A History of Mathematics Blog by Tim

Gematria - EDCP 442, Assignment 3, Ben and Tim The topic we chose for our Assignment 3 inquiry and art project was a traditional Jewish numerology called Gematria . It was, and still is, used by certain Jewish rabbis to exegete their scriptures. It is not found in every Jewish tradition but is most closely associated with a particular mystical branch of Judaism called Kabbalah . This hermeneutical technique begins with assigning each letter in the alphabet with a number. In the diversity of the Jewish tradition, this is done in many different ways however we focused on one of the more common methods knowns as מספר הכרחי ( Mispar Hekhreḥi , normative value or essential number). In this method, the numbers start at one, increase by one each time until 10, then increase by 10 each time until 100, and then increase by 100 each time until the final letter. This is shown in the chart below. The number of a word or phrase is determined by simply adding all the numbers of each letter together...

  This was article provided a fascinating look at the way the Marshallese people navigated their waters. For me, the most interesting part of the article was the way the Marshallese people developed oceanic models that could be generalized across all the islands they were familiar with. The paper notes that in an exchange, one of the Marshall Islanders maintained that, "the chart was not where [a particular island] lay, but where land was. They stoutly maintained that it could be some island in another part of the world, one they had never seen" (p. 352). This deep understanding of the nature of wave movement around land is a clear example of the complex mathematical thinking that took place even if it doesn't look similar to the form of mathematics that we are familiar with in the Western world.  I think embodied math is not just significant in the history of mathematics, but arguable essential. This paper gives an example of a group of people using a mathematical style ...

    (Sorry, this was originally posted to Duncan's blog page by accident!) Ben and I are planning to work together on creating some sort of representation around the Jewish mystical mathematical ideas around  gematria . We are initially thinking of using English gematria to investigate our BC School Act, or another important piece of policy that relates to education. This would be printed out along with the number relating to each word and links between ideas shown visually as well as noted throughout. Sources: Clawson, C. C., (1996).  Mathematical mysteries: The beauty and magic of numbers . Springer Science+Business Media Gematria  (2013). (3rd ed.). Oxford University Press. Derovan, D., Scholem, G., Idel, M. (2018, June 11).  Gematria . Encyclopaedia Judaica. https://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/gematria Britannica, T. Editors of Encyclopaedia (2013, October 18).  gematria . Encyclopedia Britannica. ...

  " The Greeks were concerned with the  education of free men as future citizens." This quote is interesting in the way that it shows the way Greece valued education, but also how it was only available to men and to citizens. Because ancient Greece has been so influential in western culture, those inequities continued to perpetuated even in recent times and still continue to today. We need to be asking ourselves how we can decouple our education system from socio-economic statuses.  " Towards the end of this period, the  Hindu-Arabic number system was be  ginning to be known in Europe." This quote reminds me of how much math migrated into Europe from places other than Ancient Greece. Because I was taught such a Eurocentric and Greekcentric mathematics history, I never learned how so many ideas from India, China and the Arabic world flowed into Europe and lead to so many European mathematics ideas. "Th e student  had simply to swear ...

  In the poem Euclid Alone has Looked on Beauty Bare by Edna St. Vincent Millay, she is arguably defining beauty as geometric proofs. Euclid certainly defined his geometry with precision, clarity and simplicity that is regarded by many (including myself) as beautiful. However, I do not agree that Euclid was alone in seeing this beauty as he based his work on those who came before him (especially Eudoxus), and many have came after him who have even expanded upon his work.  Moving past the idea that geometrical proofs are the purest form of beauty which is certainly debatable, the poem in general seems to fall into the "great man fallacy". This is the idea that history is defined by specific great people (usually men) who alone contribute to the advancement of ideas, science and societies. While many specific individuals have contributed important and influential ideas, the fallacy often ignores the other factors that lead to those ideas. Even the greatest mathematicians a...

Both the video and the paper on "Dancing Euclidean Proofs" brought several interesting ideas to light. The notion of embodying mathematics is not one that I have encountered before, and it certainly provides new ways to engage with math. In particular, I found their discussion about the differences and similarities between constructing proofs with pencil and paper compared with using bodies. While I immediately recognized the imagination and simplification that is required when embodying the proofs, it was helpful to be shown how those same elements apply to a proof drawn on paper. The points we draw aren't infinitely small, the lines we draw don't extend infinitely, and the circles we draw definitely aren't perfect circles! In both cases of embodiment and 'empaperment' (is that a word?), we are simply representing abstract ideas in a concrete way. This limits how "exactly" we can show these abstract ideas, but both methods encapsulate the concep...

  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 ...

          As someone who grew up learning math in the “traditional” way, presented primarily with objective theorems and axioms, math history was often provided as a side-dish not meant to be incorporated with the entrée. If you had already eaten your fill with the main course, you could forget the side-dish, it was interesting, perhaps, but certainly not essential. Additionally, this “side-dish” of math history was inevitably European centric. It lacked the intense spices found in traditional Indian cuisine, the fragrant herbs from Arabic cooking, or the rich flavours of Chinese and other east Asian foods. This, predictably, contributed heavily to my own philosophy around math education but this chapter by Tzanakis, C. et al . has opened my eyes in a number of ways.             Something that jumped out at me immediately, from section 7.3.2 was the idea of integrating history directly into the teaching of math. The idea o...