Goys, I just solved the trisection of the angle. The angle between

What is the flaw?

>>8986077

how do you ensure it's a perfect parallelogram?

File: Scan0001.jpg (104KB, 1700x2200px) Image search: [Google]

104KB, 1700x2200px

>>8986151
well for starters it doesn't work

File: not even close.jpg (103KB, 1360x726px) Image search: [Google]

103KB, 1360x726px

>>8986166
here's another one I cooked up in geometer's sketchpad

>>8986166
9:00
https://www.youtube.com/watch?v=6Lm9EHhbJAY
What is she doing wrong then?

>>8986171
she trisected the segment, not the angle

>>8986177
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.

File: not even close.jpg (31KB, 559x611px) Image search: [Google]

31KB, 559x611px

>>8986171
>>8986177
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.

File: not even close.jpg (52KB, 911x543px) Image search: [Google]

52KB, 911x543px

>>8986184
that statement is trivially false

File: whoops.png (31KB, 852x364px) Image search: [Google]

31KB, 852x364px

>>8986184
>>8986189
I have corrected the diagram
it's still false

>>8986189
Obviously you have to connect the blue line to the black line.
Just like in the video i posted.

File: not even close.jpg (59KB, 1005x529px) Image search: [Google]

59KB, 1005x529px

>>8986194
here is a much more extreme example illustrating why your construction doesn't work

>>8986193
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.

>>8986200
Thanks a lot! Fuck am I stupid.

>>8986204
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.

>>8986214
Why is 2 so special?

File: 1473436982804.gif (367KB, 320x223px) Image search: [Google]

367KB, 320x223px

So the trisection of an angle is essentially a trisection of an arc, who would have thought. But now its much clearer.

>>8986214
Yes i know.

File: meme.jpg (41KB, 584x238px) Image search: [Google]

41KB, 584x238px

>>8986219
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.

>>8986226
Angles have always been about arcs... That's how they're defined...

>>8986219
Because we can only draw 2dimensional. It sounds like a joke, but i guess its true.

>>8986230
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