Tuesday, June 04, 2024

Ugh. This thing again.

I know I've done this before, but this stupid thing keeps showing up in my feeds. And it pisses me off to no end.

What happened to that little square of area?
It isn't missing. IT ISN'T MISSING!
There's a trick here.
It relies on the way the eye handles those colors and the zoom level.

Let's take a closer look at the left triangle:
And there it is. The triangles aren't similar.
The Red triangle is 7 units wide and 3 units tall, so the slope ≈ 0.4286
The Orange triangle is 12 units wide and 5 units tall, so the slope is ≈ 0.4167
When they are arranged this way, there's a slight concavity to the figure.

Now let's look at the re-arranged triangle on the right:
Now there's a slight convexity.
This figure has the area of the first figure minus the "missing" chunk PLUS the area of the original concavity PLUS the area of the convexity.
Guess what the area of the concavity plus the convexity equals.

Later,