Okay ************* ...
Lets call the smallest angle in the green triangle A:
Before rearranging Tan A = 3/8
Making A 20.566 Degrees
After rearranging Tan A = 5/13
Making A 21.038 Degrees
Therefore we can see that there are minor changes to the angles, creating the extra square.
The slopes do not match up. They look like they do to the human eye, but there is really a small sliver of empty space running across theï»¿ rectangle diagonally.
I DONT UNDERSTAND THIS... ive been looking at this for half an hour, playing with it in various photo editors and still dont understand how this works! can you explain this to me!
I'm sitting here in the laundry room in college, having a few drinks, doing some laundry (There's nothing else to do in here) and this post was going to drive me ******* crazy. Thank you a million times for posting this. I just might love you.
It's simple, red and green have slopes of 3/8 while blue and orange have a slope 2/5.
Thus the lines are not exactly straight. there is a small gap in between the blue and the green piece, and the red and the orange piece. That gap creates the extra 1 area.
If you were to enlarge the scale of this to something much more... colossal, you'd notice that the slopes don't match up.
At a glance, no matter how long, it seems to match, but that's because the scale is 8x8 and the margin is just a singular unit spread out to the point it's impossible to notice.
Right, because the slope of 3/8 (the division of the red and green triangles) is not equal to a slope of 2/5 (or 5/2, when you rotate it 90 degrees, the division of the orange and blue trapezoids)
Mhm, but because 3/8 and 2/5 are so close to each other, as well as being put in as small a size as a simple gif, it's incredibly difficult to tell the difference without any form of check-up, so most people assume the gif was correct.
Not exactly sure what you meant by that, but basically the lines aren't actually straight so by fudging it a bit, you can get it to look like its one unit^2 bigger even though its not
if you look the lines in the second arrangement they are slightly offset, accounting for the gaining of one square. i've seen a gif that shows it but i dont have it or the effort to look for it