A History of Mathematics Blog by Tim

  This article brings up several interesting ideas and expands the history of math significantly from what most of us have grown up with. As we as are culture slowly starting to recognize the importance of representation in the media we consume, but the conversation around representation in our education system seems to be still developing. In math classes, we have the opportunity to vastly expand the scope of our students' mathematical role models and historical figures beyond the 'traditional' Greek and European people.  Many theories are named after the Greek or European thinkers who popularized them in that particular area of the world. I think it's still important to teach students those names for the theories so that they can understand, and communicate well with, mathematicians throughout the world. However, finding other thinkers from other ancient cultures and associating their names with those theories as well broadens students' learning and possibly allow...

Perhaps the most straightforward answer to whether the Eye of Horus is mathematical, mystical or medical is yes... all of the above, but diving into the interesting relationships between the three leads to some fascinating discussions around this ancient civilization.  The symbol gets its name from a mythical figure: the god Horus, son of Osiris and Isis, so it ties in to the mythological culture central to ancient Egypt. It also has been linked to several unit fractions with denominators that are powers of 2; this links it as well to the mathematical ideas originating out of this area of the world at that time. Finally, it is also thought to represent the senses as they were know to the ancient Egyptians (smell, sight, thought, hearing, taste, and touch) and mysteriously matches quite well with modern anatomy's understanding of the structure of the human brain, linking it to the ancient culture's understanding of medicine and anatomy.  The different parts of the symbol are th...

While much of this class has been spent looking at very different ways of writing and solving math problems, researching and working through the problems related to the volume of a pyramid opened my eyes to some of the similarities between ancient and modern ways of conceptualizing mathematical problems. One similarity that fascinated me was the cross-cultural relevance of geometric reasoning. Though it was often difficult in past lessons to wrap my head around the Babylonian sexagesimal system, the geometric reasoning from Lui Hui (the mathematician from ancient China) was reasonably straight forward to understand.  For me, this reinforces the importance of trying to find simple geometric ways to demonstrate solutions for future students instead of relying only on algebraic solutions. As math teachers we will be teaching students the 'language' of math, which certainly includes algebra, however understanding that many of our students not be 'fluent' yet, we need to loo...

If we have learned anything from our mathematical past, it's that the world never splits cleanly into practical problems and abstract problems. A few simple examples of this might be the number  π , which started very simply as a practical relationship between the circumference and diameter of a circle, but can also be calculated in a very abstract way with an infinite series (the Leibniz formula for  π /4). Another example might be the many number theorist who prided themselves in pure abstraction of their field, only for a practical uses for their methods coming with the arrival of computers and the need for encryption techniques.  This article brings up some interesting interplay between practicality and abstraction in ancient Babylonian word problems. Firstly it seems clear, from the examples provided at the beginning and throughout the text, that many word problems were inspired by what was familiar in their everyday lives, so in a sense they have a level of practica...

          For someone taught a primarily Europe-centric math history, such as myself, there was a wealth of new and enlightening information to be gleaned from this chapter. One of the first things to catch me by surprise was the foundational beginning of math originating not in Greece, but in Egypt. The vision I was often presented with was one of famous Greek thinkers coming up with new ideas, as if out of thin air. The intelligence and creativity of the classic Greek thinkers is beyond doubt, but their reliance and debt to even earlier Egyptian mathematicians is essential to understand when trying understand a complete history of mathematical development. What makes this common omission so egregious is that the Greek thinkers themselves attributed the foundation of many of their ideas to Egyptian mathematics.            In the chapter, this neglect of anything mathematical originating prior to ancient Greece was exempli...

I will begin this blog post with some un-researched speculation about why the ancient Babylonians chose to use a base 60 (sexagesimal) number system. It so happens that 60 divides evenly by the first 6 numbers, i.e. 60/1=60, 60/2=30, 60/3=20, 60/4=15, 60/5=12, 60/6=10. This allows quick and accurate calculations of whole numbers when dividing  by 1, 2, 3, 4, 5, or 6 without recurring decimals (or I suppose recurring sexagesimals) showing up.  We see base 60 still present in certain parts of our lives, specifically in how we tell the time as possibly our measurements of degrees. 60 seconds in a minute, 60 minutes in a hour and even the 12 hours of AM and 12 of PM could be seen to be base 60 to some degree, as it's one fifth of 60. Additionally, measuring 360 degrees in a circle might come from 60x6. My guess as to why 360 was chosen is that splitting a circle into 60 parts proved too rough for accurate measurements, whereas splitting a circle into 3600 (60x60) parts proved too ...