pizza: The pizza is circular, radius 1 foot. The pizza is cut into 4 equal area slices. They lie flat without overlapping in a square box. What is the smallest box that can be used?|||I woud use box with side 1,942942333... As at the picture: http://i524.photobucket.com/albums/cc321鈥?/a> Side of the little square in the middle is 0,172622951... *************************** Rita, there is a trigonometry relation for side of square: a = 1 + tan伪 + cos伪 - sin伪 Minimum is for: sin伪 + cos伪 = 1/(cos伪)^2|||Oh that's too bad, you closed this one out too fast. I think I have a better answer, so maybe I'll repost this another time. Report Abuse |||Sorry, I'd certainly be interested in a better result. Report Abuse |||If I do have one, but it's really messy. Report Abuse |||Yes, I can definitely nip a tiny bit off of Dragan K's own solution, even though I think there are still better solutions. Too many different possibilities. The point is, Dragan K's solution is not definitive, even while meeting Rita's requirement that all 4 pieces are congruent. Report Abuse |||If the 4 pieces only merely have to have equal areas, that expands the possibilities. Report Abuse |||Yes, no requirement of congruent was mentioned. If you want me to re-ask the question let me know. Report Abuse |||Rita, there's too many different possible solutions, which makes it herculean to find the "best". As for Dragan K's solution, you can cut tiny teeth into the straight cuts so that the outer tips of the pieces are transferred to the center, thus allowing a smaller square box to contain them. Report Abuse |||Still using exactly 4 congruent pieces cut from the round pizza. Report Abuse |||Note that 6 x 0.172622951.. = 1.0357746... which is barely > 1, allowing the last "teeth" to project into the small square. Then it's a matter of how large the 4 teeth can be to all fit into the small square. Report Abuse |||However, even this isn't exhaustive as for the "best" solution using 4 congruent pieces using this idea. Report Abuse |||@Scythian: Do you have a picture for this? I'm having a hard time visualizing it. Report Abuse |||All right, Rita, now that I've solved your other posted problem, I'll work up a graphic, which will take me some time. Report Abuse |||Do me a favor, don't post any more interesting problems until I've had the chance to finish my graphic, or I'll never get to it. Gimmie a day or two? Report Abuse |||Okay, here's the link to the graphic, which is more of a sketch than a computed one: http://i254.photobucket.com/al鈥?/a> Report Abuse |||Note that I have drawn the notches only in one place, not all four, because it's too much work plugging in the graphics for the rest. But from this you should be able to get the idea of how this works. The limiting factor is being able to crowd 4 of these teeth into the small center square. Report Abuse |||This will in fact reduce the size of Dragan K's box, but only by just a tiny, tiny bit. Report Abuse |||Yes, I get the idea. Pretty clever. Thanks for taking the trouble to make the graphic. Report Abuse |||Pity. All this suffering could have been avoided, if only people would *Just* *Finish* *Their* *Pizza*! I mean, c'mon, if there's that much left over, it's probably not worth keeping, anyway. Seriously, good work, guys! And the problem seems to be still open a bit. Report Abuse |||pizza|||Radius is 1 foot so the area of the whole pizza is 3.14 feet^2. The smallest square number that is bigger than 3.14 is 4. So the area of the square box is 4 feet. Each side of the box is 2 feet.|||A box With About the length of 2 and width of 2. In Feet. Those are some big slices of pizza... Diameter is 2 X radius so the diameter going across is 2 Feet|||Just grab a small box and smash all the pizza in it. It will still taste the same in the end.|||the fact that there are 4 slices is irreleant, box needs to be 4 square feet.|||A box with 2 feet side