Every shape can be cut exactly in half with one straight line

Am I being stupid? Isn't this mind-numbingly obvious? Collapse the shape into a function describing the area of the left side if you were to cut the shape at that X coordinate in that orientation. On one end the function has value zero and on the other its value is the area of the shape. Is there any reason why this function might not be continuous?

I wanted to like this, but the article is rife with Claudisms. I don't really care if you use LLMs to generate interesting articles, but maybe re-write it, or prompt it to not produce output like this?

1. The Guarantee: A Smooth Sweep Across Flatland 2. The Surprising Part: Existence Does Not Help You Find It 3. Why the Obvious Answer Fails: The Center-of-Mass Trap 4. It Gets Stranger: The Ham Sandwich Theorem 5. How I Turned the Math into a Game 6. Why This Is Harder Than It Looks

At least there's nothing loadbearing about it.

I still don't know which huge part of the training corpus led to this style. It had to be something massive that I never interact with in real life. Maybe marketing presentations? Pitch meetings? LinkedIn posts?

Where did the LLMs start to learn to talk like this? Are there actual examples from the pre-LLM era that anyone can point to that resulted in this style of output?

The math behind the interactive bits is terribly broken. You may want to add testing to the prompt that wrote this article.

How about a circular shape that has an odd number of spiral shaped lobes around the outside.

No straight line cut can cut it in half because all straight line cuts that give 50% area on each side of the line would slice the spirals into disconnected shapes.

The game is very nice: https://bisecto.com/

AI can't do math. An AI-generated article discussing how to do this in which it's painfully obvious it's wrong is just sad.

Please, do better.

The math behind why you can always find a perfect 50/50 cut, even for weird shapes.

Why on Earth is this flagged?