Calculus and Archeology
Calculus relates to many different jobs in all different fields, even those that seem
very different from the typical view most people have of math and how it is involved in
their daily life. Calculus is the study of how things change. It allows people to make
predictions of models based on modeling systems. While these systems and models may
not be completely accurate, they give a glimpse into the nature of what something may do
in the future.
To me, calculus relates to almost everything in life and to many of my possible
future career paths. One subject that definitely relates to calculus and math in many ways
is archeology. Archeologists study historical ruins to find artifacts such as tools,
ceramics, and weapons to learn more about previous civilizations. To be a good
archeologist, you must study math to analyze data. In archeology, many different
techniques are used to compute exact locations of artifacts and other things to ensure that
the collected data is as accurate as possible.
Archeologists have recently begun to use different technologies, such as a
theodolite, remote sensing tools, and 3D image scanners to have even more accurate data.
While digging a plot, archeologists use simple math with a tape measure to measure
distance and the dimensions of artifacts. They can also use statistical math to calculate
how many of each artifact type is found in a plot or the average size of the artifacts.
Archeologists use many types of math, in addition to calculus, such as
trigonometry and geometry. A theodolite is a machine that is used to measure horizontal
and vertical angles in triangulation. Triangulation is the process of determining where a
point is by measuring different angles to it from known points. Instead of measuring the
distance from the known points to the unknown point, archeologists can instead calculate
the angles and then determine the location of the unknown point. By calculating the
length of one side of the triangle and finding the angles of the triangle, an archeologist
can use the Law of Sines to determine the distance to the unknown point.
If an archeologist finds carbon in the field, they can use radiocarbon dating to
determine how old the carbon is. Radioactive decay of carbon-14 is exponential, meaning
it decreases at a rate that is proportional to its value. The decay of carbon-14 can be found
using derivatives. This makes sense, because derivatives are essentially slope, and
archeologists are trying to find the rate of decay of carbon. The differential equation used
dN/dt = -CN,
in which N is the quantity of carbon-14 and C is the decay constant (a positive number).
It is very helpful to know how to solve derivatives to compute dates in archeology.
Another important tool that has been recently used in archeology is the 3D image
scanner, which allows archeologists to take 3D models of a pottery shard and compare it
to others or document it for later use. The 3D laser image scanner works by measuring
the distance to a target point on the artifact and also the vertical and horizontal angles to
that point. By getting multiple scans from different positions on the artifact from the
scanner, the laser scanner creates a 3D model of the artifact. Professor John Rick of
Stanford University told me that the scanner uses 3D geometry to produce a
mathematically accurate map of the artifact. By taking different pictures, or views, of the
object from many different angles, the scanner can capture an object in as little as 12
views. The 3D scanning system also uses multiple laser stripes to cross-validate the
geometric data it collects. The scanner that Dr. Rick uses has a 0.005 inch accuracy with
a maximum of 400 samples, or points, per inch. This technology is important for
comparing different ceramics and their engravings. It is also helpful to make an easily
accessible database of finds. Archeologists cannot only use the 3D scanners to document
artifacts but also to produce accurate models of buildings and ruins. Archeologists can
also use calculus to try to compute the rate of decay of ruins or how a site „behaved‟ in
Even though calculus and archeology seem very different, they are in fact very
related. Archeologists need a good basic understanding of calculus to be successful in
both surveying and documenting their finds. Calculus is very important in the profession
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