Two students make 2 shadow plots on the same day at the same location. The plots look different in size and direction of shadows. Why? Should they be the same if the gnomon was the same and location too?

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There are a few things I can think of that are variables that the question does not mention.  They both can cause the plots to appear different, although the result of true (geographic) north should be the same for both plots.

The times that the positions of the shadow are...

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There are a few things I can think of that are variables that the question does not mention.  They both can cause the plots to appear different, although the result of true (geographic) north should be the same for both plots.

The times that the positions of the shadow are recorded will make the points on the plot appear at different locations.

The slope of the ground can make the points on the plot appear at different locations or even appear "skewed" to one side or the other.

Even with these differences, once you have completed the plotting of your points and drawn a curve connecting your points, a line drawn from your gnomon to the closest point on your curve will be your true north/south line.

I hope this helps.

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