[/math] so it's possible to trisect an angle by making an infinite number of bisections, and then adding them up. But it will take your entire life and it still won't be finished when you die. And you'd need to have really steady hands, a really sharp pencil, and a microscope.
Why is 2 so special?
So the trisection of an angle is essentially a trisection of an arc, who would have thought. But now its much clearer.
Yes i know.
Because if you have one thing and you cut it in half you now have two half-things.
2 is the smallest integer larger than 1, which is the smallest integer larger than zero.
Binary is the smallest complete base (by that I mean you can express any number in base 2; you can only express integers in base 1)
Take your pick from these three properties. I would say the third is the most relevant to this discussion.
Angles have always been about arcs... That's how they're defined...
Because we can only draw 2dimensional. It sounds like a joke, but i guess its true.
Shure, thats why i feel so dumb. If I would have thought about that earlier, it would have been clear, because a trisected line segment isnt equal to an arc segment