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I did a search, and nothing useful came up.

I am trying to calculate the area ($\operatorname{cm}^2$) of the sole of my shoe (size UK $8$) and am unsure how to do it because I'm not good with maths.

Could someone tell me how to do it please?

To add more context, the shoe in question was an Adidas Hamburg shoe. The problem I was attempting to solve was to figure out how many 2cm diameter magnets I would need to fit inside the shoe, assuming each magnet is spaced about 1/2 an inch apart.

I kind of solved the problem in a very hacky way by tracing my shoe on some paper, measured out a 1cm grid and then deducing from that I'd likely need around 14-16 magnets. Of course, I could be entirely wrong. ;)

Thank you all.

cornishninja
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  • I'm not good with shoes. Expecially when their size is given in those weird numbers. For instance, I really can't see why I sometimes need $48\frac12$ and some other time I need $46$ (EU). –  Dec 18 '15 at 15:15
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    isn't it possible for the soles of the same size shoe to be shaped differently? High heels would be differently shaped than sneakers. – R_D Dec 18 '15 at 15:17
  • Of course. But presumably he's asking for his shoe, not an arbitrary shoe. – Batman Dec 18 '15 at 15:22
  • I was enquiring about the sole of my Adidas Hamburg shoe. – cornishninja Dec 22 '15 at 16:13

2 Answers2

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There is no nice and precice way of doing this. Here are three approximate ways that might work, though:

  • Draw a rectangle approximately the right size, and measure the area of that.
  • Draw an outline on a piece of graphing paper and count the number of squares inside the outline. Equivalently, take a picture of it next to a ruler, upload it to the computer, and count how many pixels it fills, and use the ruler to tell how big a pixel is.
  • Make a box with the bottom being the shape of the sole (follow the outline from point 2, for instance) and fill it to some specific height (like $1$ cm) with water. Then measure the volume of that water using your favourite volume measuring tool. (Fair warning: this is not a fast method.)
Arthur
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  • Thank you, and I ended up doing something similar. But I'm curious about volume. Why would I need to work out the volume, as suggested in your last method? – cornishninja Dec 22 '15 at 16:18
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    The volume approach is just like Batman's weighing the paper. Arthur is using a 1 cm layer of water instead of a sheet of paper as a constant thickness object. That amount of water is probably easier to weigh accurately than the paper. On the other hand, it is more work to make the box than to cut out the paper. – Ross Millikan Dec 22 '15 at 16:28
  • Most shoes taper a bit in around the sole, so there is some variation there. If you want to be accurate, just put the shoe on a paper, trace it, fill the outline and count how many pixels are filled out of the whole picture, then the area is # of pixels filled/total # of pixels * area of paper. Same idea as the sheet of paper. – Batman Dec 22 '15 at 21:15
  • @Batman Why include the whole paper? See my point 2. – Arthur Dec 22 '15 at 21:37
  • Cause you know the area of the whole paper by looking it up on the package. – Batman Dec 22 '15 at 22:14
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An easy way that used to be used a lot by analytical chemists back in the day (to measure area for GC and other things) is as follows:

1) Trace the sole of the shoe on a piece of paper (e.g. printer paper).

2) Cut it out carefully and weigh it (call this measure w).

3) Weigh a 1 cm x 1 cm sq (call this measurement d).

Then, the area in $cm^2$ is $w/d$.

This works because the density of the paper is pretty darn uniform.

Batman
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  • Alternatively, the density of the paper is probably written down somewhere on the pack you took the paper from, so you wouldn't have to weigh the $1$ cm $\times 1$ cm square. – Arthur Dec 18 '15 at 15:23