Eye of Horus

Researching this was so much fun, I remember in grade 7 we had units on Greek, Roman, and
Egyptian Mythologies, I always found their stories of their Gods to be so exciting. I had seen the Eye of Horus before, but at first I thought it was the Eye of Ra; Ra being a god of the sun. Both eyes are connected to one another and represent similar concepts, but learning of the Eye of Horus was extremely interesting. The Eye of Horus has been seen as a symbol of protection, royalty, and good health; the eye was lost in a battle and magically healed and restored -- the restoration symbolized making whole and healing, cool!

According to the myth, the eye was separated into pieces and lost, each part of the eye representing a different fractional value (1/2, 1/4, 1/8, 1/16, 1/32, and 1/64), and different part of the eye. What I found most interesting was that "these fractions, all with powers of two in their denominators, were used to represent the fractions of hekat, the unit measure of capacity for grains" (source). This ties into what we were learning in class, and how ancient Egyptians may have used calculations for something like payment in wheat, or hekat in this case.

Two things popped into my mind when I thought of 'special meanings of numbers', the first being anniversaries, and the next being lucky numbers. Anniversaries, being represented by dates, can also be represented numerically. These dates can have special meaning to the individuals it effects, we often celebrate my parents anniversary every time it comes around! Another example would be 'lucky numbers'. I've played hockey for over 20 years now, and been coaching for the past 8. One thing I've always noticed with teammates and players is how excited, protective, and disappointed they can be towards their jersey numbers. Some players are so attached to their numbers that they find identity within it, and feel dejected or disappointed when they don't receive it. It's easy to say "your number doesn't define you", but players can be extremely superstitious. 

Personally, my favorite number, and number I've played with since I was around 8/9 was the number 10. My story with it is: when I first started playing, I always wanted my jersey number to match how old I was. Somehow, when I was 8 I took 10, so I told myself I would wear 10 until I was old enough, then move onto 11 when I turned 11; but after 2 extra years of wearing the number, I somehow got attached! I haven't changed my number since 

Constructing a Magic Square

 I was first introduced to the concepts of the Magic Square in this video: A Sudoku With Only 4 Given Digits. As an aside, this Sudoku video was unbelievable to watch someone solve; I struggle enough with the basic versions of Sudoku, let alone this kind of stuff!

I remember when it was first mentioned, I thought it was such an interesting idea that almost didn't seem feasible. It felt a little unfair making this then because I had some previous knowledge of how to approach it (although I didn't completely remember how to solve it). The one thing that I remembered was important was the number 5, as when we construct the possibilities of 3 numbers added together between 1-9 to equal 15, 5 was the most common number that allowed the most possibilities, therefore it was placed in the center square. 

The easiest way to approach this was deciding what would happen with 1. If I added 1+5+9 I get 15, but I also get 1+6+8 to be 15 too. If 9 was on the diagonal, then it has to intersect with 6 or 8 on the vertical or horizontal! The problem with that is it's >=15 with only 2 values, so we know that wouldn't work. So I then wrote 1 and 9 on the horizontal and was able to solve the square going from there! It helped to write out a couple other equations that would help me logically reason through the pattern of the square. Once I was able to have 2 equations down (1 + 5 + 9 and 6 + 1 +8), the rest logically followed as there was a missing spot in the top right corner where I was able to fill in the 2...and so forth. It reminded me of a Sudoku puzzle as well, once you know the spot of a few numbers, the rest seem to flow!

Method of False Position Example

 

2 spaceships are intertwined in a galactic fight; each have a limited number of lasers to fire. One pilot fires one sixth of their lasers and are left with 40 shots left; how many lasers did that pilot start with? 

Solution:

x - x/6 = 40

(try x = 6)

6 - 6/6 = 6-1 = 5 

since 40/5 = 8, we can try x = 48 

48 - 48/6 = 48 - 8 = 40

So the pilot initially had 48 shots

A Response to Was Pythagoras Chinese

  I believe that acknowledging non-European sources of mathematics makes a big difference to the students. The western schooling system is very Euro-centric, and it's extremely prevalent in mathematics; all theories seem to come from the Ancient Greeks, and it can give the student the impression or underlying belief that only white males are capable of finding such theories. Acknowledging non-European sources of mathematics may give students of different backgrounds someone to look up to, or connect them to their culture. Also, as teachers it is our job to give accurate and correct facts, so when we acknowledge only part of history, we are doing disservice to our students. I think the best way to connect this is: imagine you created some new invention, succeeded locally, and had recognition from those in your city. You're the only person in that market (you're aware of) for years, and one day someone across the continent announces they've come up with a 'new invention', which is the same as yours. Now imagine if that other person, who claimed to have discovered this invention, gets all the praise and glory for it, and is taught about for years to come. This is what happens when we do not acknowledge the other cultures that had similar discoveries, hundreds of years before. We are discrediting them, when we should be celebrating their achievements! 

I believe that theorems shouldn't be named after people, as we've learnt that there is no historical accuracy to whether that person 'really' discovered it or not. We've also learnt that different civilizations have come up with similar theories, in different time periods, but have named them differently. For example, Pythagoras was the first to come up with a proof (or was he?) for the right-triangle, but he wasn't the first person to notice or use it, as the Gougu theorem was used by the Chinese. I believe that theories should be named after what they solve, like Pythagoreans theorem should really be named: Right Triangle Theory (as stated in the text), as this doesn't assign credibility, but also centralizes terminology.

Assignment 1 - Solutions & Extensions

 Here is a link to our slides which includes the solutions and extensions to the problem (Presentation). 

A response to Babylonian Word Problems

 I think the idea of 'pure' vs 'applied' mathematics is an interesting one brought up in this chapter, as it also comes from a stance of '2020 vision'. As a student who has grown up with the benefits of history, the conceptualization of the mathematics was always readily available to me; I had to link abstractions and concepts together, but I never had to 'invent' mathematics for a population. This is echoed on page 8 that "Babylonian documents predate Greek ones by 1500 years and Babylonians may have been the first people in the world to conceive of mathematics as a unified and distinct area of study" (Gerofsky, 8). What was serviceable and needed at the time was an applicable sense of mathematics that could be used in day-to-day life. On top of that, they (potentially) needed to invent their own mathematical system, so their applications only needed to apply to their real-world. As we have progressed forward with math, we have seen the usage and need for such applications like algebra. We have benefited from the historical context and built upon their foundations to push beyond and question more abstractly. 

Eventually as technology also moved forward, there was need for more applicable mathematics than what the Babylonians provided; and the trend continues to this day. We use different formulas than the Greeks did because our technology has advanced; but their applications of real world mathematics was useful for their time. If used correctly, the use of word problems allows students to connect history and mathematics and create a relational understanding with the material and appreciate the struggles of those who designed the methods. I also think though that we need to find the connections between history and the word problems we do now. If we give a historical question, what are the applications we can give a student today where the application is still useful? Behind every question, there should be a purpose.