Timeline for Using squares to prove e > 2.7
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2021 at 17:40 | comment | added | 2012rcampion | By the way, you can use just 19 bins of width 1/3, with total area 2.70093... (and at most 43 cuts) | |
| Sep 1, 2021 at 14:42 | comment | added | loopy walt | @JaapScherphuis thanks! There are obvious ways of hand-optimising this. Like using adaptive interval widths or puttting one square whole under the curve (bottom left corner at the origin) But I do not see a systematic approach. | |
| Sep 1, 2021 at 14:07 | comment | added | loopy walt | @justhalf not using bars, using trapezoids (bars with sloped top). so the top of the bar is not horizontal but the tangent to the midpoint. This just fits and works for bars up to width 2. | |
| Sep 1, 2021 at 12:09 | comment | added | Jaap Scherphuis | A quick estimation of the number of cuts this method needs: First cut the three pieces into strips of width 1/4, which takes 9 cuts, and lay these end to end as one long strip. Then cut this strip into 6*4=24 rectangles of the correct heights, which takes 23 more cuts. Lastly change one end of each rectangle to the correct slope, which takes a further 24 cuts. So 9+23+24=56 cuts all together. Assuming things can be arranged so that no cuts intersect previous ones, this uses 3+56=59 pieces. | |
| Sep 1, 2021 at 12:03 | comment | added | justhalf | Oh, but if you use the midpoint wouldn't the bars overlap the curve at the lower part of the curve? | |
| Sep 1, 2021 at 11:49 | vote | accept | Carl Witthoft | ||
| Aug 31, 2021 at 4:47 | history | edited | loopy walt | CC BY-SA 4.0 | edited body |
| Aug 31, 2021 at 4:35 | history | answered | loopy walt | CC BY-SA 4.0 |