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.
Yeah, I think so.
>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?
Not for this reason, though...
Please, do better.
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?
bpx51•47m ago