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Every shape can be cut exactly in half with one straight line
- bpx51 1mo agoThe math behind why you can always find a perfect 50/50 cut, even for weird shapes.
- Obscurity4340 1mo agoWhat about chiral molecules, like say D-phenylalanine?
- Lerc 1mo agoHow 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.
- bpx51 1mo agoGood point, but "cutting in half" here refers to total area, not keeping each half as a single connected piece. Slicing through spirals will definetely cut one side into multiple disconnected fragments, but as the straight line sweeps across the shape, the sum of the areas on the left side still grows continuously from 0% to 100%, so it is guaranteed to cross the exact 50% mark at some point.
- margalabargala 1mo agoThe math behind the interactive bits is terribly broken. You may want to add testing to the prompt that wrote this article.
- bpx51 1mo agoFair point, I used AI to quickly build the interactive widget and English isn't my native language so ofc I used it to help edit the text. I'm looking at the code right now, what did you see that was broken?
- margalabargala 1mo agoSeems fixed now. But when I posted my comment, on mobile, the triangle bisector appeared to be measuring whether you were bisecting the long leg of the triangle, very much not the area.
- bpx51 1mo agoYes, it was a floating point rounding issue when slicing holes. Just pushed a fix, thank you for pointing it out
- fluoridation 1mo agoAm 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?
- analog31 1mo agoAlong similar lines, if you hang the shape by a string, the line of the string will go through the center of mass, and you can cut along that line.
- asplake 1mo ago> 3. Why the Obvious Answer Fails: The Center-of-Mass Trap
- fluoridation 1mo agoI'm pretty sure that's incorrect. The whole point of the center of mass is that it's at the intersection of all the bisecting lines. If you slice a shape in two and you don't get two parts of equal area then you didn't pass through the center of mass.
- gus_massa 1mo agoThe vertial bisection of this: XX XX XX|XXXXXXXXXX XX XX is the | symbol, but the center of mass is near the o in the next graphic. XX XX XXXXoXXXXXXXX XX XX
- fluoridation 1mo agoYou're just asserting that. Why would the center of mass be further to the right from the vertical bisection? That would make it so the left side has a mass of 12.5 versus 8.5 on the right. If you were to pivot that shape freely from that point, it wouldn't stay balanced, it would swing until it ends up as an upside-down T.
- VCFundedGenYer 1mo agoAI 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.
- Intermernet 1mo agoI 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?
- ano-ther 1mo agoThe game is very nice: https://bisecto.com/ https://bisecto.com/
- bpx51 1mo agoThank you
- josefritzishere 1mo agoWhy on Earth is this flagged?
- minitech 1mo agoSlop article generated to promote their game that they also posted yesterday.