David Terr's Website



“Fibonacci Expansions and ‘F-adic’ integers,” The Fibonacci Quarterly, v. 34, 1996

“On the Sums of Digits of Fibonacci Numbers,” The Fibonacci Quarterly, v. 35, 1996..

A Modification of Shanks’ Baby-Step Giant-Step Algorithm,” Mathematics of Computation, v. 69, 2000

Here's a copy of my resume

Time Measuring Devices

Throughout history, various devices of increasing accuracy have been used to measure time.

The sundial was invented in ancient Egypt and was also used in ancient China, Greece, and Rome. Sundials consist of a shadow-maker known as a gnomon, which casts a shadow onto a surface below, usually marked with the hour. As the sun moves through the sky, the shadow moves accordingly, indicating the time of day. Sundials are accurate to within a few minutes but must be adjusted for daylight savings time.

Candles are simple time-telling devices which work simply by burning at a fixed rate. To indicate the time, candles are marked with hours. Candles were commonly used for telling time during the Middle Ages and are still used in churches for this purpose.

The hourglass tells time roughly in terms of an amount of sand which pours through a small hole at a nearly fixed rate. As the name implies, the sand in most hourglasses pours for one hour. Egg timers, which run out in 3 to 5 minutes, are small versions of hourglasses. Hourglasses were once used in navigation.

Water Clock
The water clock was a clock commonly used in ancient and medieval times. It works by maintaining a steady flow of water.

Mechanical Clock
The mechanical clock was an improvement of the water clock developed around 1280. Mechanical clocks work by hanging a weight from a string and using an escapement to make the clock tick at a nearly fixed rate.

Pendulum Clock
The next significant improvement in time measurement was the pendulum clock. Galileo Galilei discovered the principle of the pendulum in 1581 and Christian Huygens invented the pendulum clock in 1656. Until the 1930s, the most accurate clocks were pendulum clocks.

Navigators needed a very accurate portable seaworthy clock in order to measure longitude on long sea voyages. John Harrison built the H4 Chronometer in 1761 for this purpose. Chronometers like this were used on ships until they were replaced by more accurate quartz clocks in the 1970s.

Atomic Clock
The atomic clock is the most accurate clock currently in use. The first atomic clock was built in 1949 at the U.S. National Bureau of Standards (NBS). The first accurate atomic clock, based on the transition of the cesium-133 atom, was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. This led to the internationally agreed definition of the second being based on atomic time. With an accuracy of 1 part in 10^15 or 0.1 ns per day, the NIST-F1, built in 1999 at the National Institute of Standards and Technology (NIST, formerly NBS), is the world's most accurate clock.