Triangle hole trick: made 3D from cubes and explained

Also known as the "missing square puzzle," this great little trick is sure to get a reaction at parties- especially from those who haven't had time to think about it before! If you are going to build one, I recommend the cubes over the flat parts: the cubic version is easier to handle, more convincing, and more forgiving. This video first outlines some of the construction process, and then provides a conceptual explanation for what's happening here. Spoiler: there are three triangles, and all three are slightly different- the video explains how.

The overall puzzle has an area of ½bh, or ½(13)(5), or 32.5 units^2. The sum of the areas from the four parts is still one unit less, so something is amiss. There is a slight variation to the shapes of the three triangles here, but that is not easily visible to us, especially since we have a natural tendency to quickly make assumptions about the things that we see. I'm not criticizing; sure, this tendency can cause problems, but it's also the source of some great advantage to us. Because we can make assumptions, we can learn from both the world and others readily, which lets us quickly adapt to changing circumstances. There will always be those who consider this trusting trait as gullibility, and as a thing to be exploited, but that is only because dishonesty is so rampant. If it weren't for those selfish fools who are endlessly attempting to swindle the honest with some new snake oil, humanity would suffer much less from lost productivity. Your greed and aims for personal success are the result of a short-sighted, self-oriented evolutionary origin that you should really consider suspect. Our little, harmless personal biases can have lasting social reverberations, which reflect themselves in our so many failed attempts in the political and economic sphere(s) throughout history.

Slight numerical differences can have amplifying ramifications as a system becomes larger and more complex; many of these emergent effects are not immediately apparent at the outset, given the small values in differing orientation to the seed variables (the initial conditions), which may splinter and then crystallize into trees of branching potentialities. This is another one of those butterfly effect things, but the point is that details matter. In a more real-life example, using a six-inch pocket level to make sure that an eight-foot bench is level can be disastrous if you're off a bit: there is a total of 16 lengths of 'pocket level' within the length of your bench, so your error will be multiplied by that factor. Thus, ⅛" out of level becomes two inches on your bench. Little mistakes, err, or, error- can be projected; error becomes amplified in affect as time, space, frequency, use, or any other dimensionality is added into the parameters of a given system.

Rabbit hole:
   • the triangle puzzle's mathematical and phi...  

Music:
"Desert City" Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/b...