andyr Posted October 2, 2022 Posted October 2, 2022 Well, I do have 3 degrees involving mathematical subjects! Andy
sdotmouse Posted October 2, 2022 Author Posted October 2, 2022 hey Andy, that's 3 more than I have but I have always liked geometry. anyway doing some child minding duties and chores today and this came up from one of the kids. you know when folding a towel or sheet, blanket whatever, how the edges don't match up, is there anyway to fold so that they do. hope this makes sense thanks, mouse
sdotmouse Posted October 2, 2022 Author Posted October 2, 2022 I'm thinking along the lines of mathematics involving packing the maximum number of objects into a particular space mouse
sdotmouse Posted October 2, 2022 Author Posted October 2, 2022 and while I'm at it the same kid asked about the route that the garbage collection trucks take. presumably this is worked out for best efficiency? mouse
sdotmouse Posted October 2, 2022 Author Posted October 2, 2022 sorry if this is garbled I've had a few sherbets watching the footy final mouse 2
Hazzzy Posted October 2, 2022 Posted October 2, 2022 (edited) Never mind. Edited October 2, 2022 by Hazzzy
andyr Posted October 2, 2022 Posted October 2, 2022 (edited) 10 hours ago, sdotmouse said: anyway doing some child minding duties and chores today and this came up from one of the kids. you know when folding a towel or sheet, blanket whatever, how the edges don't match up, is there anyway to fold so that they do. hope this makes sense thanks, mouse Very smart kid! 10 hours ago, sdotmouse said: I'm thinking along the lines of mathematics involving packing the maximum number of objects into a particular space That branch of mathematics is called "Operational Research" - which is what my 2 postgraduate degrees are in. Same branch of mathematics that optimises aircrew / teacher timetables. 10 hours ago, sdotmouse said: and while I'm at it the same kid asked about the route that the garbage collection trucks take. presumably this is worked out for best efficiency? Same branch of mathematics. I actually worked for 3 years for a guy who developed a "route optimisation" program! This was back in the mid-70s! Yes, your Council should be using such a program - but I suspect (if Moreland's is any example) they probably prefer to spend their rate revenue on less "sensible" things. Andy EDIT: I forgot to give an answer to your kid's question. I suggest why, when folding a "towel, sheet or blanket", the edges don't line up ... is because they are woven items - and woven items stretch more in one direction, with use, than the other. (Don't know which stretches more - the warp or the weft. ) Because you can fold a sheet of paper so that its edges line up. Edited October 2, 2022 by andyr 2
Volunteer sir sanders zingmore Posted October 2, 2022 Volunteer Posted October 2, 2022 1 hour ago, andyr said: Same branch of mathematics. I actually worked for 3 years for a guy who developed a "route optimisation" program! This was back in the mid-70s! Isn’t that a variation of the Bridges of Koenigsberg optimisation problem? My daughter studied that as part of VCE Algorithmics
wasabijim Posted October 2, 2022 Posted October 2, 2022 At uni (IT degree sorry) we did a unit on the application of maths to such real world problems. I remember a similar scenario for a delivery driver with a few dozen stops across town. There's actually a formula. But I can't for my life remember the jist of it!
andyr Posted October 2, 2022 Posted October 2, 2022 19 minutes ago, sir sanders zingmore said: Isn’t that a variation of the Bridges of Koenigsberg optimisation problem? My daughter studied that as part of VCE Algorithmics Don't know, Trev - we never considered that problem in our course.
bob_m_54 Posted October 3, 2022 Posted October 3, 2022 (edited) 6 hours ago, andyr said: Because you can fold a sheet of paper so that its edges line up But how many times? Edit: Top to bottom, left to right... Edited October 3, 2022 by bob_m_54
Cloth Ears Posted October 3, 2022 Posted October 3, 2022 4 hours ago, andyr said: Don't know, Trev - we never considered that problem in our course. No graph theory? Although I guess that's more of a pure maths topic than most applied ones. 6 hours ago, andyr said: EDIT: I forgot to give an answer to your kid's question. I suggest why, when folding a "towel, sheet or blanket", the edges don't line up ... is because they are woven items - and woven items stretch more in one direction, with use, than the other. (Don't know which stretches more - the warp or the weft. ) Because you can fold a sheet of paper so that its edges line up. Agree there. When it comes to the other part of the problem (packing the maximum number of objects into a particular space), there's a number of different things to consider. Folding is, in itself, inefficient. Which is why paper is packed flat. But sheets often have edges (or they'd fall apart after a couple of washes), so a couple of folds actually benefits storage efficiency. After that, it's simply the size of the cupboard, the shelves, and how easily you want to be able to get the sheets out (less folds equals harder). Towels are a whole other issue!
andyr Posted October 3, 2022 Posted October 3, 2022 Just now, bob_m_54 said: But how many times? I believe that depends on how thick the paper is - tissue paper vs., say, wedding invitation paper. But I remember reading way back that the correct answer is '8'!
