foot, at about 13.2 inches (33.5 centimeters; see above for more about the Harappan).
Around 1700 BCE, the Babylonians put their foot forward: A Babylonian foot was two-
thirds of a Babylonian cubit. There are even records from Mesopotamia and Egypt show-
ing yet another measurement system that included a foot of 11.0238 inches (300 mil-
limeters). This was also known as the Egyptian foot, and it was standard in Egypt from
predynastic times to the first millennium BCE. The Greek foot came close to today’s foot,
measuring about 12.1 inches (30.8 centimeters); a Roman foot measured in at 11.7
inches (29.6 centimeters). The list goes on, depending on the country and time period.
How was the standard foot determined?
Whatever the true story, the foot we are familiar with today is equal to 12 inches
(30.48 centimeters). The true standardization of the foot came late in the 19th centu-
ry, after the United States and Britain signed the “Treaty of the Meter.” In this treaty, 45
MATHEMATICS THROUGHOUT HISTORY
What was the first civilization to use a
decimal system of weights and measures?B
etween 2500 and 1700 BCE, the Harappa (or Harappan) civilization of the
Punjab—now a province in Pakistan—developed the earliest known decimal
system of weights and measures (for more about decimals, see “Math Basics”).
The proof was first found in the modern Punjab region, where cubical (some say
hexahedral) weights in graduated sizes were uncovered at Harappa excavations.
Archaeologists believe that these weights were used as a standard Harappan
weight system, represented by the ratio 1:2:4:8:16:32:64. The small weights have
been found in many of the regional settlements and were probably used for trade
and/or collecting taxes. The smallest weight is 0.8375 grams (0.00185 pounds),
or as measured by the Harappa, 0.8525; the most common weight is approxi-
mately 13.4 grams (0.02954 pounds), or in Harappa, 13.64, the 16th ratio. Some
larger weights represent a decimal increase, or 100 times the most common
weight (the 16th ratio). Other weights correspond to ratios of 0.05, 0.1, 0.2, 0.5,
1, 2, 5, 10, 20, 50, 100, 200, and 500.
There is also evidence that the Harappan civilization had some of the most
advanced length measurements of the time. For example, a bronze rod found at
an excavation was marked in units of precisely 0.367 inch (0.93 centimeter).
Such a measuring stick was perfect to plan roads, to construct drains for the
cities, and even to build homes. An ivory scale found at Lothal, once occupied by
the Harappan civilization, is the smallest division ever recorded on any measur-
ing stick yet found from the Bronze Age, with each division approximately
0.06709 inch (0.1704 centimeter) apart.