That’s a fascinating thread to pull on—sundials are really a perfect example of how craftsmanship can creep into science. In the earliest days, the whole idea was pretty crude: a stick or a simple gnomon on a flat slab, with little thought to the sun’s declination. Accuracy was a rough estimate, often only good enough to tell noon from a half‑hour off. When the Greeks stepped in, they began to use mathematical ratios. They’d carve a scale of hours on the base, often in a circle, and start to account for the sun’s path across the sky. Materials were still stone or wood, but the precision of the cuts improved the shadow’s definition. By the Roman era, you start to see the use of bronze or iron for gnomons, which made the instruments more durable. They even began to incorporate meridian lines that could be calibrated with star sightings, giving them a better idea of true solar noon. The Islamic world brought glass and polished metal, allowing for clearer markings and even the use of water clocks as auxiliary timekeepers. The precision of the shadow became a visual cue that could be matched against known astronomical tables. Fast forward to the Renaissance, and you see the incorporation of trigonometry in design. Sundials became sophisticated enough to correct for the equation of time. They used bronze with intricate etchings, and the accuracy could get down to a few minutes over a day. So each leap in material—stone to bronze to polished metal—and each technique—from crude stick to trigonometric correction—slid the accuracy forward incrementally. It was a slow, methodical climb, and the story of sundials is really the story of how humanity turned observation into measurable science, one shadow at a time.

The Greeks didn’t go hunting for fancy new cycles; they stuck to what the sun actually did each day. Their trick was to set the gnomon’s angle to match the local latitude so that the shadow would swing neatly across the dial. That angle gives a ratio of height to horizontal distance that mirrors the tangent of the sun’s altitude at noon. With that, the hour lines could be spaced using simple ratios—like 1:1 for each hour—because the sun’s apparent motion in the sky is essentially linear when you’re looking at a flat, horizontal dial. So in short, their ratios were built straight from the geometry of the sun’s path, not from any mysterious astronomical tables.

They were mostly happy with the single fixed angle; the Greeks thought the sun’s daily path was enough to tell time. Seasonal changes did shift the shadow’s length a little, but they didn’t try to tweak the dial each month—those were better handled with a water clock or a star sighting. So the ratio stayed constant, the simple tangent of the latitude, and the sundial stayed true for most everyday use.