Method of False Position: An Example


 

Comments

Post a Comment

Popular posts from this blog

From the Eye of Horus to Grothendieck Primes: Math and Mythology

According to the Encyclopaedia Britannica, the Eye of Horus is a symbol of mythological significance, originating in a story in which the Egyptian gods Set and Horus clashed, and Set damaged or destroyed Horus’ eye. The eye was later restored by another of the gods (according to Wikipedia, most often Thoth, though the Encyclopaedia Britannica says Hathor); as a result, the Eye of Horus took on meanings of health and restoration. In fact, the association with health may have been so strong that the image has been passed down to the modern day: according to some sources, the ¼, 1/64, and 1/32 segments of the eye can still be seen today in the Rx symbol, used to denote a medicine prescription. Numerically, it is interesting to note that the fractions present in the eye represent the first six terms in the infinite series \sum 1/2^n. It doesn’t seem like a coincidence that this series sums to 1, given that the Eye of Horus symbolizes wholeness and restoration. This raises the question of w...
Read more

Reflection on Assignment 1

My biggest takeaway from last week’s presentations was the potential value of using historically-inspired geometry problems in a contemporary mathematics classroom. I want to start out this blog post with a quote by the Fields Medal-winning British-Lebanese mathematician Michael Atiyah. Speaking on the topic of contemporary algebra, he claimed that “ Algebra is the offer made by the devil to the mathematician. The devils says ‘I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine.’” While intentionally provocative, I think that Atiyah’s observation contains an important nugget of wisdom: modern algebra, while extremely powerful, is also very abstract and formulaic. I, for example, remember having to memorize the volumes of a number of 3-dimensional shapes, and besides rectangular prisms, these formulas often remained unmotivated and unexplained.  Looking specif...
Read more

What's in a Name: On the Acknowledgement of Non-European Mathematical Traditions in the Classroom

I want to state from the outset of this post that, by necessity, I come to this question from a position of relative blindness. While I can speculate all I want about the benefits of acknowledging non-European mathematicians and mathematics, I have neither the evidence base nor the lived experience that would be required to more strongly ground my musings. What I can speak to, however, is how I have benefitted from the heavy acknowledgement given to European and Western sources of mathematics. To start with, I have never felt culturally out-of-place is a mathematics classroom or venue; while certainly a large portion of this must have to do with the current demographics and culture of mathematics, I was also brought up (as were many if not all of my peers) with the idea that mathematics was mostly the product of white Europeans. Implicit in this view is that me, and people like me, were natural inheritors of our ancestors’ mathematical legacy. At an even more fundamental level, even wh...
Read more