Can you resist a sundial? Interesting dials beckon everyone, and while the garden varieties so often disappoint, the ones designed with razor precision, the ones that exhibit mathematical and artistic creativity, are ever fascinating. Sundials, the sublime ones, are sculptures of mathematical theorems, and the shadows trace out mathematical demonstrations every day. They embody a mix of the technical and the artistic, the ancient and the new, the timeless and the timely. This section of my website will approach sundials from a mathematical point of view, describing the basis and tools for designing precision dials for those with a mathematics interest and background.
Sundials exist in a dizzying variety of designs—equinoctial, ring, polar, analemmatic, polyhedral, azimuth, vertical declining, armillary, card, bifilar, and so on—in many sizes. In addition to displaying the time of day (and of course a motto!), the more interesting ones include such features as shadow traces for particular days of the year, the sun's declination and azimuth, the times of sunrise and sunset, unequal hours, times in other cities, and corrections for civil time.
Precise, elegant dials offer a mix of the technical and artistic that makes them so appealing. Their designs involve areas of mathematics that include conic sections, geometrical constructions, analytical geometry, trigonometry, and often calculus. Those with a mathematical bent can create breathtakingly elegant devices. This is meant to be an introduction to a very creative and engaging field.
Why Sundials Appeal to Me
- They offer such a unique and fascinating mix of technical and artistic achievement.
- Precise, elegant dials are sculptures of mathematical theorems, and their shadows trace out mathematical demonstrations every day. Their designs combine various areas of mathematics. The creative spirit of mathematics, usually not recognized by the general public, is dramatically revealed in the more artistic designs.
- Sundials are a true link back through ancient cultures with our common yearning to understand our place in the universe. And yet, these creations prod our sense of mortality with their odd, almost disconcerting, conjunction of being “in the moment” and yet outside of it in a timeless sort of way.
Reasons for the Unfortunate Reputation of Sundials
- Sundials need to be mounted in a way appropriate for the latitude (ex. If a horizontal dial has the gnomon angle correct for the latitude of England, it needs to be rotated)
- Incorrectly mounted dials (a shocking number of examples…)
- No mean-time and longitude corrections to get Standard Time (can lead to 45-min errors!)
- Vandalism, neglect, or public misunderstanding
Sundials: Mathematics as an Art Form. An Introduction to the Mathematical Aspects of Sundial Design: A few years ago I gave the 2003 Anderson Lecture at Muskingum College in Concord, Ohio to kick off their Technology Week. The flyer for that talk is here. The presentation consisted of a 57-slide PowerPoint presentation backed with models and large illustrations of sundials. A small set of sample slides from this presentation are located here. I am available for this sort of talk on sundials--email me if you are interested.
Spherical Trigonometry -- The Early Days: This essay on my blog describes the ancient use of the Analemmas of Vitruvius and Ptolemy to lay out day shadow traces on horizontal sundials.
More materials and information will be posted soon.