bob_m_54 Posted October 3, 2022 Posted October 3, 2022 (edited) 2 minutes ago, andyr said: I believe that depends on how thick the paper is - tissue paper vs., say, wedding invitation paper. But I remember reading way back that the correct answer is '8'! LOL yes, the theory says (almost) infinite... But finding a piece of paper that is microns thick and kilometers by kilometers big, is the problem.. Edit: Is wedding invitation paper thicker or thinner than than funeral invitation paper? Edited October 3, 2022 by bob_m_54
andyr Posted October 3, 2022 Posted October 3, 2022 7 minutes ago, bob_m_54 said: Edit: Is wedding invitation paper thicker or thinner than than funeral invitation paper? Haha - they both probably use the same thick stock. 1
wasabijim Posted October 3, 2022 Posted October 3, 2022 7-8 times is the practical fold limit of paper regardless of size or grade 1
bob_m_54 Posted October 3, 2022 Posted October 3, 2022 (edited) 33 minutes ago, wasabijim said: 7-8 times is the practical fold limit of paper regardless of size or grade For a piece of commercially produced stock... But what about if you had a 1km X 1km piece of tissue paper.. so it's only the practical limit for a practically available piece of paper... Edit: And I reckon you'd be pushing to do 8... Edited October 3, 2022 by bob_m_54
sdotmouse Posted October 3, 2022 Author Posted October 3, 2022 Well I'm pleased to see responses to a topic I thought I probably shouldn't have started. Regarding the route thing has anyone else noticed their navigation gadget (whatever you call it) provide a different route back home from where you have just come? s.m
andyr Posted October 3, 2022 Posted October 3, 2022 15 minutes ago, sdotmouse said: Well I'm pleased to see responses to a topic I thought I probably shouldn't have started. Any topic is valid here on SNA, mouse! (Well except religion ... politics ... and anything else that will divide us as one happy family!) 15 minutes ago, sdotmouse said: Regarding the route thing has anyone else noticed their navigation gadget (whatever you call it) provides a different route back home from where you have just come? Not that I'm aware of.
Addicted to music Posted October 3, 2022 Posted October 3, 2022 (edited) 8 hours ago, bob_m_54 said: LOL yes, the theory says (almost) infinite... But finding a piece of paper that is microns thick and kilometers by kilometers big, is the problem.. Edit: Is wedding invitation paper thicker or thinner than than funeral invitation paper? That depends on the individual who decides what should be supplied on the day. For example, most wedding invites are usually matt coated between 200-300gsm where many require special order thats not common to printer stock. That obviously increases as ink or toner is laid down. Sometimes in several passes as gold or silver bold text is used. Never seen a Funeral invite, hence Im never going to mine! its just a eulogy, that's usually in a some form of booklet with a 200-300gsm cover and 2 staples in the centre with 80-160gsm pages. Edited October 3, 2022 by Addicted to music
aechmea Posted October 3, 2022 Posted October 3, 2022 For sheet folding Each simple fold halves the area and doubles the thickness, so you are looking at 1,2,4,8,16,32... and 1, 1/2,1/4,1/8 etc 1,2,4,8,16 etc are the values of bits in a binary number and fundamental to computing and digital audio. Therefore computers should be able to fold the sheet whilst singing along. I have checked my text books from the good old days and there is no mention of garbage trucks, so no luck there. I suspect though that someone may get somewhere by using linear programming. I can remember briefly studying LP in applied maths. It seemed to be about finding the min/max cost method of getting from A to B, but memory dims after 50 years. From memory, the bridges of Konigsberg single crossing problem is solvable if you project the map onto a torus (3D donut) and sneak around the back of the torus. Something like that. Good old topology.
Cloth Ears Posted October 3, 2022 Posted October 3, 2022 13 hours ago, sdotmouse said: Regarding the route thing has anyone else noticed their navigation gadget (whatever you call it) provide a different route back home from where you have just come? s.m It doesn't matter about the gadget...you are taking a different route back home, even if you are using exactly the same streets. But now we're really getting into the philosophy side of mathematics!!!
t_mike Posted October 4, 2022 Posted October 4, 2022 Without using math at all, I've shown that on an overnight drive along the Hume Hwy from Goulburn to Walan in Victoria, by using the shortest possible path rather than staying in the left lane the trip is 50km shorter. Surprised me too.
sdotmouse Posted October 7, 2022 Author Posted October 7, 2022 Hey there, couple of comments. 1. on folding, but say paper because it's easy. What about the view that you could fold a sheet of paper in half to make a perfect piece of paper that is half the size but twice as thick. You could now start with that bit of paper and fold it in half and so on until I guess it is so thick as to be unmanageable. Doesn't explain why I can't even fold a tea towel neatly though. 2. I read about the bridges of Konigsberg on Wikipedia and about Leonard Euler. He is described as a mathematician, physicist, astronomer, geographer, logician and engineer. Is there anyone like this today? I have studied enough to recognize his name but remember the saying physicists were failed mathematicians and engineers were failed physicists. mouse
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