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The Challenge: Build accurate clocks

We could build a horizontal sundial on a flat, level base plate and make sure that the shadow stick is angled so that it is parallel to the earth's north-south axis. However, marking the points where the shadow will fall at each hour is not as simple as it might seem. These points change depending on latitude.

At a high northerly latitude the marks would look like this:
But closer to the equator, they would look like this:
Latitude marks
Latitude marks

As a result, there are two significant drawbacks:

1. Trigonometric calculations are required to work out the hour mark positions - easy to do with a calculator but very tricky without.

2. Even if the hour marks could be calculated the gaps between them would be unequal, making measurement of periods shorter than an hour difficult.