Re: [math-fun] Estimating the aspect ratio of a rectangle
(My Swiss Army knife has a ruler in it.) On 2018-07-27 10:24, Eugene Salamin via math-fun wrote:
Measure it with your own ruler. And take your future business to a different hardware store.
-- Gene
Gene is spoiled. He used to live near the _unbelievably_ knowledgeable and helpful https://ww3.truevalue.com/latvh/Home.aspx . --rwg
On Friday, July 27, 2018, 7:34:59 AM PDT, James Propp <jamespropp@gmail.com> wrote:
I just took a small cylindrical part to a hardware store, where the
clerk,
after determining that it wasn't a standard-sized (American) part and therefore was probably metric, seemed pretty unhappy about letting me borrow his metric ruler to take the part's measurements; together we were able to measure the diameter of the cylinder (1 cm) but he got pretty annoyed with me during the process so I didn't feel I could further impose on him by measuring the length.
(Side-note: he placed the small cylinder with one circular face resting on the table, positioned it between the 9cm mark and the 10cm mark, and announced that the diameter was 10 centimeters. I expressed incredulity, and said "No, it can't be 10 centimeters. ... Look, 10 minus 9 is 1." Maybe I should have been gentler about it.)
While walking home, I tried to figure out the length of the cylinder by eye, using the fact that a cylinder viewed from its side is a rectangle, and using the fact that I already knew one side of the rectangle (i.e. the measured diameter of the cylinder). I found a pretty good method; I'm wondering if any of you will think of better (or more amusing) ones.
I'll post my method after others post theirs.
Jim Propp
I guess I haven’t succeeded in making these puzzles appealing, so I’ll just give quickie descriptions of my solutions. To estimate aspect ratio, play “mental billiards”! Hold the rectangle so that all four sides have slope +1 or -1. Then shoot an imaginary billiard ball from a corner (alternately horizontally and vertically) until it hits a corner again. The pattern of the bounces gives a rational approximation to the aspect ratio. To decide by eye whether octagon ABCDEFGH is regular, hold it so that segment AB is horizontal, and see if the octagon appears to have bilateral symmetry. Then hold it so that segment AE is vertical, and see if it still appears to have bilateral symmetry. Jim Propp On Friday, July 27, 2018, Bill Gosper <billgosper@gmail.com> wrote:
(My Swiss Army knife has a ruler in it.)
On 2018-07-27 10:24, Eugene Salamin via math-fun wrote:
Measure it with your own ruler. And take your future business to a different hardware store.
-- Gene
Gene is spoiled. He used to live near the _unbelievably_ knowledgeable and helpful https://ww3.truevalue.com/latvh/Home.aspx . --rwg
On Friday, July 27, 2018, 7:34:59 AM PDT, James Propp <jamespropp@gmail.com> wrote:
I just took a small cylindrical part to a hardware store, where the
clerk,
after determining that it wasn't a standard-sized (American) part and therefore was probably metric, seemed pretty unhappy about letting me borrow his metric ruler to take the part's measurements; together we were able to measure the diameter of the cylinder (1 cm) but he got pretty annoyed with me during the process so I didn't feel I could further impose on him by measuring the length.
(Side-note: he placed the small cylinder with one circular face resting on the table, positioned it between the 9cm mark and the 10cm mark, and announced that the diameter was 10 centimeters. I expressed incredulity, and said "No, it can't be 10 centimeters. ... Look, 10 minus 9 is 1." Maybe I should have been gentler about it.)
While walking home, I tried to figure out the length of the cylinder by eye, using the fact that a cylinder viewed from its side is a rectangle, and using the fact that I already knew one side of the rectangle (i.e. the measured diameter of the cylinder). I found a pretty good method; I'm wondering if any of you will think of better (or more amusing) ones.
I'll post my method after others post theirs.
Jim Propp
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participants (2)
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Bill Gosper -
James Propp