ilovepyramids

4 ms·

1. 1.▲
   by ilovepyramids 7y ago

   Took me a moment. Interesting! So you're saying: Divide the pyramid into very thin slices, parallel to the base (horizontal). Above each slice, insert a duplicate of that slice. If using infinitely small slices, you have effectively do
2. 2.▲
   by ilovepyramids 7y ago

   This feels like a perfectly intuitive 3d proof to me. Thank you.
3. 3.▲
   by ilovepyramids 7y ago

   I did consider this, and it seemed to make it feel a little clearer—but when I first posted, I didn't feel it was obvious that the fraction of the rectangle occupied by the triangle would remain constant if you stretched it. But I th
4. 4.▲
   by ilovepyramids 7y ago

   Okay, maybe I can accept this readily. Easy enough to prove that doubling the height of a convex 2-d shape will double the area if you stretch all of its vertical proportions to double. If that shape is on a graph, the x axis is what it nor
5. 5.▲
   by ilovepyramids 7y ago

   Very interesting! It's not clear to me why it's so obvious that doubling the height of a pyramid while keeping the side constant would double the volume of the pyramid. The reason it is not obvious to me is that the proportions of