1. Technique
    Optical fiber sundial  Fractal sundial  Theorem  Application 

2. References

A digital sundial is a clock that indicates the current time with numerals formed by the sunlight striking it. Like a classical sundial, the device contains no moving parts. It uses no electricity nor other manufactured sources of energy. The digital display changes as the sun advances in its daily course.

Technique

There are two basic types of digital sundials. One type uses optical waveguides, while the other is inspired by fractal geometry.

Optical fiber sundial

Sunlight enters into the device through a slit and moves as the sun advances. The sun's rays shine on ten linearly distributed sockets of optical waveguides that transport the light to a seven-segment display. Each socket fiber is connected to a few segments forming the digit corresponding to the position of the sun.^[1]

Fractal sundial

The theoretical basis for the other construction comes from fractal geometry.^[2] For the sake of simplicity, we describe a two-dimensional (planar) version. Let {{math|L{{sub|θ}}}} denote a straight line passing through the origin of a Cartesian coordinate system and making angle {{math|θ ∈ [0,π)}} with the {{math|x}}-axis. For any {{math|F ⊂ ℝ{{sup|2}}}} define {{math|proj{{sub|θ}} F}} to be the perpendicular projection of {{math|F}} on the line {{math|L{{sub|θ}}}}.

Theorem

Let {{math|G{{sub|θ}} ⊂ L{{sub|θ}}}}, {{math|θ ∈ [0,π)}} be a family of any sets such that  {{math|G{{sub|θ}}}} is a measurable set in the plane. Then there exists a set {{math|F ⊂ ℝ{{sup|2}}}} such that

• {{math|G{{sub|θ}} ⊂ proj{{sub|θ}} F}};
• the measure of the set {{math|proj{{sub|θ}} F ∖ G{{sub|θ}}}} is zero for almost all {{math|θ ∈ [0,π)}}.

There exists a set with prescribed projections in almost all directions. This theorem can be generalized to three-dimensional space. For a non-trivial choice of the family {{math|G{{sub|θ}}}}, the set {{math|F}} described above is a fractal.

Application

Theoretically, it is possible to build a set of masks that produce shadows in the form of digits, such that the display changes as the sun moves. This is the fractal sundial.

The theorem was proved in 1987 by Kenneth Falconer. Four years later it was described in Scientific American by Ian Stewart.^[3] The first prototype of a digital sundial was constructed in 1994, it writes the numbers with light instead of shadow as Falconer proved. In 1998 for the first time a digital sundial was installed in a public place (Genk, Belgium).^[4] There exist window and tabletop versions as well.^[5] Julldozer in Oct, 2015 published an open-source 3D printed model sundial.^[6]

References

• John Lambie (footballer born 1940)
• John Lambie (footballer, born 1940)
• John Lamb (left-handed pitcher)
• John Lamb (musician)
• John Lambourne
• John Lamb (pitcher, born 1990)
• John Lambrick Vivian
• John Lamb (rugby)
• John Lambton, 1st Baron Durham
• John Lamon (lacrosse)
• John Lamont Dow
• John La Mountain
• John Lamrock
• John Lanaway
• John Lancaster House
• John Lancelot Blades Percival
• John Lancelot Cowan
• John Lancelot Lithgow
• John Lancelot Stirling
• John Lancelot Todd
• John Landa
• John Lander Harper
• John, Landgrave of Lower Hesse
• John Landon
• John Landowski