The Geometry of Flatland

Here is another literary reference to mathematics. In fact, this story has often been called mathematical fiction. It is the satirical novella “Flatland: A Romance of Many Dimensions,” (1884) which was written by Edwin Abbott Abbott (1838-1926), an English schoolmaster and theologian. This story explores the nature of dimensions from the point of view of a two-dimensional world of geometry. The narrator is the humble square, who ends up visiting the one-dimensional world of Lineland as well as the three-dimensional world of Spaceland.

He is even introduced to the world of Pointland. There are certainly some thought-provoking social elements to this geometry-filled story, and I recommend it to any math student who is studying geometry. Although the book was not ignored when it was published, it did not achieve great success. However, it experienced a surge in popularity when Albert Einstein’s Theory of General Relativity, and its introduction of the fourth dimension, was made known to the public. The text of the original books is made available to the public at WikiSource.
This story also inspired the making of a 30-minute animated movie, “Flatland: The Movie”. It was released and sold to the public as an educational edition DVD, private home-use DVD, and digital download in June, 2007. The educational edition is primarily intended for educators, teachers, schools and institutions that will use the movie as part of classes, lectures, and courses. Visit the movie’s website and watch the trailer. I found it to be a very contemporary and entertaining adaptation of this mathematical literary classic.  I hope you do too.

π (Pi)

The most recognizable constant  in mathematics is the ratio of the circumference to the diameter of a circle. Today, we use the Greek symbol, π,  to represent this ratio. The existence of this constant has been known for a very long time.  It actually comes from nature, so it was always there, waiting for us to discover it.  The earliest textual evidence of this ratio dates back to the Babylonian and Egyptian civilizations.  One particular artifact fascinates me.  It consists of a list of eighty-four (84) practical problems encountered in administrative and building works.  It is known as the Rhind Mathematical Papyrus, now in the British Museum. It does not explicitly state the value of the ratio.   Instead, one of the problems calculates the area of a circle as the square of eight-ninths of its diameter.  The resulting solution was 3.16.  Explore this fascinating artifact.   Learn how math was used to solve practical problems in the world of the ancient Egyptian civilization.

By the way,  the symbol, π, has been used in this mathematical sense for only the past 250 years.  But that’s a topic for another blog.

Parts of a Circle

A circle is a  two-dimensional geometric object whose points are all the same distance from the center. The circle has  four basic components.  We will begin by identifying the components of a circle visually and verbally.  The words are labels used to name the components depicted in red and are used to translate the geometric illustrations into verbal descriptions.  Different words would be used if your native language is not English.Mathematical equations express relationships.  There are mathematical equations that define the relationships between these components of a circle in various ways.  These equations are used to find the lengths of the circumference, radius, and diameter of a circle as well as its area.   We’ll look into these relationships beginning in the next blog.

Do you know of any other math terms that describe some part of a circle?